Doc 8.5, ver. 1.0 | 15 March, 2021

ALMA Cycle 8 2021 Technical Handbook

ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC(Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile.
The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.

2User Support
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Portal at www.almascience.org. Helpdesk tickets will be directed to the appropriate ALMA Regional Center at ESO,NAOJ or NRAO.

Revision History
Cycle

Version Date

Editors

Remarks

5
6
7
7

1.1
1.0
1.0
1.1

2017-03-21
2018-03-20
2019-03-19
2019-06-29

R. Warmels and A. Remijan
R. Warmels
A. Remijan
A. Remijan

8

1.0

2021-03-01

A. Remijan & P. C. Cortes

Cycle 5
Cycle 6
Cycle 7
Cycle 7 - Fixed Typo in Table 7.2 Caption
Cycle 8

EditorPaulo C. Cortes - (With a special thanks to Anthony Remijan for passing the flag with a well structured andmatured document!)

Authors of this Edition
Anthony Remijan - Chapter 1; Antonio Hales - Chapter 2 and Appendix A; John Carpenter - Chapter 3; Bill
Dent - Chapter 4; Seiji Kameno - Chapter 5; Bill Dent and Eric Villard - Chapter 6; Brian Mason - Chapter 7;
Baltasar Vila Vilaro and Paulo Cortes - Chapter 8; Andy Biggs - Chapter 9; Ed Fomalont and Paulo Cortes Chapter 10; Bill Dent and Eric Villard - Chapter 11; Rachel Rosen - Chapter 12; Felix Stoehr - Chapter 13;
Kamaljeet Saini - Appendix B

Contributors to this Edition
Tim Bastian, Crystal Brogan, John Carpenter, Chinshin Chang, Geoff Crew, Paul Fisher, Misato Fukagawa,
Melissa Hoffman, Chat Hull, Hugo Messias, Todd Hunter, Ruediger Kneissl, Andy Lipnicky, Sergio Martin,
Lynn Matthews, Luke Maud, Yusuke Miyamoto, Tony Mroczkowski, Hiroshi Nagai, Kouichiro Nakanishi, Masumi Shimojo, Richard Simon, Jeremy Thorley, MCarmen Toribio, Catarina Ubach, Catherine Vlahakis, Martin
Zwaan
In publications, please refer to this document as
Cortes, P. C., Remijan, A., Biggs, A., Dent, B., Carpenter, J., Fomalont, E., Hales, A., Kameno, S., Mason,
B., Philips, N., Saini, K., Stoehr, F., Vila-Vilaro, B., Villard, E. 2020, ALMA Technical Handbook, ALMA
Doc. 8.4, ver. 1.0
ISBN 978-3-923524-66-2

Contents
1 Introduction

9

2 Array Components
2.1 The ALMA Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The 12-m Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 The Atacama Compact Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 The 7-m Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 The TP Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11
11
11
13
13
13

3 Principles and Concepts of Interferometry
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Single-dish Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Visibilities and Aperture Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 The Visibility or (u,v) Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Fields-of-view and Mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Spatial Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Multi-configuration Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 Units and Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15
15
15
19
22
22
23
27
28
28

4 Receivers
4.1 Local Oscillators and IF Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 The Cycle 8 Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Band 3 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Band 4 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Band 5 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Band 6 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.5 Band 7 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.6 Band 8 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.7 Band 9 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.8 Band 10 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29
31
32
33
36
39
42
45
48
51
54

5 The Correlators
5.1 The 64-input Correlator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 TDM mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 FDM mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Correlation and Realtime Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 The ACA Correlator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Digitizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Offline WVR Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Capabilities of the Correlators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Spectral Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57
58
58
59
60
60
62
63
64
64
64

4

CONTENTS

5.5.3 Time Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.4 Phase Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Practical Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.2 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Final data product - the ASDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65
68
69
69
69
70

6 Spectral Setups
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Frequency Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Spectral Setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Observing Frequencies for Continuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Multiple Spectral Windows in the Same Baseband . . . . . . . . . . . . . . . . . . . . . .
6.3.3 Spectral Setups for Lines near the Edge of the Bands . . . . . . . . . . . . . . . . . . . .
6.3.4 Spectral Setup in Bands 9 and 10: DSB Considerations and 90-degree Phase Switching .
6.4 Usable Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Spectral Resolution and Channel-averaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Spectral scans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 Spurious Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Doppler Setting and Velocity Reference Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71
71
73
73
74
76
77
77
78
78
79
79
80

5.6
5.7

7 Imaging with ALMA83
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.2 Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7.3 Shadowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7.4 Angular Resolution and Beam Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.4.1 Definition of angular resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.4.2 Effects of weighting scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.4.3 Other factors affecting beam size and shape . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.5 Snapshots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.6 Large Spatial Scale Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.7 Mosaicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.8 Multi-array and Multi-configuration Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.9 Multi-array and Multi-configuration Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
8 Observing Modes
107
8.1 Observing Project Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
8.2 Execution Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.3 The Observing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
8.3.1 The Source Selection Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
8.4 Single Field Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.5 Pointed Mosaic Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.6 Total Power (Single Dish) Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.7 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.7.1 Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
8.8 Multiple Region Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.9 Observation of Ephemeris Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.10 Solar Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.10.1 Solar Observing Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
8.10.2 Array Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
8.10.3 Single-Dish Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.10.4 ALMA Solar Ephemeris Generator Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.11 VLBI Observing Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.11.1 General VLBI Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.11.2 ALMA Considerations for VLBI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

CONTENTS

5

8.11.3 Observing Targets Fainter than 500 mJy with Passive Phasing . . . . . . . . . . . . . . . 128
8.11.4 Phased-Array Observing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
8.12 High Frequency Observing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
9 ALMA Sensitivity Calculator
133
9.1 Calculating the System Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.1.1 Sky Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.1.2 CMB Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
9.1.3 Receiver Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
9.1.4 Ambient Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.1.5 DSB Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.1.6 System Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
9.1.7 System Temperature (web application and OT GUI) . . . . . . . . . . . . . . . . . . . . . 137
9.2 The Sensitivity Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9.2.1 12-m and 7-m Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
9.2.2 Total Power Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
9.3 User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
9.4 Total Time Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
10 Calibration and Calibration Strategies
141
10.1 Fundamental Synthesis Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
10.2 Calibration Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
10.2.1 Calibrated and Measured Visibility Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
10.2.2 Calibration Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
10.2.3 Reference Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.2.4 Calibration Measurements Using Hardware Devices . . . . . . . . . . . . . . . . . . . . . . 143
10.2.5 Calibration Measurements Using Astronomical Sources . . . . . . . . . . . . . . . . . . . . 143
10.2.6 Source Catalog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
10.2.7 Flagging Data Based on Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
10.3 Observatory Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
10.3.1 Antenna Primary Beam Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.3.2 Antenna Surface Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.3.3 Antenna Pointing Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.3.4 Antenna Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.3.5 Antenna Integration Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.4 Execution Block Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
10.4.1 Making the Measurement Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
10.4.2 Amplitude Calibration Procedure (System Temperature Measurement) . . . . . . . . . . . 148
10.4.3 Water Vapor Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.4.4 Antenna Pointing Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
10.4.5 Antenna Position Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.4.6 Bandpass/Frequency Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.4.7 Flux Density Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.4.8 Amplitude Temporal Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
10.4.9 Phase Referencing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
10.4.10 Check Source Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
10.4.11 Estimate of Image Quality in QA0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
10.4.12 Calibration for Specific Observing Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
10.5 Additional Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
10.5.1 Self-Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
10.5.2 Astrometric Observations/Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
10.5.3 Band-to-Band Phase Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
10.5.4 Band-Width-Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6

CONTENTS

11 Quality Assurance
165
11.1 Cycle 8 Quality Assurance Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
11.2 QA0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
11.2.1 QA0 criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
11.2.2 Execution Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
11.3 QA0+ and imaging quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
11.3.1 Relationship between image quality and phase noise criteria . . . . . . . . . . . . . . . . . 169
11.4 QA1: Observatory calibration and QA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
11.5 QA2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
11.6 QA3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
11.7 The Quality Assurance Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
11.8 QA in Solar Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
11.9 QA in VLBI Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
11.10QA in Pulsar Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
12 Data Flow and Logical Data Structure177
12.1 Data and Control Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
12.2 The ALMA Science Data Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
13 Data Archiving
181
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
13.2 Data Flow and Archive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
13.3 Calibrator Source Catalogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
13.4 PI Data and Data Delegation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
13.5 Archive Query . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
13.6 Request Handler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
A Antennas
187
A.1 Design and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
A.2 Antenna Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
A.3 Antenna Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
A.4 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
A.5 Amplitude Calibration Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
A.5.1 Atmospheric Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
A.6 Water Vapor Radiometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
B The LO and IF System
199
B.1 Functions of the LO and IF System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
B.2 Summary of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
B.3 Frequency Generation and Distribution in ALMA . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
B.3.1 Reference and LO Signal Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
B.3.2 LO1 Signal Generation and Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
B.3.3 Line Length Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
B.3.4 The First Local Oscillator (LO1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
B.3.5 LO2 and the IF Processor Units and IF Switch . . . . . . . . . . . . . . . . . . . . . . . . 205
B.3.6 Digitization and Signal Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
B.4 Other functions of the LO/IF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
B.4.1 Delay Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
B.4.2 Sideband Suppression - LO Offsetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
B.4.3 Interference Rejection - 180 degree Phase Switching . . . . . . . . . . . . . . . . . . . . . 208
B.4.4 Sideband Separation - 90 degree Walsh Switching . . . . . . . . . . . . . . . . . . . . . . . 209
C Acronym Dictionary

211

7

CONTENTSThis page was intentionally left almost blank8

CONTENTS

Chapter 1

Introduction
The Atacama Large Millimeter/Submillimeter Array (ALMA) is an aperture synthesis telescope consisting of
66 antennas that can be positioned in a number of different configurations. It operates over a broad range of
observing frequencies in the millimeter and submillimeter regime of the electromagnetic spectrum.
ALMA Early Science Operations started with Cycle 0 in September 2011 and the official inauguration took
place in March 2013.
Starting with Cycle 8 operations, the distinction between standard and non-standard observing modes are
removed. Unlike previous Cycles, there will be no upper limit on the amount of time allocated to non-standard
observing modes in Cycle 8. Like previous Cycles, however, some observing programs, such as Large Programs,
will still be restricted to specified observing modes. Users should refer to Appendix A (ALMA Capabilities)
in the ALMA Cycle 8 2021 Proposer’s Guide, for the latest information and a description of all the available
observing modes including those programs with restricted observing modes.
The Technical Handbook concentrates on the technical aspects of the Cycle 8 observing capabilities as wellas on the hardware and software available for ALMA users. It should, however, not be necessary to use theTechnical Handbook to prepare an ALMA proposal.
The Technical Handbook is divided into three main sections: The concepts of interferometry and the ALMA
hardware components (Chapters 2–5), the observing concepts and software (Chapters 6–9), and finally the data
quality and handling (Chapters 10–13). It also includes a number of appendices with expanded information on
specific ALMA hardware components and calibration and an acronym list widely used by ALMA staff.
Chapter 2 describes the ALMA Array components: The 12-m Array and the Atacama Compact Array(ACA), also known as the Morita Array which is comprised of the 7-m and Total Power (TP) Array. A generaldescription of the different array elements and hardware components is provided.
Chapter 3 gives a brief introduction to interferometry, including a description on the concepts of basic radio
astronomy and the principles of aperture synthesis.
Chapter 4 describes the details of the eight receiver bands offered for Cycle 8 observations. The generaltechnical specifications and a brief explanation on local oscillators and intermediate frequency (IF) range ispresented. Plots with the atmospheric transmission and the typical system temperatures per receiver band arealso included.
Chapter 5 describes the correlators and the data processing taking place in these special purpose supercomputers. A description of the 64-input Correlator (used for the 12-m Array) and the ACA Correlator (used by the
7-m and the TP Arrays) is provided. Observing modes available for continuum and spectral line observations
are presented.
Chapter 6 describes how the spectral setup is done in the correlators. A description of the signal path andlocal oscillator (LO) chain used between the frontends and the correlators is covered and how the hardware isconfigured to define spectral setups for an observation.
Chapter 7 describes several aspects of imaging to consider in ALMA observations. A short description on
the different configurations proposed for Cycle 8 is included. Note that in Cycle 8, the two longest baseline
configurations will not be available (Configuration-9 with a maximum baseline of 13.9 km and Configuration-10
with a maximum baseline of 16.2 km). Concepts of shadowing, beam shape, and spatial scale filtering arerevisited. Mosaicing and 12-m and 7-m Array data combination are also presented.

10

CHAPTER 1. INTRODUCTION

Chapter 8 describes the observing modes offered for Cycle 8 and the observing sequence of projects. Single field interferometry, mosaics, single-dish observations, polarization, multiple region modes, Solar, VLBI,
astrometry and ephemeris observations are detailed in this section.
Chapter 9 gives a brief overview how sensitivities and integration times are calculated at ALMA.
Chapter 10 describes how calibration is performed at ALMA, providing a description on how to calibrate
long-term and short-term effects as well as how calibrators are selected.
Chapter 11 describes the data quality assurance (QA) process. A description of the criteria used for passing
quality assurance as well as the pipeline heuristics used in data reduction and calibration which are used indetermining the overall quality of the data are presented.
Chapter 12 describes the data flow and structure of ALMA data. A description of all the main software
subsystems involved from data acquisition to archiving is provided as well as a description of the ALMA Science
Data Model (ASDM) which defines the metadata structure adopted by ALMA.
Chapter 13 describes how the data are stored, the data flow and the user interface to the ALMA Archive.
The Technical Handbook concludes with three appendices, which contain supplemental material about theantenna design and ALMA transporter (Appendix A), the Local Oscillator (LO) and Intermediate Frequency(IF) system (Appendix B) and a list of acronyms widely used by ALMA staff (Appendix C).

Figure 1.1: ALMA antennas on the Chajnantor Plateau.

Chapter 2

Array Components
This chapter describes the main characteristics of each ALMA array. Unless otherwise noted, the description isappropriate for the fully completed ALMA telescope.

2.1

The ALMA Telescope

ALMA is composed of 66 high-precision antennas. Fifty of these antennas are 12-meter antennas in the 12-m
Array, used for sensitive, high-resolution imaging. These fifty 12-m antennas are complemented by the Atacama
Compact Array (ACA), also known as the Morita Array1 , composed of twelve closely spaced 7-m antennas (the7-m Array), and four 12-m antennas for single-dish (or Total Power) observations (the TP Array), to enhancewide-field imaging of extended structures. In Cycle 8, ALMA will cover most of the wavelength range from 3.6
to 0.32 mm (84–950 GHz), and during Full Operations, will cover a range from 8.5 to 0.32 mm (35–950 GHz).
The array is located on the Chajnantor plain of the Chilean Andes (lat.=–23.02917◦ , long.=–67.754649◦ ),a site that normally offers the exceptionally dry and clear sky conditions required to observe at millimeter andsubmillimeter wavelengths2 . The ALMA antennas, weather stations, the two correlators and their computerinterfaces, Local Oscillator generation hardware, timekeeping hardware, and the related array Real-Time Machine computer are all located at the 5000-meter altitude site referred to as the Array Operations Site (AOS).
This site is connected via Gigabit fiber links to the Operation Support Facility (OSF), located at an altitude of2900 meters, about 22 km from the AOS and 40 km from the town of San Pedro de Atacama. Science operations
are conducted from the OSF and coordinated from the JAO central office in Santiago. All three ALMA arrays
are controlled via control software developed on the ALMA Common Software (ACS).
There are 192 antenna foundations (stations) distributed over the Chajnantor and Pampa la Bola plateaus.
The antenna foundation distribution yields baselines (distances between two antennas) ranging from 15 m to
∼16 km, which are crucial in determining the image quality and spatial resolution of ALMA (see Chapter 7).
The antenna foundations provide the stiffness required for precise antenna pointing, as well as electrical powerand digital connectivity to the main AOS building (See Appendix A.2). The antennas can be re-configured into
the different array configurations (Chapter 7) using the two special purpose ALMA antenna transporters (seeAppendix A.3).
The number of antennas in each array component (12-m, 7-m and TP Arrays), and the specific configurations
available for an observing season (e.g. Cycle 8) will be published in the Capabilities section of the document
ALMA Proposer’s Guide. Complementary background information on ALMA and its capabilities for Cycle 82021 can be found in the document Observing With ALMA: A Primer. Both documents can be found on thelink http://www.almascience.org/documents-and-tools/.

2.2

The 12-m Array

The 12-m Array consists of fifty 12-m diameter antennas designed and built by the European and North
American ALMA partners (each providing 25 units), according to the stringent ALMA Antenna Performance
1 dedicated to the honour of K.-I. Morita
2 http://www.almascience.org/about-alma/weather

12

CHAPTER 2. ARRAY COMPONENTS

Figure 2.1: The ALMA 12-m Array in its compact configuration (left hand side of the image). The ACA withall 7-m antennas (dashed orange circles) and four single-dish 12-m antennas (blue circles) are distributed in theright hand side of the image. A few unoccupied stations can be seen, to which antennas of the 12-m Array canbe moved by the transporter as the array is being reconfigured. At its most extended configuration, antennas
in the 12-m Array will be about 16 km apart.
specifications (see Appendix A). Each antenna contains one front end, including a cryostat (see Appendix A.4),
amplitude calibration device (ACD; A.5), water vapor radiometer (WVR; A.6), and back-end electronics (analog
and digital racks). The WVRs are used to correct the phase fluctuations caused by water in the atmospherealong the line of sight of each 12-m Array element. The cryostat can contain up to ten cartridges, each covering
one frequency band (see Chapter 4). Only one band observes at any time, but up to three can be switchedon simultaneously. Rapid switching between receiver bands is possible but currently only used for observatory
calibration (see Chapter 4). Each receiver band (Chapter 4) detects two orthogonal linear polarizations anddown-converts the signals to an intermediate frequency with 7.5 GHz of bandwidth per polarization3 . Bands
3-8 cartridges are dual sideband (2SB) and Bands 9 and 10 are double sideband (DSB).
The Local Oscillator (LO) signals (Appendix B) are transmitted to the antennas on optical fibers with around trip measurement to correct for changes in the fiber length. There are four independent LO reference
systems so that the 7-m Array, the TP array and two subsections of the 12-m Array (e.g., two ‘sub-arrays’)
can conduct simultaneous independent observations. Please note that the sub-arrays feature of the 12-m Array
is not yet a capability that is offered for PI science observations. The 7.5 GHz total IF bandwidth from theselected receiver is divided into four 1.875 GHz-wide basebands which are digitized at four Gsamples/s, withthree-bit resolution, and transmitted on optical fibers. Total data rates are therefore 96 Gbits/s per antenna.
With formatting, the bit rate is 120 Gbits/s.
On arrival at the central building, the data are recovered and processed in one of the two correlators: the64-input Correlator and the ACA Correlator (see Chapter 5). All antennas can feed either correlator. The
64-input Correlator (Section 5.1) is normally used for the 12-m Array, but it can also take inputs from the
7-m Array or TP antennas. It is an XF correlator (cross-correlates first, then Fourier transforms), but thecorrelator proper is preceded by Tunable Filter Banks, which makes it a digital hybrid XF correlator or FXF.
These can select sub-bands from the 2 GHz-wide basebands in a very flexible manner. From each of these,
the correlator then generates 2016 cross-correlations and 64 auto-correlations (requiring 1.7×1016 operations
per second). Either 2-, 3- or 4-bit resolution is used, and the sampling can be Nyquist or twice Nyquist. See
Table 6.1 for an example table of spectral setups. These correlated data are fed to a group of processors which
do the transforms and carry out integration and data compression.
Both correlators have minimum dump rates of 16 ms for cross-correlation and 1 ms for auto-correlation,although these dump rates can only be achieved using a reduced number of channels to prevent exceeding the
maximum transmission and storage rates. The systems are designed for a maximum data rate of 64 MB/s,
3 See Section 4.1 for the maximum instantaneous bandwidth available for PI science observations.

2.3. THE ATACAMA COMPACT ARRAY

13

although the mean data rate will be considerably less.
The 12-m Array configurations have been designed so that at the highest frequencies in the most extended
configurations, the spatial angular resolution will be as small as 5 milliarcseconds at 950 GHz.

2.3

The Atacama Compact Array

Using an interferometer to obtain images of extended or large-scale structures leads to the well known “zerospacing” problem. This problem arises from the constraint that, to avoid collisions, it is not possible to packantennas closer than their diameter, leaving a hole in the distribution of baselines at short and zero baseline
separations (corresponding to large angular structure). As a result, spatial information from baselines shorter
than the closed-packing ratio is not recovered4 . This problem has considerable impact on observations ofextended objects, particularly those in which the emitted power is dominated by their large-scale structures.
To achieve high-fidelity imaging of sources with emission on angular scales larger than those corresponding
to the minimum spacing of the 12-m Array (the “Maximum Recoverable Scale" for that array - see Section 7.6),
ALMA has been designed to include the Atacama Compact Array (ACA), also known as the Morita Array.
The ACA is composed of twelve 7-m antennas for interferometry (the 7-m Array) and four 12-m antennas
for single-dish observations (TP Array). The four single-dish antennas provide spatial information samples
equivalent from 0 m up to 12 m spacings as auto-correlations. The 7-m Array samples baselines from 9 m to
30 m, bridging the baseline sampling gap between the 12-m Array and the TP Array. The number of arrayelements available is published for each observing cycle.
The ACA is controlled via control software developed on the ACS platform and is operated in a similar
fashion to the 12-m Array. To achieve this unified operation, the ACA system is as compatible with the 12-m
Array as possible at the level of hardware, interface, data, and observing modes. The standard observing modes
for the TP Array include spectral line and continuum observations with raster or Lissajous on-the-fly (OTF)
scans, or position switching. The raw time-series signals from the ACA antennas are processed in the ACA
Correlator (see Section 5.2) to produce the cross-correlated and auto-correlated data.

2.3.1

The 7-m Array

The 7-m Array is composed of twelve 7-m diameter antennas designed and built by East Asia to the ALMA
specifications (see Appendix A). Each antenna contains one front end, including a cryostat, amplitude calibration
devices, and one back end. Similar to the 12-m antennas, each cartridge (see Chapter 4) receives two orthogonal
polarizations. Unlike the antennas of the 12-m Array, the 7-m antennas do not contain Water Vapor Radiometers(WVRs). However, since the 7-m Array is quite compact, atmospheric phase fluctuations will be smaller thanfor the 12-m Array.
The 7-m antenna cryostats are fitted with receivers nearly identical to those on the 12-m antennas, withsmall differences in the warm optics. The Local Oscillator signals transmitted to the 7-m antennas are originatedidentically to the ones sent to the 12-m Array, i.e., from inside the AOS building.
The ACA Correlator is normally used for the ACA, and can work with two sub-arrays. It is an FX correlator(Fourier transform first, then cross-correlate) with 3−bit input and 4 bits in the correlation. The correlator
generates 120 cross-correlations and 16 auto-correlations for each baseband. These are passed to a (specialpurpose) data processing computer at up to ∼0.6 Gbits/s per baseband.
Even in its most compact configuration the 12-m Array does have spacings smaller than 15 m. The array
configuration of the 7-m Array is designed to fill in these shorter spacings from about 9 m to ∼30 m (see Chapter
7).

2.3.2

The TP Array

The TP Array can fill in baseline coverage from 0 m to about 12 m, complementing the 7-m and 12-m Array’s
baseline coverage. It consists of four 12 m diameter antennas built by East Asia (Appendix A). The specificationsof the TP antennas are almost identical to the ones for the 12-m Array. The TP antennas are located on stations
surrounding the 7-m Array.
4 Strictly speaking, mosaicing with imaging using a joint-deconvolution algorithm allows the recovery of more spatial information
than normal synthesis imaging, but the problem caused by absent short and zero spacing information still remains.

14

CHAPTER 2. ARRAY COMPONENTS

The TP Array is usually connected to the ACA Correlator, but its antennas can also be connected to the
64-input Correlator and used for cross-correlation. The ALMA Cycle 8 2021 Proposer’s Guide describes theobserving modes and capabilities offered for the TP Array for each cycle.
Due to the poorer point-source sensitivity of the 7-m Array, during Cycle 8 Operations, the TP Array will
be routinely used in the calibration observations of the 7-m Array.

Figure 2.2: The Morita Array - In remembrance of Professor Koh-Ichiro Morita. Koh-ichiro Morita, a professor
at the NAOJ Chile Observatory, was one of the world’s renowned scientists in the field of aperture synthesis.
He made a great contribution to designing the configuration of 16 antennas composing the Atacama Compact Array (ACA) manufactured by Japan, as well as to realizing high-resolution and high-quality imaging at
millimeter/submillimeter wavelengths to further enhance the performance of ALMA. The picture above shows
Professor Koh-Ichiro Morita taken at his office in the Joint ALMA Observatory in 2011 September.

Chapter 3

Principles and Concepts of Interferometry
3.1

Introduction

Interferometry is the technique ALMA uses to obtain very high angular resolution observations of astronomical
phenomena. Figure 3.1 shows examples of two other observatories, the IRAM NOrthern Extended Millimeter
Array (NOEMA) Interferometer in France and the Submillimeter Array in Hawaii, which also use this technique.
In this chapter, the principles and concepts behind interferometry are described, so that ALMA users can planand understand their observations better.
Interferometry involves the combination of signals received from the sky by two or more physically separated
antennas. The signals are interfered, allowing a sky brightness distribution to be sampled on an angular scale
smaller than possible with a single antenna. The interference modifies the angular sensitivity of the antennas
to include a sinusoid of constructive and destructive nodes. In this sense, the only emission measured by theinterferometer is that from the scale defined by the angular extent of the sinusoidal wavelength, equivalently,
the “spatial frequency”. This wavelength is inversely proportional to the projected distance between the twoantennas. Each datum from the interferometer is called a visibility, and is a measure of the brightness of theemission on the angular scale sampled (i.e., related to the amplitude of the sinusoid) and the relative positionof that brightness on the sky (i.e., related to the phase of the sinusoid. )A range of discrete angular scales can be sampled by including many pairs of antennas in an array. Importantly, by tracking a source across the sky, the rotation of the Earth can be used to change the projected
separations of the antenna pairs, allowing more angular scales to be sampled. An ensemble of the data (i.e.,
sinusoids of various amplitude and phase) can be then “summed” via the Fourier transform to produce an imageof the sky brightness distribution. How well this image reflects the actual sky brightness distribution depends
on how completely the relevant angular scales have been sampled. With its emphasis on delivering images athigh angular resolution, interferometry works extraordinarily well for observing intrinsically compact targets.
The following sections expand upon these basic ideas. We begin by introducing the basic concepts of radio
astronomy, and then move to the principles of aperture synthesis.

3.2

Single-dish Response

The brightness, or equivalently specific intensity, Iν , is defined as the electromagnetic (EM) power δP within arange of frequencies (a bandwidth) δν received from a solid angle δΩ and intercepted by surface area δA:Iν = δP/δΩδAδν,(3.1)

where Iν has typical units of W m−2 Hz−1 sr−1 . In addition, the flux density, Sν , is defined as the integrationof brightness over the solid angle of the emitting source:ZSν =Iν dΩ,(3.2)

16

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

Figure 3.1: The NOrthern Extended Millimeter Array (NOEMA) (top) and the Submillimeter Array (SMA)(bottom) are two of the precursors to the ALMA telescope; both are still in full operation and helped pioneer
the science of millimeter wave interferometry.
where Sν has typical units of W m−2 Hz−1 . In millimeter/radio astronomy, the power received is typicallyso weak that a convenient unit to use for Sν is the Jansky (Jy), where 1 Jy = 10−26 W m−2 Hz−1 . A radio
telescope with effective area Ae receives power Prec per unit frequency from an unpolarized source:
Prec =1Iν Ae δΩ.
2

(3.3)

The coefficient of 1/2 in Equation 3.3 comes from the fact that a receiver is generally sensitive to only one
mode of polarization. (ALMA’s receivers, however, have been constructed with two independent receptors sothat both modes of polarization can be detected simultaneously, so the coefficient is actually 1 for ALMA.) The
antennas bring incident EM power to a focus after reflecting it off a primary surface. The antenna response(i.e., its relative sensitivity) is a summation of all EM power brought to the focus.
The antenna response is actually dependent on the angle from the on-axis pointing direction of the antenna
due to diffraction; i.e., self-interference. To demonstrate the angular dependence, Figure 3.2 shows in the top
panel the case for EM power of wavelength λ arriving along the axis of an unobstructed antenna of diameter D.
Since the source of the EM power is very distant, the EM power arrives at the primary surface essentially as
plane-parallel wavefronts. Note that the antenna surface is parabolic in shape, so the path that each part of thefront travels to the focus is constant. With zero path difference, the EM power arriving on-axis is coherently
summed at the focus. This arrangement is only true, however, along the axis of the antenna. In the lower
panel of Figure 3.2, the case for EM power arriving from an off-axis direction is shown. In this situation,
the EM power does not add as constructively. In addition, the diameter of the antenna projected along theoff-axis direction is less than the true diameter, decreasing the amount of power received from that direction.
As a result, the antenna power response, i.e., its relative sensitivity, will be less than that found on-axis. In
particular, at the off-axis angle of λ/D radians, where λ is the wavelength of observation and D is the diameterof the antenna, the path difference across the antenna diameter, the aperture, will equal one wavelength of theincident emission. The combination of such emission at the focus eads to destructive interference at that angle.
As an illustration, Figure 3.3 shows an example of a one-dimensional antenna power response with angle fora 12-m diameter parabolic antenna uniformly illuminated by emission of wavelength ≈ 0.85 mm (350 GHz). The
power response is largest on-axis but it declines to almost zero in ∼18 arcseconds. The central Gaussian-likefeature is called the primary beam or the antenna beam size and it has a Half Power Beam Width (HPBW)
given by:

17

3.2. SINGLE-DISH RESPONSE

Figure 3.2: Schematic of an incoming plane-parallel wavefront reflecting off an antenna of diameter D and beingbrought to a focus. The top panel shows the case for a wavefront arriving on-axis. The bottom panel shows
the case for a wavefront arriving off-axis. Note that the paths of incident EM power in the first case are all of
equal length, and hence the power is summed constructively at the focus. In the second case, the path lengths
differ, leading to less constructive summations at the focus.

(3.4)

HPBW Primary Beam = 1.02 × λ/D.

For example, the FWHM of a uniformly illuminated antenna of 12 m diameter at λ = 0.85 mm is 14.9 . HPBW
is sometimes referred to as Full Width at Half Power or FWHP. In one dimension, the FWHP is equivalent to
the Full Width at Half Maximum or FWHM, a quantity sometimes used to describe the width of a Gaussian
approximation to the central feature.
Note that the antenna power response rises and declines repeatedly at ever larger angles. The constructive
and destructive interference at larger angles leads to successive sidelobes (whose maxima decline with increasing
angle) and nulls respectively. The first sidelobes have a relative response of only 1.74% that of the primarybeam. Nevertheless, incident emission, if bright enough, coming in at angles well beyond those of the primarybeam can make a large contribution to the received EM power. The angular distance between the first nulls is
termed the Full Width Between Nulls (FWBN), and is given by:
00

FWBN Primary Beam = 2.44 × λ/D.

(3.5)

Half the FWBN of the primary beam, ∼1.22 λ/D, is considered the Rayleigh resolution of the antenna, i.e.,
its ability to distinguish objects on the sky separated by some angular distance. For convenience, the antenna

18

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

power response is typically normalized to 1.0 along the axis. Figure 3.3 illustrates the antenna power response in
one dimension (in log units); on the actual sky, the antenna power response is two-dimensional, and is obtainedby rotating the function shown in Figure 3.3 about its central axis.

Figure 3.3: Normalized 1-D antenna power response for a 12-m antenna uniformly illuminated at 350 GHz.
The power is in log units to emphasize the sidelobes. The HPBW of the primary beam is ∼1.02 λ/D and the
FWBN is ∼2.44 λ/D. The angle of the first null, i.e., the resolution, is 0.5×BWFN = ∼1.22 λ/D. Note thatthe HPBW measured for actual ALMA 12-m and 7-m antennas is ∼1.13 λ/D because the illumination is not
uniform.
Up until now, an idealized antenna was described. The power response of an actual antenna, however, canbe altered by various effects, including the degree by which the secondary is illuminated, diffraction by the arms
supporting the secondary, and surface imperfections. For ALMA, each 12-m antenna has a secondary reflector
and support arms that block an effective area of 0.75 m diameter on the primary surface. The actual ALMA
feedhorns were designed to provide an antenna power response with a nearly Gaussian primary beam and low
sidelobes, preserving as much resolution and sensitivity as possible. The actual ALMA 12-m antennas (and the
ALMA 7-m antennas) have measured primary beam HPBW values of ∼1.13 λ/D.
An equivalent way to consider the antenna power response is in terms of the voltage response, V (θ), whereP (θ) ∝ V 2 (θ). In the far-field, i.e., under the Fraunhofer approximation, a diffraction pattern at the pointof observation is the Fourier transform of the field distribution at an aperture. Hence, the voltage responseat the focus is the Fourier transform of the aperture shape. For an unobstructed antenna, the aperture is a
uniform circle, and V (θ) = J1 (θ)/θ, where J1 (θ) is the Bessel function of the first kind. P (θ) is correspondingly
proportional to (J1 (θ)/θ)2 . The normalized version of the antenna power response, PN , is also known as the
Airy function.
Defining θ and ϕ as orthogonal directional variables (e.g., sky coordinates), Iν (θ, ϕ) and PN (θ, ϕ) can be19

3.3. VISIBILITIES AND APERTURE SYNTHESIS

defined as the directional functions of the sky brightness and the normalized antenna power, respectively. The
total received power of an antenna at a given pointing is the integration over the sky of the product of the skybrightness distribution and the antenna power response:Z
1
Prec = AeIν (θ, ϕ)PN (θ, ϕ)δΩ.
(3.6)
2
4π
In addition, the solid angle of the antenna power response PN (θ, ϕ) is defined by:ZΩA =PN (θ, ϕ)δΩ.

(3.7)

4π

3.3

Visibilities and Aperture Synthesis

Observing at millimeter/radio wavelengths is essentially diffraction-limited, as the angular diameter of the Airy
disk is the FWHM for a circular aperture of diameter D is ∼ 1.22 λ/D. Millimeter/radio wavelength (single-dish)observations have lower resolutions than optical wavelength (single-dish) observations because λ is larger bymany orders of magnitude. Though the D of millimeter/radio single-dish telescopes can also be much larger
than those of optical wavelengths, the increase in D possible for single-dish telescopes is generally never enoughto obtain angular resolutions comparable to ground-based optical telescopes, e.g., 100 or better. For example,
the JCMT 15-m diameter antenna has an angular resolution at 850 µm of ∼1400 .
To obtain higher angular resolution images at millimeter/radio wavelengths, signals from physically separated
antennas can be combined through interferometry. With this technique, sometimes called aperture synthesis,
it is possible achieve a resolution that emulates the effect of having a radio telescope with a larger diameter.
Observers, however, must contend with the reality that only certain angular scales (i.e., those determined by the
projected separations of each pair of antennas) will be sampled. This section builds on the concepts introduced
previously to discuss aperture synthesis in more detail. This powerful technique of aperture synthesis was
pioneered by Sir Martin Ryle, who shared the Nobel Prize in Physics in 1974 in part for its development.
As there are no path differences in the case of a plane-parallel wavefront arriving on-axis an antenna, EM
power from across the antenna is brought together in phase at the focus. Now imagine that the parabolic surface
is divided into N smaller contiguous areas; i.e., elements. In this situation, the received voltage V (t) is the sumof contributions ∆Vi (t) from each of element i:
V (t) =X

∆Vi (t)(3.8)

i

The power received by the antenna is proportional to the running time average of the square of the contributions
from each element. Assuming illumination is the same for each element, the expression for received power interms of the sum of time averages of the products of voltages from element pairs can be rewritten:
h Xi2  X X
hP i ∝∆Vi=h∆Vi ∆Vk i.
(3.9)
Next, this expression can further be rewritten in terms of the sums of element pairs which are the same andthose which are not as:
hP i ∝XXX
h∆Vi2 i +h∆Vi ∆Vk i.

(3.10)

i6=k

The first and second sets of terms in Equation 3.10 are called auto-correlation and cross-correlation terms, respectively, since the voltages multiplied in each term are from either the same or different elements, respectively.
From Equation 3.10, any measurement with a large filled-aperture telescope can be understood as being
a sum in which each term depends on contributions from only two of the N elements. As long as the contributions from each element arrive at the focus in phase, there is no need for the elements to be physicallycontiguous. Generalizing, each cross-correlation term h∆Vi ∆Vk i in Equation 3.10 can be measured with two
smaller, physically separated antennas (at locations i and k) by measuring the average product of their output
voltages with a correlating, or multiplying, receiver. Moreover, if the source properties do not change, there is

20

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

no need to measure all pairs at the same time. A given parabolic surface with N elements has N (N − 1)/2 pairsof elements, and these could be observed sequentially to “synthesize” a measurement by a large filled-aperture
telescope. Alternatively, numerous pairs of antennas, with each antenna considered an element, can be distributed to positions at distances much larger than it is possible to build a single filled-aperture telescope, andthe signals received by these antennas can be combined in phase to approximate the resolving power of a single
filled-aperture telescope.
The above situation only describes the emission received on-axis from antenna pairs. Of course, as noted
above, emission also arrives at the antennas from other directions, leading to phase differences. To understandthe power response expected from a pair of antennas, let’s look at the ideal 1-D situation of a two-antennainterferometer.
Figure 3.4 shows a schematic picture of a two-antenna interferometer separated by distance b, known as abaseline. This distance can be measured in units of the observing wavelength, λ. In terms of familiar unitsof length, b = L/λ, where L is the distance between antennas and λ is the wavelength in the same unit; e.g.,meters. Both antennas observe a common position so located at an angle θ from the meridian. The projected
separation of the two antennas towards so from the perspective of the source is u = b cos θ. In this example, an
on-axis wavefront incident to both telescopes reaches antenna 2 first and the wavefront reaches antenna 1 a little
later, having traversed an extra path length of b · so = b sin θ. In other words, emission received by antenna 1
experiences a geometrical delay relative to that received by antenna 2, where the time equals τg = b·so /c. To
compensate for the geometrical delay, an artificial delay can be inserted into the signal path of antenna 2 (e.g.,
electronically) so that the signals from both antennas arrive at the correlator with the same phase.

Figure 3.4: An ideal 1-D interferometer consisting of two antennas, 1 and 2, separated by physical distance (i.e.,a baseline) b. The antennas are both pointed towards a sky location given by so , which is at an angle θ fromthe meridian. The projected distance between the two antennas in that direction is thus u = b cos θ. The twoantennas are connected to a correlator where the voltages detected from each are combined.
Moving slightly off-axis, a small angle from the axis can be described as α, and its 1-D sky position as21

3.3. VISIBILITIES AND APERTURE SYNTHESISl = sin α, i.e., the direction cosine. At angle α, an off-axis signal reaching antenna 1 will have to travel aslightly longer path than an off-axis signal reaching antenna 2, even with the geometrical delay introduced tocompensate for an on-axis signal. This extra path length is x = u sin α = ul. All distances can be consideredin this situation in units of the wavelength of the emission, λ, so that x is the number of wavelengths within agiven distance. The extra path lengths result in phase differences with α that can be characterized where thevoltage response of antenna 2, V2 , can be written in terms of the product of the voltage response of antenna 1,
V1 , and a phase delay factor sinusoidally varying as a function of angle:(3.11)

V2 = V1 e2πi(ul) .

Expanding to two dimensions introduces β, a direction on the sky orthogonal to α. Also, m = sin β isdefined as the small angle analog to l in this new direction. Note that the baseline here is actually a 2-D vector
with components in both dimensions, i.e., b1 and b2 . Hence, we define u = b1 cos θ and v = b2 cos ϕ where ϕis the angle of the position so on the sky from the reference position orthogonal to θ. Finally, y is defined as
the extra path length introduced in this new direction, in units of the wavelength of emission, i.e., y = v sin β= vm. With these changes, the two-dimensional voltage response of antenna 2 is:V2 = V1 e2πi(ul+vm) ,(3.12)

where u and v are identified as specific spatial frequency components of the sinusoid in the E-W and N-S
directions respectively, and these are the projected lengths of the antenna separations measured in units of the
wavelength at the time of observation. Also, l and m are identified as direction cosines relative to a reference
position in the E-W and N-S directions, respectively. Typically, the on-axis position so has l = 0 and m = 0
and is called the phase center.
The correlator acts as a multiplying and time-averaging device for the incoming signals from antennas 1 and2. Hence, its output is:ZZ
hV1 V2 i = hZZV1 (l, m)dldm

V2 (l, m)dldmi.

(3.13)

Under the assumption that signals emanating from different parts of the sky are incoherent (i.e., they have nosimilarities in phase), the time averages of the correlation of those signals will be zero. Thus, the product of
the integrals in Equation 3.13 can be simplified to:ZZ
hV1 V2 i = h
V1 (l, m)V2 (l, m)dldmi
ZZ
hV1 (l, m)V2 (l, m)idldm(3.15)hV1 (l, m)2 ie2πi(ul+vm) dldm.

(3.16)

hV1 V2 i =ZZ
hV1 V2 i =(3.14)As V 2 ∝ P (see Equation 3.9) and P ∝ Iν (see Equation 3.3),
ZZ
hV1 V2 i ∝I(l, m)e2πi(ul+vm) dldm

(3.17)

where I(l,m) is the intensity distribution on the sky. The correlator therefore measures a quantity known as
the complex visibility, V, which is formally the Fourier transform of the intensity distribution on the sky:
ZZ
V(u, v) =I(l, m)e2πi(ul+vm) dldm = Aeiφ .

(3.18)

Note that V is a complex number, and can be described by an amplitude, A, and a phase, φ. The amplitude andphase contain information about the source brightness and its location relative to the phase center, respectively,
at spatial frequencies u and v.

22

3.4

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

The Visibility or (u,v) Plane

The relationship between the sky brightness distribution and the complex visibility distribution is governed by
the van Cittert-Zernike theorem and it is the basis of aperture synthesis. Given that the complex visibility is
the Fourier transform of the sky brightness distribution in the image plane, it follows that the sky brightness
distribution is in turn the inverse Fourier transform of the complex visibility distribution in the visibility plane:
ZZ
V(u, v) =I(l, m)e2πi(ul+vm) dldm
(3.19)
ZZ
I(l, m) =V(u, v)e−2πi(ul+vm) dudv.

(3.20)

p
Here, A(l, m) and 1/ (1 − l2 − m2 ) are omitted, as they are usually close to unity. By measuring the distribution of complex visibilities (in the visibility or (u, v) plane), in principle the sky brightness distribution can berecovered. In essence, an image is a “sum” (i.e., the Fourier transform) of the visibilities where each visibility
has an amplitude and phase representing the brightness and relative position of emission on a specific angularscale. The image and its Fourier transform are conjugates of each other, and each contains the same amount of
information.
Two antennas at a given physical distance b can have signals interfered to sample the sky brightness distribution on a scale inversely proportional to the projection of that distance on the sky. As shown above, theresponse of the interferometer is sinusoidal, and is sometimes referred to as a fringe, with spacing on the sky inthe 1-D case of:Fringe Spacing = 1/u (radians) = 1/(b cos θ) = λ/(L cos θ).

(3.21)

In effect, the interference of the signals modifies the angular response of the antennas and the antennas can“see” the true sky brightness distribution only on the scale defined by the wavelength of the sinusoid. As thefringe spacing depends inversely on the projected distance, antennas closer together measure emission on larger
scales. Conversely, those antennas spaced further apart measure emission on smaller scales. Since fringe spacing
also depends on the wavelength of emission, as b is measured in numbers of wavelengths, observing shorter or
longer wavelengths also can sample smaller or larger scales, respectively. These ideas can be easily generalized
to two dimensions, with the fringe spacing and on-sky orientation depending on the relative magnitudes of uand v.
A given pair of antennas will only instantaneously sample a single scale of the sky brightness distribution.
Given the E-W and N-S separations of the pair, a visibility in the (u, v) plane is measured. Since visibilities
are samples of a complex-valued function with Hermitian symmetry, a single sampling gives two visibilities,
one at (u, v) and its complex conjugate at (−u, −v). To recover the true sky brightness distribution, however,knowledge of the distribution of visibilities across the (u, v) plane would be needed. Improving coverage ofvisibilities over the (u, v) plane can be done in several ways. First, multiple antennas can be incorporated into
an array, with each at a different distance from the others to prevent redundancy. An array of N antennas
will have N (N − 1)/2 independent baselines, with each pair providing a single pair of samples in the (u, v)
plane. Second, a target can be observed repeatedly by the array as it appears to move across the sky due to the
Earth’s rotation. Though the physical distances between the antennas do not change, their projected distances
do change depending on the altitude and azimuth of the target. Hence, repeated observations by all the pairs in
an array can sample many visibilities across the (u, v) plane. Finally, antennas in the array may be arrangeable
in several configurations so that pairs of antennas have different distances and can sample different parts of the(u, v) plane. Assuming the source emission is not variable, the combination of these schemes can reasonably
sample the (u, v) plane, yielding an image that can resemble the true sky brightness distribution.

3.5

Fields-of-view and Mosaics

Each antenna of an actual interferometer has finite diameter. As noted before, such antennas have their own
power responses on the sky PN = A(l, m); e.g., the Airy function for an unobstructed, uniformly illuminatedaperture. Indeed, the individual antenna response fundamentally limits the extent of an interferometric image

23

3.6. SPATIAL FILTERING

made with a single pointing. In practice, the HPBW of the primary beam serves as the “field-of-view” of thesingle-pointing interferometric image. Moreover, A(l, m), the Airy function, is actually included formally in thecorrelator output:
ZZ
V(u, v) =A(l, m)I(l, m)e−2πi(ul+vm) dldm.
(3.22)
Hence, an interferometer actually measures the Fourier transform of the sky brightness distribution multipliedby the antenna power response. To recover I(l, m), the image resulting from the Fourier transform of thecomplex visibilities must be divided by A(l, m) as the last step of image processing. This so-called primarybeam correction should be performed if the image contains scientifically relevant emission off the phase center.
Otherwise, intensities and flux densities measured at those locations will not be accurate.
To counteract the angular fall-off of sensitivity due to the primary beam response, or even to sample emission
over areas on the sky larger than the primary beam, an interferometer can observe adjacent positions, producing
a mosaic. Sensitivity across a mosaic depends on the spacing of the individual positions observed. A mosaic canhave close to uniform sensitivity with a minimum
number of pointings if the positions observed are arranged in√a grid of equilateral triangles spaced by λ/( 3D), where D is the diameter of the antenna. With this spacing,
the fall-off of the primary beam response at one pointing is made up by the responses of the primary beams at
adjacent pointings, except of course at the edge of the mosaic (see Section 7.7 for a more complete description).
Mosaics can be made with adjacent positions that are spaced either closer or more distant, with non-uniform
sensitivities. Mosaics provide increased areal coverage but at a cost of more observing time. For example,
uniform sensitivity can be obtained across the primary beam of a single pointing but requires a minimum of six
other pointings aroundthe single pointing. These six pointings are arranged in a hexagonal pattern with each√vertex spaced λ/( 3D) from each other (and the single pointing). A single image is produced by combining
the visibilities obtained at all pointings into a single ensemble that is simultaneously Fourier transformed.

3.6

Spatial Filtering

Through the principles described in Sections 3.3-3.5, the true sky brightness distribution can be recovered.
It is, however, impossible in practice to sample completely the (u, v) plane and obtain all visibilities. The
incomplete (u, v) plane sampling effectively provides a fundamental limit to the level of detail discernible in thesky brightness distribution; i.e., down to a minimum scale defined as the resolution. In addition, incomplete
sampling results in spatial filtering of the true sky brightness distribution; i.e., the resulting images do notcontain information on angular scales unobserved by the interferometer. In particular, the lack of coverage at
the shortest baselines (i.e., lower than those sampled by the smallest baselines) results in an intrinsic lack ofsensitivity to large-scale emission. It is crucial for ALMA users to understand these limitations. Below, we
describe the ideas behind spatial filtering and provide a few illustrative examples. Further examples can befound in Sections 7.6 and 7.7.
First let’s discuss resolution. The resolution of any interferometric image depends on the distribution ofvisibilities sampled. Assuming a finite number of M visibilities has been obtained, the (u, v) plane has beensampled at 2M discrete points. The sampling distribution can then be characterized as an ensemble of 2M(Dirac) delta functions:
B(u, v) =2MX

δ(u − uk , v − vk ).

(3.23)

k=1

Given the sampling function B(u, v), we can calculate the function IVD , which is the dirty image:
ZZ
D
IV (l, m) =V(u, v)B(u, v)e−2πi(ul+vm) dudv.

(3.24)The inverse Fourier transform of this ensemble of visibilities can then be written as:
I D (l, m) = F T −1 {B(u, v)V(u, v)}.

(3.25)

Following the convolution theorem, the Fourier Transform of a convolution of two functions is the product of
the Fourier Transforms of those functions. Hence, Equation 3.24 can be rewritten as

24

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRYI D (l, m) = b(l, m) ∗ I(l, m)A(l, m).

(3.26)

In effect, the image obtained is the convolution of the true sky brightness distribution (modified by theantenna power response A(l, m)) with the point spread function, b(l, m) = F T −1 {B(u, v)}, which is the Fouriertransform of the (u, v) plane sampling distribution. The point spread function is sometimes called the synthesized
beam or the dirty beam. It is important to distinguish this beam from the single-dish response function A(l, m),which in the interferometry context is called the primary beam. The image resulting from the Fourier transformof a finite number of visibilities, I D (l, m), is sometimes referred to as the dirty image.

Figure 3.5: Imaging concepts. Panel a (upper left): Example of a dirty beam, b(l, m). Panel b (upper right):
The related ensemble of discrete points sampled in the (u, v) plane, B(u, v). The black points were obtained
from a compact configuration while the red ones were obtained from an extended configuration. Panel c (lowerleft): Example of a true sky distribution, I(l, m). Panel d (lower right): The dirty image I D (l, m) resulting
from observing I(l, m) over the baselines of B(u, v), or equivalently the convolution of I(l, m) by b(l, m). The
antenna power response, A(l, m), has been ignored in this illustration since it is much wider than the true skybrightness distribution. (Figure courtesy of D. Wilner.)
The measure of how similar an image is to the true sky distribution is sometimes referred to as image fidelity.
Image fidelity depends on the specifics of coverage of the (u, v) plane sampled by the interferometer. Since thenumbers of samples are necessarily finite and discrete, there are invariably gaps in any practical sampling of the(u, v) plane. These gaps mean that no information is obtained about the true sky brightness distribution on
those specific angular scales. Note that visibilities corresponding to those unobserved scales can have any value.
With no information, however, it is typically assumed that V(u, v) = 0 at unsampled locations in the (u, v)
plane. Including these visibility domain gaps through the Fourier transform produces aliased features in the
resulting image, the magnitude of which depends on the extents and locations of gaps in the (u, v) plane and thebrightness of emission on sampled scales. If the (u, v) plane has been reasonably well sampled, the synthesized
beam will consist of a compact positive feature surrounded by positive and negative features of lower relative

25

3.6. SPATIAL FILTERING

amplitude. These latter features, also called sidelobes, can complicate the image since brightness is distributed
via the point spread function throughout the image. The resulting image can have significant artifacts dependingon the sky brightness distribution and the sampling of the (u, v) plane. A dirty image, however, can be improved
through deconvolution techniques to minimize the effect of incomplete spatial frequency sampling (e.g., CLEAN
and its variants; see Chapter 7).
Though speaking generally about true sky brightness distributions so far, a special note should be made forthe case of point sources. Obviously, a point source is a distribution of emission that is not extended relative
to the resolution of the observation. In this case, the morphology of the dirty image will equal that of the dirty
beam (e.g., see Equation 3.25). Moreover, the complex visibilities of the point source have the same amplitudes
on all observed angular scales. Of course, sources may appear point-like at low resolutions but may appear
extended in higher-resolution observations.
Figure 3.5 illustrates the concepts of dirty beam and dirty image and their impact on the recovered image.
Panels a and b (upper pair) show respectively the dirty beam and the related ensemble of locations observedin the (u, v) plane; i.e., the (u, v) coverage. Note in panel a the positive feature in the center of the dirty beam
distribution and the surrounding positive and negative features of lower amplitude. These latter features arise
from the incomplete sampling of the (u, v) plane seen in panel b. As an aside, note that two sets of (u, v)
plane samples are identified in panel b; these result from observations by the same antennas in two different
configurations, a compact one (black) and an extended one (red). Panels c and d (lower pair) show respectively
an example of a true sky distribution (here, a model of a ring of emission) and the dirty image. The dirty
image is the convolution of the true sky distribution by the dirty beam, and one can easily see how incomplete
sampling of the (u, v) plane leads to the appearance of significant artifacts in the resulting dirty image.
The resolution of the dirty image is defined effectively by the compactness of the central feature of the dirty
beam; e.g., half its FWBN. Since the structure of the dirty beam is generally more complicated than that ofa single-dish antenna (e.g., the beam from a uniformly illuminated antenna shown in Figure 3.3), it is not soeasy to measure FWBN. Instead, the resolution is typically approximated to first order by the FWHM of a
Gaussian fit to the central feature of the dirty beam. The resolution of the dirty image depends ultimately on
how the interferometer antennas are arranged. In general, distributions connected via a Fourier transform scale
inversely to each other. For example, narrow distributions in one domain have wide ones in the other, and viceversa. By analogy, an ensemble of discrete points, B(u, v), clustered around the (u, v) plane origin provided by
a compact configuration yields a low-resolution image since the central beam feature b(l, m) is wide. Conversely,
an ensemble of discrete points distributed more widely from the (u, v) plane origin yields a high-resolution image
since the central beam feature is narrow. Indeed, resolution is fundamentally limited by the extent of the longest
baselines in a given configuration. The minimum scale discernible in the image is limited by these maximum
baselines. A handy formula for the approximate resolution provided by an interferometer is:Interferometer Resolution = θres = k λ/Lmax ,(3.27)

where k is a factor that depends on the how the visibilities are weighted during inversion (typically ∼1; see
Figure 7.6) and Lmax is the longest baseline in the array.
Another important limitation of interferometric array observations is insensitivity to large angular scales.
This insensitivity arises because interferometric arrays alone cannot sample spatial frequencies lower than thosesampled by a baseline equal to an antenna diameter. In effect, visibilities at locations on the (u, v) plane at ornear its origin are not sampled, leading to the so-called zero-spacing problem. The lack of sensitivity to larger
scale emission due to the zero-spacing problem biases the resulting image to the compact, small-scale emissionof the true sky brightness distribution. As a guideline, the interferometer image has a maximum recoverable
scale given roughly by:
Maximum Recoverable Scale = θM RS ≈ 0.6λ/Lmin ,(3.28)

where Lmin is the minimum baseline in the array configuration. Strictly speaking, for an input Gaussian
visibility distribution of FWHM θM RS , the ratio of the brightness at source center of an image made by anarray with Lmin to the same made with no central hole in its visibility sampling (i.e., no zero spacing problem)
is 1/e1 . The smallest baseline possible in an array occurs when two antennas are adjacent to each other. Of
1 see Wilner, D.J., Welch, W.J. 1994, ApJ, 427, 898

26

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

Figure 3.6: Examples of spatial filtering using the CASA task simobserve on representative ALMA configurations
for Cycle 8. Panel a (upper left): An optical image of the galaxy M51 used as a template for a true skybrightness distribution for the simulations. The frequency of the emission has been changed to 100 GHz,
the image size has been scaled to ∼30 × 30 , and its declination has been changed to -40◦ to allow ALMA
observations to be simulated. For the simulations, the galaxy was “observed" over a mosaic of 33 pointings,
for ∼10 hours in total. The resulting dirty images were CLEANed. Panel b (upper right): The high-resolution
image of the galaxy obtained when observed in the ALMA C43-6 configuration with maximum baseline of2516.9 m, respectively. The resulting synthesized beam is ∼0.4700 and the maximum recoverable scale is ∼400 .
Panel c (lower left): Medium-resolution image of the galaxy when observed in the ALMA C43-4 configuration
with maximum baseline of 783.5 m, respectively. The resulting synthesized beam is ∼1.300 and the maximum
recoverable scale is ∼1100 . Panel d (lower right): Low-resolution image of the galaxy when observed in ALMA
configuration C43-1 with maximum baselines of 160.7 m, respectively. The resulting synthesized beam is ∼4.300
and the maximum recoverable scale is ∼2800 .
course, the antennas cannot be moved physically closer together than their diameters. Note that in projection,antennas can appear closer than their diameters. In those cases, found typically when observing low elevation
sources in compact configurations, the antenna in front partially blocks the reception by the antenna in therear. The resulting visibilities are distorted; e.g., the antenna in the rear receives less power than the one infront. This situation is called shadowing and affected data are typically removed from the ensemble of observed
visibilities.
Figure 3.6 illustrates the idea of spatial filtering using simulations of notional ALMA configurations. In
Cycle 8, as in the three previous ALMA Cycles, ALMA aims to observe with at least 43 antennas on the 12-m
Array. However, there are often times during the year where more than 43 antennas are available for PI scienceobservations - even up to 50! As such, starting with Cycle 8, the "C43-X" convention for configurations has3.7. MULTI-CONFIGURATION OBSERVATIONS

27

been deprecated in favor of a "C-X" notation to account for the fact that more than 43 antennas may be used.
See Chapter 7 and Table 7.1 for the full range of configurations offered for Cycle 8 and their corresponding
resolutions. Simulations should still be done using the notional ALMA "C43-X" configuration files as that
represents the minimum expected results from an observation. In practice, data will often be of higher quality
than what the simulations predict.
The simulations were performed using the Common Astronomy Software Applications (CASA2 ) package,
the suite of data reduction and analysis software used by ALMA. Here, panel a shows an optical image of thegalaxy M51 used as an example of a true sky brightness distribution, after changing the frequency of the image
to 100 GHz and placing the image center at δ = -40◦ , a declination easily observable with ALMA. Panels b,c, and d show the recovered images obtained by simulating 43-antenna observations of the galaxy using the
CASA task simobserve in extended (C43-6), somewhat extended (C43-4), and compact (C43-1) configurations,
respectively, and CLEANing. Angular resolutions of ∼0.4700 , 1.300 , and 4.300 are obtained, respectively, andthe corresponding maximum recoverable scales are ∼400 , ∼1100 , and ∼2800 , respectively. Larger-scale emission
from the galaxy has been filtered out in the extended configuration observations (panel b), leaving only thecompact structures of its arms. On the other hand, these compact structures are not very discernible in thecompact configuration observations (panel d). A reasonable compromise is found in the somewhat extended
configuration observations (panel c), yet some small-scale detail and larger-scale emission remain missing. Notethat though these images are missing angular scales, good science can still be obtained with them, as long as
their limitations are properly understood. Combining data obtained from multiple configurations, or having
more antennas, would increase the fidelity of recovered images.

3.7

Multi-configuration Observations

As previously discussed, a given configuration with baselines ranging from Lmin to Lmax is sensitive to angularscales from ∼ θM RS to θres . Sensitivity to a broader range of angular scales is possible by combining dataobtained in multiple configurations, where more extensive coverage of the (u, v) plane is attained. For example,
the same source can be observed in different configurations of the 12-m Array, with more extended configurations providing higher angular resolutions. For sensitivity to extended structures, the more compact 12-m Arrayconfigurations or the more tightly clustered 7-m Array can be used. Finally, the individual Total Power (TP)Array antennas of the ACA can be used to map the largest angular scales and address the zero-spacing problem. In this section, we briefly describe so-called multi-configuration observations. Discussion of how ALMA
implements such observations in practice can be found in Sections 7.8 and 7.9.
During proposal preparation, ALMA users should take note of the maximum recoverable scale needed toensure that the proposed observations will be able to recover the scales needed to address the science in question.
The ALMA Observing Tool will determine which combination of configurations will yield the desired angularresolution and maximum recoverable scale.
Data combination appears to work best when the signal-to-noise ratios (SNR) of the datasets are similar on
overlapping spatial scales. Otherwise the noise in the lower-SNR dataset will corrupt the overlapping spatial
scales in the map and degrade the image quality. In addition, the accuracies of the astrometry and calibrationof the different datasets are important. Assuming the SNR of the individual datasets is high, combination isbest done in the visibility domain rather than the image domain. By combining data in the visibility plane, the(non-linear) deconvolution has access to all available information, which tends to produce more robust, higher
fidelity images.
Single-dish and interferometric data are typically combined by a technique called “feathering”, which is
described in greater detail in Chapter 7. To feather the single dish an interferometric data together, they images
or cubes are Fourier transformed to the spatial frequency domain; weighted appropriately, down-weighting highspatial frequency information in the single dish map and down-weighting low spatial frequency informationin the interferometric map; added together; and inverse Fourier transformed back into a single image or cube.
This procedure works best if the single-dish and interferometric data sample some common (overlapping) spatial
scales, for example, if the single-dish antenna has a diameter which is twice the minimum baseline sampled by
the interferometer. Multiple interferometer pointings (mosaics) can also in some circumstances partially recover
missing low spatial frequency information in the absence of single dish data.
2 For more information on CASA, see http://casa.nrao.edu

28

3.8

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

Units and Conversions

This chapter ends with a discussion of various units used in millimeter and radio astronomy and describe some
useful conversions. Returning to the concept of specific intensity, this quantity can be described alternatively
in terms of a temperature:2kν 2
Tb (θ, ϕ).
(3.29)
c2
In this equation, Tb is the brightness temperature, the temperature of a blackbody with the same specificintensity at a given frequency in the Rayleigh-Jeans limit, i.e., hν/kT  1. Brightness temperature serves as anequivalent way of expressing the specific intensity of an astronomical source. The unit of brightness temperature
is Kelvin (K).
In turn, brightness temperature can be included into the definition of flux density, Sν (Equation 3.2), whereIν (θ, ϕ) =2kν 2Sν = 2cZ
Tb dΩ.

(3.30)

Assuming the beam is Gaussian, one can then connect brightness temperature to flux density following:

 
"

2  00   00 #TSν
300 GHz
1
1
=
13.6
,
(3.31)
1K
1 Jy
ν
θmax
θmin
where ν is the observing frequency, and θmax and θmin are the major and minor axis of the synthesized beam,
respectively. Note again that flux densities observed by ALMA are typically in units of Janskys, where 1 Jy =10−26 W m−2 Hz−1 = 10−23 erg s−1 cm−2 Hz−1 . The ALMA Observing Tool converts between temperaturesand flux densities using these formulae.
An important point ALMA users must consider when proposing their projects is the dependence of brightness
temperature sensitivity on synthesized beam size. Using Equation 3.30, one sees that an rms value in flux density(∆S) can translate to an rms value in brightness temperature (∆T ), assuming a given synthesized beam size.
Larger beam sizes correspond to lower ∆T , i.e., the surface brightness sensitivity increases. In turn, extended low
surface brightness objects may be harder to detect at higher angular resolutions as the corresponding sensitivities
may be too low. Typically, a compromise must be obtained between angular resolution and brightness sensitivity
when planning interferometric observations.

3.9

Further Reading

If more information about interferometry is desired, the topic is covered in more detail in the following seminal
texts:• Interferometry and Synthesis in Radio Astronomy - Third Edition, by Thompson, A. R., Moran, J. M.,& Swenson, G. W. (Springer), now available online at https://link.springer.com/content/pdf/10.1007%2F9783-319-44431-4.pdf• Tools of Radio Astronomy - Sixth Edition, by Wilson, T. L., Rohlfs, K., & Hüttemeister, S. (Springer), Fifth
Edition now available for free online at https://link.springer.cpm/content/pdf/10.1007%2F978-3-540-851226.pdf• Synthesis Imaging in Radio Astronomy II, PASP Conference Series, Vol. 180, eds. G. B. Taylor, C. L.
Carilli, & R. A. Perley (San Francisco - ASP)
• Millimeter Interferometry: Proceedings of the IRAM Millimeter Interferometry School, ed. A. Dutrey,
available online at http://iram.fr/IRAMFR/IS/IS2002/archive.html.

Chapter 4

Receivers
The ALMA front end can accommodate up to 10 receiver bands covering most of the wavelength range from
8.5 to 0.32 mm (35–950 GHz). Each band is designed to cover a tuning range which is approximately tailoredto the atmospheric transmission windows. These windows and the tuning ranges are outlined in Figure 4.1.
This illustrates the broad, deep absorption features, mostly due to H2 O in the lower few km of the atmosphere,
as well as some O2 transitions. The many narrow features seen in this plot are mostly from stratospheric O3 ,along with some transitions of CO and other trace species. In Cycle 8, Bands 3, 4, 5, 6, 7, 8, 9, and 10 are
available, and the basic characteristics of the bands are outlined in Table 4.1. Each of the ALMA receiver bands
is described in more detail in the following sections as well as in the references listed in Table 4.2.

Transmission in All ALMA Bands at Zenith
100
1
2
3
4
5
6
7

Transmission (%)

80

60

40

20

0
100

200

300

400

500

600

700

800

900

1000

Frequency (GHz)
Figure 4.1: The ten ALMA receiver bands along with atmospheric transmission. The receiver coverage is shown
shaded, superimposed on a zenith atmospheric transparency plot at the Array Operation Site (AOS) for the
first seven octiles of observing conditions at ALMA (see Table 9.1).
The ALMA receivers in each antenna are situated in a single front-end assembly (see Appendix A, Section

30

CHAPTER 4. RECEIVERSBand

Frequency/
Wavelength
range(GHz)1 /(mm)LO range(GHz)

Sidebandmode2

IF range
(GHz)

Inst.
IF bandw.
(GHz)4Trx over80% ofband(K)6

Trx atany frq.
(K)63

84.0 - 116.0/
2.59 - 3.57
125.0 - 163.0/
1.84 - 2.40
158.0 - 211.0/
1.42 - 1.90
211.0 - 275.0/
1.09 - 1.42
275.0 - 373.0/
0.80 - 1.09
385.0 - 500.0/
0.60 - 0.78
602.0 - 720.0/
0.42 - 0.50
787.0 - 950.0/
0.32 - 0.38

92 - 108

2SB

4–8

7.5

<397

<437

133 - 155

2SB

4–8

7.5

<51

<82

166 - 203

2SB

4–8

7.5

<55

<75

221 - 2652SB

4.5–103

7.5

<83

<136

283 - 365

2SB

4–8

7.5

<147

<219

393 - 492

2SB

4–8

7.5

<196

<292

610 - 712

DSB

4–12

7.5(15)5

795 - 942

DSB

4–12

7.5(15)5

<175
(DSB)
<2308
(DSB)

<261
(DSB)
<344
(DSB)

4
5
6
7
8
9
10

Table 4.1: ALMA Receiver Specifications. Notes to Table: 1. Frequency ranges are the maximum available,at the extreme upper and lower limits of the IF passband. In reality, because of filter roll-off, the coverage is∼60MHz less (See Section 6.4) 2. Sideband modes: 2SB means dual sideband receiver where the two sidebands
are available simultaneously, DSB means double sideband receiver. See text for details. 3. Usable IF range is
extended to allow simultaneous observations of multiple lines specifically of Carbon Monoxide (CO). However,
the auto-correlation noise performance is degraded by a factor of up to about 1.2 below 5.5 GHz (Section 4.2.4)
4. Maximum instantaneous IF bandwidth, limited by the back-end filters and spectrometers. As both upper andlower sidebands both pass through the same IF bandwidth but are subsequently separated, the effective signal
bandwidth given in this column for 2SB receivers is twice the actual IF filter bandwidth. In addition, this is perpolarization, so the total effective bandwidth for each receiver is then another factor of 2 higher. Note that theeffects of the anti-aliasing filters have been included (see Section 6.4). 5. In Cycle 8, the maximum bandwidthis approximately double in cross-correlation mode, because both sidebands can be separated and correlatedusing 90-degree phase switching (see Section 6.3.4 and Section B.4.4). 6. The maximum specified SSB receivertemperatures (Trx ) are given, unless otherwise noted. These values are the average over the whole IF band. In
many cases, the average realised results are better than specifications; the sections on individual receiver bands
describe the typical values measured. The numbers adopted in the observing tool (OT) and ALMA sensitivity
calculator (ASC) are conservative values of the average value over the band. 7. The specification for Band 3
receivers are described slightly differently to other bands: at LO1=104GHz, Trx <39 K (including warm optics),
and Trx <43 K for any other valid LO setting. 8. The specification for Band 10 receivers is Trx <230 K withina selected 80 % portion of that band (787–950 GHz).
Topic

Author/YearTechnical papers or Meeting proceedings

ADS identifier

B3
B4
B5
B6
B7
B8
B9
B10
Optics
WVR

Claude et al. 2008
Asayama et al. 2014
Belitsky et al. 2017
G. A. Ediss, et. al 2004
Mahieu et al. 2012
Sekimoto et al. 2008
Baryshev et al. 2007
Uzawa et al. 2009
Rudolf et al. 2007
Emrich et al. 2009SPIE 7020
PASJ, 66 (3), 57(1-13)
A&A (doi=10.1051/0004-6361/201731883; in press)
15th Intl Symp Space Terahertz Tech
Trans. THz Sci. and Tech., 2(1) 29-39
19th Intl Symp Space Terahertz Tech
19th Intl Symp Space Terahertz Tech
20th Intl Symp Space Terahertz Tech
IEEE Trans. on Antennas & Propagation
20th Intl Symp Space Terahertz Tech

2008SPIE.7020E..33C
2014PASJ...66...57A
2004stt..conf..181E
2012ITTST...2...29M
2008stt..conf..253S
2008stt..conf..258B
2009stt..conf...12U
2007ITAP...55.2966R
2009stt..conf..174E

Table 4.2: Technical papers describing the receiver bands, optics and the water vapor radiometer.

4.1. LOCAL OSCILLATORS AND IF RANGES

31

A.4). The front-end assembly consists of a large cryostat containing the receiver cold cartridge assembly (CCA)
for each band (including the Superconductor-Insulator-Superconductor (SIS) mixers and Local Oscillator (LO)injection) and the Intermediate Frequency (IF) and LO room-temperature electronics of each band (the warm
cartridge assembly, WCA). The cryostat is kept at a temperature of 4 K through a closed cycle cooling system.
The Amplitude Calibration Device (ACD) used for ambient/hot load calibration is mounted above the front end(see Appendix A.5). Each receiver cartridge contains two complete receiving systems sensitive to orthogonallinear polarizations. The designs of the mixers, optics, LO injection scheme, and polarization splitting varyfrom band to band, depending on the optimum technology available at the different frequencies; each receiver
is described in more detail in the sections below.
Up to three bands can be switched on at a time (more would risk overloading the cryostat cooler). Froma hardware point of view, it takes only about 1-2 seconds to switch between two bands which are powered up(limited by the LO locking and antenna movement). For bands that are not switched on, it takes around aminute to power-up the band, after which it is necessary to set a nominal LO power and allow around 5 minutes
for thermal stabilization before science scans commence1 .

4.1

Local Oscillators and IF Ranges

The observed sky frequencies need to be mixed down to frequencies in the range 2 to 4 GHz in order to send
the digitized signals to the correlator (see Section 6.1). This frequency downconversion involves a set of LOs,
and the LO and IF systems are described in detail in Appendix B.
The front-end mixer uses LO1 to down-convert the sky frequencies into an IF band with a range of 4–12
GHz. This covers the needs of all the ALMA bands, since the mixers for Bands 3, 4, 5, 7, and 8 have an output
range of 4–8 GHz, Band 6 a range of 4.5–10 GHz and Bands 9 and 10 a range of 4–12 GHz (Table 4.1). The
possible sky frequency ranges covered by each receiver with the first LO, LO1, set to a frequency FLO1 are:
• For the lower sideband (LSB): (FLO1 - IFlo ) to (FLO1 - IFhi )• For the upper sideband (USB): (FLO1 + IFlo ) to (FLO1 + IFhi )where IFlo and IFhi are the lower and upper IF ranges in the “IF Range” column of Table 4.1, and the IF
bandwidth (per sideband) is IFhi –IFlo . The ranges of LO1 are given in column 3 of Table 4.1. This is illustrated
in Figure 4.2. Note that the maximum IF bandwidth in Table 4.1 may be a few percent less than the IF rangein Table 4.1 (see Section 6.4).

Figure 4.2: IF ranges for the two sidebands in a heterodyne receiver.
1 The original ALMA specifications dictate that after 15 minutes of thermal stabilization time the receivers should meet all the
ALMA technical specifications, although in practice this has been found to be excessively large, as gain drifts calibrate out in real
observations.

32

4.2

CHAPTER 4. RECEIVERS

The Cycle 8 Receivers

The receivers for Bands 3 to 8 are two-sideband (2SB) receivers, where both the upper and lower sidebands areprovided separately and simultaneously. There are 4 outputs from each of the receivers, comprising the upperand lower sidebands in each of the two polarizations. Each output has a bandwidth of 4 GHz (slightly more forBand 6) which is reduced to an effective total bandwidth of 3.75 GHz due to the anti-aliasing filters, etc., see
Appendix B.3.5. The mixers give 10 dB or more unwanted sideband rejection, which is adequate for reducing
the degradation of S/N from noise in the unwanted sideband, but not adequate for suppressing astronomicalsignals in the unwanted sideband. Further suppression is performed by offsetting LO1 and LO2 (and eventually
the tunable filter bank LO, TFB LO) by small and opposite amounts, as well as 180-degree phase-switching,
the offsets of which depend on the antenna such that the signals from two antennas in the image sideband do
not correlate (see Chapter 6).
Bands 9 and 10 use double sideband (DSB) receivers, where the IF contains noise and signals from bothsidebands. They only have two outputs, one per polarization. The IF effective bandwidth is 7.5 GHz perpolarization (after passing through the IF processing units), so the total instantaneous receiver bandwidth
is the same as Bands 3–8. However, both sidebands can be simultaneously correlated using 90-degree phaseswitching (see Chapter 6), although this does not remove the noise from the opposite sideband. The effective
system bandwidth available in Bands 9 and 10 is therefore double that of the 2SB receivers (15 GHz).
Each of the ALMA receiver bands is different in several aspects, and the following sections describe theindividual bands in more detail.
Figure 4.3 shows the layout of the ALMA receiver bands in the ALMA cryostat.

Figure 4.3: The layout of the ALMA receiver bands within the ALMA cryostat. Also shown is the orientationof the receiver polarization position angles.

4.2. THE CYCLE 8 RECEIVERS

4.2.1

33

Band 3 ReceiverBand 3 is the lowest frequency band available in Cycle 8, covering 84 to 116 GHz of spectral range (the 3 mm
atmospheric window). The cartridge is fed by a “periscope” pair of ellipsoidal pickoff mirrors located outside thecryostat, which refocus the beam through the cryostat window, allowing for a smaller window diameter (Figure4.4). A single feedhorn feeds an ortho-mode-transducer (OMT) which splits the incoming signal into two linear
orthogonal polarizations and feeds the SIS mixers.

Figure 4.4: Input optics for Band 3, showing the warm pickoff mirrors. The location of the antenna beam fromthe secondary mirror is shown by the solid line, and the Cassegrain focus is shown by the small circle to theupper right.
A block diagram of the Band 3 receiver, including the cold cartridge and warm cartridge assembly, isshown in Figure 4.5. The CCA contains the corrugated feedhorn, OMT, SIS mixers and the low-noise HighElectron Mobility Transistor (HEMT) first IF amplifiers. At room temperature, the WCA includes further IF
amplification and the LO covering 92–108 GHz.
The acceptance criteria for the Band 3 receiver noise performance (Trx ) is <39 K at LO1=104 GHz, and<43 K for any other valid LO setting (SSB Trx ). This includes a 2 K component due to the losses in theexternal warm optics. The achieved median performance is typically somewhat better than this, with Trx ∼37±6 K. The OT assumes Trx =40 K. The atmospheric transmission over most of Band 3 is very high, even witha large PWV (Figure 4.6) which means observations in Band 3 can (and do) take place with up to 10 mm ormore of PWV. The system temperature (Tsys ) shows the expected rise at the higher end due to the edge of an
atmospheric oxygen line (Figure 4.7), so this increase is mostly independent of the PWV.

34

CHAPTER 4. RECEIVERS

Figure 4.5: Block diagram of the Band 3 receiver (left) including CCA (upper) and WCA (lower). Right image
shows a Band 3 CCA. Note the single feedhorn which feeds the OMT, splitting the two polarization signals
for the 2SB mixers. The Band 3 cartridges were constructed in Canada at the National Research Council –Herzberg Institute of Astrophysics (NRC-HIA) in Victoria, British Columbia.

35

4.2. THE CYCLE 8 RECEIVERS

Transmission in Band 3 at Zenith
100
95

Transmission (%)

90
85
80
1st
2nd
3rd
4th
5th
6th
7th

75
70
65
60
85

90

95

100

105

110

115

Frequency (GHz)
Figure 4.6: Band 3 zenith transmission for the first seven octiles of observing conditions at ALMA. The decreaseat the high frequency end is due to the edge of an O2 absorption line at 118.75 GHz.

Band 3 System Temperature at Zenith
140
120

T sys (K)

100
80
60

1st
2nd
3rd
4th
5th
6th
7th

40
20
0
85

90

95

100

105

110

115

Frequency (GHz)
Figure 4.7: Typical system temperature (Tsys ) at zenith for Band 3 for the first seven octiles of observing
conditions at ALMA. Tsys was computed using only the receiver temperature values adopted in the OT andthe atmospheric contribution. No spill-over or background terms have been included. Temperature is given in
Kelvin.

36

4.2.2

CHAPTER 4. RECEIVERS

Band 4 Receiver

The Band 4 receiver covers the 125 to 163 GHz spectral range (the 2 mm atmospheric window). The signal
collected by the telescope is focused to the Band 4 cartridge using a set of warm mirrors (Figure 4.8). A single
feedhorn feeds an OMT which splits the two linear polarizations and feeds the 2SB SIS mixers.

Figure 4.8: Optical layout of the Band 4 receiver. A beam width of 5 times the Gaussian beam size (w) is
indicated in red.

A block diagram of the Band 4 receiver, including the cold cartridge and warm cartridge assembly, is shownin Figure 4.9. The Band 4 CCA contains a feed horn, an OMT as a polarization splitter, 2SB SIS mixer
assemblies, cold IF amplifiers, isolators, and LO frequency doublers. The Radio Frequency (RF) signal is down
converted to 4–8 GHz using a 2SB mixer unit.
The atmospheric transmission in Band 4 is shown in Figure 4.10 for different PWV values. Most observations
in Band 4 will be done with PWV < 5 mm. The specification for Band 4 receiver noise performance (Trx ) is
<51 K over 80% of the band, and <82 K over the whole band (SSB Trx ). The OT assumes 42 K. The resulting
system temperatures (Tsys ) for a range of PWV values are shown in Figure 4.11. The on-array performance ofthe receivers is often more typically ∼40 K over most of the band, so the achieved Tsys may be slightly lower.

4.2. THE CYCLE 8 RECEIVERS

37

Figure 4.9: Block diagram of the Band 4 receiver (left) including CCA (upper) and WCA (lower). Right image
shows a Band 4 CCA. A single feedhorn feeds the OMT, splitting the two polarization signals for the 2SB
SIS mixers. The LO is generated in the WCA, with the final x2 multiplier on the 110 K stage. The Band 4
cartridges were constructed in Japan at the NAOJ Advanced Technology Center (ATC) in Mitaka, Japan.

38

CHAPTER 4. RECEIVERS

Transmission in Band 4 at Zenith
100
95

Transmission (%)

90
85
80
1st
2nd
3rd
4th
5th
6th
7th

75
70
65
60
125

130

135

140

145

150

155

160

Frequency (GHz)
Figure 4.10: Band 4 zenith transmission for the first seven octiles of observing conditions at ALMA.

Band 4 System Temperature at Zenith
90
80
70

T sys (K)

60
50
40

1st
2nd
3rd
4th
5th
6th
7th

30
20
10
0
125

130

135

140

145

150

155

160

Frequency (GHz)
Figure 4.11: System temperature (Tsys ) at zenith for Band 4 for the first seven octiles of observing conditions at
ALMA. Tsys was computed using only the receiver temperature values adopted in the OT and the atmosphericcontribution. No spill-over or background terms have been included. Temperature is given in Kelvin.

4.2. THE CYCLE 8 RECEIVERS

4.2.3

39

Band 5 Receiver

The Band 5 receiver covers the 158 to 211 GHz spectral range (the 1.7 mm atmospheric window), slightly
extended from the original 163–211 GHz coverage. The signal collected by the telescope is focused to the Band
5 cartridge using a set of cold mirrors (Figure 4.12). A single feedhorn feeds an OMT which splits the two linear
polarizations and feeds the 2SB SIS mixers.

Figure 4.12: Optical layout of the Band 5. Placing the mixer assembly along the side of mirror M1 and thestreamlined layout of the IF system are the key to fulfill the requirements on 5wo optical beam clearance at theentrance to the cryostat.
A block diagram of the Band 5 receiver, including the cold cartridge and warm cartridge assembly, is shownin Figure 4.13. The Band 5 CCA contains a feed horn, an OMT as a polarization splitter, 2SB SIS mixer
assemblies, cold IF amplifiers, isolators, and LO frequency doubler. The RF signal is down converted to 4–8
GHz using a 2SB mixer unit.
The atmospheric transmission in Band 5 is shown in Figure 4.14 for different PWV values. The specificationfor Band 5 receiver noise performance (Trx ) is <55 K over 80% of the 163-211 GHz range, and <75 K over thewhole 158 - 211 GHz extended range (SSB Trx ). However, the realized performance of the receivers are often
better than 50 K over the band. The OT assumes 50 K. The resulting system temperatures (Tsys ) are shown in
Figure 4.15.

40

CHAPTER 4. RECEIVERS

Figure 4.13: Block diagram of the Band 5 receiver (left) including CCA (upper) and WCA (lower). Right image
shows a Band 5 CCA. Note the single feedhorn which feeds the OMT, splitting the two polarization signals forthe 2SB SIS mixers. The production design has a room-temperature ×6 multiplier in the WCA, then a ×2 cold
multiplier in the CCA (at 110K). The Band 4 cartridges were constructed in Sweden by the Group for Advanced
Receiver Development (GARD) at Onsala Space Observatory, Chalmers University of Technology, Sweden.

41

4.2. THE CYCLE 8 RECEIVERS

Transmission in Band 5 at Zenith
100

Transmission (%)

80

60

1st
2nd
3rd
4th
5th
6th
7th

40

20

0
165

170

175

180

185

190

195

200

205

210

Frequency (GHz)

Figure 4.14: Band 5 zenith transmission for the first seven octiles of observing conditions at ALMA. The strong
absorption due to H2 O at 183.31 GHz allows for observations at this frequency only when the PWV is < 1mm.
Continuum observations in Band 5 should avoid this part of the band if possible (See Chapter 6 – Spectral
Setups)Band 5 System Temperature at Zenith

300
1st
2nd
3rd
4th
5th
6th
7th

250

T sys (K)

200
150
100
50
0
165

170

175

180

185

190

195

200

205

210

Frequency (GHz)

Figure 4.15: Typical system temperature (Tsys ) at zenith for Band 5 for the first seven octiles of observing
conditions at ALMA. Tsys was computed using only the receiver temperature values adopted in the OT andthe atmospheric contribution. No spill-over or background terms have been included. Temperature is given in
Kelvin.

42

4.2.4

CHAPTER 4. RECEIVERS

Band 6 Receiver

The Band 6 receiver covers the 211 to 275 GHz spectral range (the 1.3 mm atmospheric window). This receiver
has a window with a pair of off-axis ellipsoidal mirrors inside the cryostat (Figure 4.16). A single feedhorn feeds
an OMT which splits the two linear polarizations and feeds the SIS mixers. A block diagram of the Band 6
receiver, including the cold cartridge and warm cartridge assembly, is shown in Figure 4.17.

Figure 4.16: Band 6 cold off-axis ellipsoidal mirrors feeding the single feedhorn. The off-axis beam from thetelescope secondary mirror (shown by the dashed line) feeds directly through the cryostat window, and theCassegrain focus is just inside the inner infrared blocking filter. Note the slightly inclined inner window,
designed to minimize standing waves.
The Band 6 allowed IF frequency range was 5–10 GHz, but has been extended further since Cycle 6 to allow
for multiple simultaneous line observations with more bandwidth per spw2 ; it now covers the range 4.5–10.0
GHz. Although there is up to ∼10-20% excess receiver noise below 5.5 GHz due to LO1 (but the increase of Tsysis less), the CO multi-transition setup is still considerably more efficient than observing each line separately. It
is recommended that for continuum observations, the IF range 6–10 GHz is still used. Also, it should be notedthat the full range 4.5–10 GHz cannot be completely sampled because of the limited 4 GHz width of the two
basebands per polarization.
The atmospheric transmission in Band 6 is shown in Figure 4.18 for different PWV values. Most of thenarrow absorption lines are from ozone. The specification for Band 6 receiver noise performance (Trx ) is <83
K over 80% of the band, and <136 K over the whole band (SSB Trx ). The achieved on-array results are
considerably better, typically ∼40–50 K over most of the band. The OT assumes 50 K. The resulting systemtemperatures (Tsys ) for different PWV values are shown in Figure 4.19.

2 Specifically, the 12 CO/13 CO/C18 O J =2–1 combination at 230.538/220.398/219.560 GHz, which has a minimum separation of
10.14 GHz. Since Cycle 6, the lower end of the allowed IF range has been extended to 4.5 GHz in order to cover all three lines withbroader spws.

4.2. THE CYCLE 8 RECEIVERS

43

Figure 4.17: Band 6 receiver block diagram, and (right) image of cartridge. Note the OMT used to split thepolarizations feeding the two 2SB mixers. The LO around 80 GHz requires an extra ×3 multiplier inside thecryostat. Note that the IF output range has been extended to cover 4.5–10 GHz; the range shown is the one
recommended for continuum observations (see text). The Band 6 cartridges were built in the United States at
the NRAO Technology Center in Charlottesville, Virginia.

44

CHAPTER 4. RECEIVERS

Transmission in Band 6 at Zenith
100
95

Transmission (%)

90
85
80
1st
2nd
3rd
4th
5th
6th
7th

75
70
65
60
220

230

240

250

260

270

Frequency (GHz)
Figure 4.18: Band 6 zenith transmission for the first seven octiles of observing conditions at ALMA. Most of
the narrow absorption lines are from ozone.

Band 6 System Temperature at Zenith

300
250

T sys (K)

200

1st
2nd
3rd
4th
5th
6th
7th

150
100
50
0
220

230

240

250

260

270

Frequency (GHz)
Figure 4.19: Typical system temperature (Tsys ) at zenith for Band 6 for the first seven octiles of observing
conditions at ALMA, based on measured values of the receiver temperatures. Tsys was computed using only thereceiver temperature values adopted in the OT and the atmospheric contribution. No spill-over or backgroundterms have been included. Temperature is given in Kelvin.

4.2. THE CYCLE 8 RECEIVERS

4.2.5

45

Band 7 Receiver

The Band 7 receiver covers the 275 to 373 GHz spectral range (the 0.85 mm atmospheric window). It has asimilar cold optics design as Band 6, but uses a wire-grid polarization splitter instead of an OMT (Figure 4.20).
A block diagram of the Band 7 receiver, including the cold cartridge and warm cartridge assembly, is shown in
Figure 4.21.

Figure 4.20: Band 7 cold optics arrangement, showing the off-axis ellipsoidal mirrors and the polarization
splitter wire grid.
The atmospheric transmission in Band 7 is shown in Figure 4.22 for different PWV values. The original
specification of the Band 7 receiver noise temperature was Trx <147 K over 80% of the range and <219 K over
the whole tuning range, except at the upper end of the band (370-373 GHz), where the specifications were <300
K (SSB Trx ). However, the performance of the receiver as measured in the lab and on the array is considerably
better than this, with typically 65 K achieved, in mid-band. The OT assumes 72 K over the whole band.
The resulting system temperatures (Tsys ) for different PWV values are shown in Figure 4.23. Note that theatmospheric transmission (and hence Tsys ) at frequencies below 300 GHz is considerably better than that of the
top half of Band 7; in that respect the performance is closer to that of Band 6. Also to maximise continuum
sensitivity, the deep water absorption lines around 325 GHz should be avoided if possible.

46

CHAPTER 4. RECEIVERS

Figure 4.21: Band 7 front-end receiver block diagram, and (right) annotated image of the Band 7 cartridge.
Note the polarization-splitting grid and LO injection in the cold optics above the mixers. The Band 7 cartridges
were built in France at the Institut de Radio Astronomie Millimétrique (IRAM) in Grenoble, France.

47

4.2. THE CYCLE 8 RECEIVERS

Transmission in Band 7 at Zenith
100

Transmission (%)

80

60

1st
2nd
3rd
4th
5th
6th
7th

40

20

0
280

290

300

310

320

330

340

350

360

370

Frequency (GHz)
Figure 4.22: Band 7 atmospheric zenith transmission for the first seven octiles of observing conditions at ALMA.
The deep atmospheric absorption at 325 GHz is due to water, and the narrower feature at 369 GHz is due tooxygen.

Band 7 System Temperature at Zenith

500
1st
2nd
3rd
4th
5th
6th
7th

T sys (K)

400

300

200

100

0
280

290

300

310

320

330

340

350

360

370

Frequency (GHz)
Figure 4.23: Typical Tsys at zenith for Band 7 for the first seven octiles of observing conditions at ALMA. Tsys
was computed using only the receiver temperature values adopted in the OT and the atmospheric contribution.
No spill-over or background terms have been included. Temperature is given in Kelvin.

48

4.2.6

CHAPTER 4. RECEIVERS

Band 8 Receiver

The Band 8 receiver covers the 385 to 500 GHz spectral range (the 650 µm atmospheric window). The cryogenic
optics of this receiver adopts a single mirror to couple a feed horn in front of an SIS mixer block to the subreflector. A single feedhorn feeds an OMT which splits the two linear polarizations and feeds the 2SB SIS mixers(Figure 4.24).

Figure 4.24: Optical layout of the Band 8 receiver.
A block diagram of the Band 8 receiver, including the cold cartridge and warm cartridge assembly, is shownin Figure 4.25. The Band 8 CCA consists of a cold optics, a feed horn, an OMT, 2SB SIS mixers assemblies,
cold IF amplifiers, isolators, and LO frequency sextuplers.
The atmospheric transmission in Band 8 is shown in Figure 4.26 for different PWV values. The specificationof the Band 8 receiver noise temperature is Trx <196 K over 80% of the range and <292 K over the whole tuning
range (SSB Trx ). However, the performance of the receiver as measured in the lab and on-array is considerably
better than this, with typical values of 70-120 K. The OT assumes 135 K. The resulting system temperatures(Tsys ) for different PWV values are shown in Figure 4.27. Note that transmission in the lower part of the bandis almost as high as Band 7, whereas at the high frequency end of the band (e.g. around the CI line at 492
GHz) the transmission is as low as the center of Band 9.

4.2. THE CYCLE 8 RECEIVERS

49

Figure 4.25: Block diagram of the Band 8 receiver (left) including CCA (upper) and WCA (lower). Right image
shows a Band 8 CCA. Note the single feedhorn which feeds the OMT, splitting the two polarization signals
for the 2SB SIS mixers. The Band 8 cartridges were constructed in Japan at the NAOJ Advanced Technology
Center (ATC) in Mitaka, Japan.

50

CHAPTER 4. RECEIVERS

Transmission in Band 8 at Zenith
100
1st
2nd
3rd
4th
5th
6th
7th

Transmission (%)

80

60

40

20

0
390

400

410

420

430

440

450

460

470

480

490

500

Frequency (GHz)
Figure 4.26: Band 8 atmospheric zenith transmission for the first seven octiles of observing conditions at ALMA.
The atmosphere in the Band 8 frequency range has some deep absorption features due to water and oxygen.

Band 8 System Temperature at Zenith

3000

1st
2nd
3rd
4th
5th
6th
7th

2500

T sys (K)

2000
1500
1000
500
0
390

400

410

420

430

440

450

460

470

480

490

500

Frequency (GHz)

Figure 4.27: Typical Tsys at zenith for Band 8 for the first seven octiles of observing conditions at ALMA. Notethat some of the values for Tsys in the worst octiles, which should never be used for high-frequency observations,are off scale in this plot. Tsys was computed using only the receiver temperature values adopted in the OT andthe atmospheric contribution. No spill-over or background terms have been included. Temperature is given in
Kelvin.

4.2. THE CYCLE 8 RECEIVERS

4.2.7

51

Band 9 Receiver

The Band 9 receiver covers the 602 to 720 GHz spectral range (the 450 µm atmospheric window). It uses awire grid in order to separate the two orthogonal polarizations, as well as to provide the LO injection scheme(Figure 4.28).

Figure 4.28: Basic Band 9 optics layout. The signal path is symmetrical for the vertical polarization (P0) andthe horizontal polarization (P1). For P1 the path is as follows: the telescope focal point (FP) is followed bymirror M3, wire grid polarization splitter, mirror M4, a beam splitter for LO insertion, and finally the mixer
horn U1. For P0 the signal follows from FP to the same mirror M3 and then, reflected by the grid, comes tomirror M4, a beam splitter, and mixer horn U10 .
The mixers are double sideband (DSB), and therefore additional techniques must be employed during theobservations to either separate the sidebands or reject the unwanted sideband. LO offsetting can be used toreject one of the two sidebands, which can be chosen independently for each spectral window (spw). Note that
LO offsetting does not reject the noise from the unwanted sideband, it simply moves any correlated signal to ahigh fringe rate so that the signal is smeared over a larger bandwidth increasing noise incoherently. Since Cycle
6, 90-degree phase switching is used to correlate both USB and LSB simultaneously (see Chapter 6). The IF
bandwidth in this receiver is 8 GHz per polarization (7.5 GHz effective bandwidth after the IF Processor units,
see Section 6.4), covering 4-12 GHz. A block diagram of the Band 9 receiver, including the cold cartridge andwarm cartridge assembly, is shown in Figure 4.29.
The Band 9 atmospheric transmission is strongly dependent on the PWV, as illustrated in Figure 4.30,
where only the lower values of PWV have significant transmission. The specifications for the receiver are Trx<175 K over 80% of the band and <261 K over all the band. However, the performance is considerably better
than this, with engineering and typical on-array values for Trx of 65–120 K. The OT assumes 105 K. Figure 4.31
shows the expected Tsys for different PWV values using the given OT default expected receiver noise values.
However, the achieved Tsys is extremely dependent on the line-of-sight PWV. Phase stability also limits whenobservations can be made, therefore, most observations in Band 9 are done at night and early morning (andmore commonly during austral winter). As well as having a lower atmospheric transmission and a less stable

52

CHAPTER 4. RECEIVERS

Figure 4.29: Block diagram of Band 9 cartridge (left) and a schematic image (right). Note that there are only
two IF outputs, one from each polarization in this DSB receiver. The extra Faraday rotation mirror in the LO
system is part of the ALMA fiber optic Line Length Corrector (LLC) system (see Appendix B.3.3), and meansthat the Band 9 receiver must be available on all the antennas for this to work. The Band 9 receiver was built
in the Netherlands at the Nederlandse Onderzoekschool voor Astronomie (NOVA) in Leiden, Netherlands.

53

4.2. THE CYCLE 8 RECEIVERS

atmosphere, Band 9 observing provides additional challenges, including finding sufficiently bright calibrators(most QSOs are relatively faint at this frequency), requiring accurate pointing for the relatively small primarybeam (although the actual pointing is done in Band 6), and the need for the highest level of stability in the restof the system.

Transmission in Band 9 at Zenith
100
1st
2nd
3rd
4th
5th
6th
7th

Transmission (%)

80

60

40

20

0
610

620

630

640

650

660

670

680

690

700

710

720

Frequency (GHz)
Figure 4.30: Band 9 zenith transmission for the first seven octiles of observing conditions at ALMA. Most of
the band is affected by the wings of pressure-broadened H2 O at 620 GHz.
Band 9 System Temperature at Zenith

5000

T sys (K)

4000

3000

1st
2nd
3rd
4th
5th
6th
7th

2000

1000

0
610

620

630

640

650

660

670

680

690

700

710

720

Frequency (GHz)

Figure 4.31: Typical Tsys at zenith for Band 9 for the first seven octiles of observing conditions at ALMA. Notethat the values for Tsys in the worst octiles, which should never be used for high-frequency observations, areoff scale in this plot. Tsys was computed using only the receiver temperature values adopted in the OT andthe atmospheric contribution. No spill-over or background terms have been included. Temperature is given in
Kelvin.

54

4.2.8

CHAPTER 4. RECEIVERS

Band 10 Receiver

The Band 10 receiver covers the 787 to 950 GHz spectral range (the 350 µm atmospheric window). Band 10 isthe highest frequency receiver of the ten bands envisioned for the ALMA front-end system. The developmentof the Band 10 receiver was extremely difficult and faced many technical challenges from its material selection.
Niobium (Nb) superconducting tuning circuits, which are used in other ALMA receiver bands, cannot be used
for Band 10 SIS mixers due to large losses from pair-breaking above a superconducting gap frequency of about
700 GHz. Therefore, niobium-titanium-nitride (NbTiN) with a critical temperature of about 15 K, has beenutilized in the tuning circuit of Band 10 mixers. The Band 10 Nb/AlOx/Nb tunnel junctions with NbTiNbased tuning circuitry achieved ALMA requirements and the best DSB receiver noise temperature was 125 K,
corresponding to about 3 times the quantum limit for 4 K operation.
It uses a wire grid in order to separate the two orthogonal polarizations, as well as to provide the LO injection
scheme (Figure 4.32). The mixers are double sideband (DSB), and therefore LO offsetting can be used to reject
one of the two sidebands. As in the case of Band 9, 90-degree phase switching is used to correlate both USB
and LSB simultaneously (see Chapter 6). The IF bandwidth in this receiver is 8 GHz per polarization (7.5 GHz
effective bandwidth after the IF Processor units, see Section 6.4), covering 4–12 GHz. A block diagram of theBand 10 receiver, including the cold cartridge and warm cartridge assembly, is shown in Figure 4.33.

Figure 4.32: Schematic of ALMA Band 10 optics. ALMA Band 10 optics are composed of two ellipticalmirrors, M1 and M2, a wire grid and two corrugated horns. The wire grid is used to separate the two linear
polarizations, P0 and P1, and it is located after the two elliptical mirrors to minimize the number of opticalcomponents required.
The Band 10 atmospheric transmission is significantly dependent on the PWV, as illustrated in Figure 4.34
for different values of PWV. The specifications for this receiver are Trx <230 K over 80% of the band and <344
K over all the band. Typical on-array Trx values are 175–275 K. The OT assumes 230 K. Figure 4.35 showsthe expected Tsys for 0.472 mm of PWV, over most of the band given the OT-assumed receiver noise. Phasestability also limits when observations can be made, therefore, most observations in Band 10 will generally only
be performed at night and early morning, when the sky is most stable. Also the antenna surface accuracy has asignificant effect on the aperture efficiency at this high-frequency band; improvements to the surface accuracyof the 12-m antennas during 2017 has doubled the aperture efficiencies in Band 10. As well as having a lower
atmospheric transmission and a less stable atmosphere, Band 10 observing provides the most challenges forobserving, including finding sufficiently bright calibrators (most QSOs are relatively faint at this frequency),
requiring accurate pointing and focus for the relatively small primary beam (although pointing and focus isnormally done in lower Bands), and the need for the highest level of stability in the rest of the system.

4.2. THE CYCLE 8 RECEIVERS

55

Figure 4.33: Block diagram of Band 10 cartridge (left) and a schematic image (right). Note that there are only
two IF outputs, one from each polarization in this DSB receiver. The Band 10 cartridges were constructed inJapan at the NAOJ Advanced Technology Center (ATC) in Mitaka, Japan.

56

CHAPTER 4. RECEIVERS

Transmission in Band 10 at Zenith
100
1st
2nd
3rd
4th
5th
6th
7th

Transmission (%)

80

60

40

20

0
800

850

900

950

Frequency (GHz)
Figure 4.34: Band 10 zenith transmission for the first seven octiles of observing conditions at ALMA. Transmission of most of the band is affected by the wings of pressure-broadened lines of H2 O at 841 and 916 GHz.

Band 10 System Temperature at Zenith

5000

T sys (K)

4000

3000

1st
2nd
3rd
4th
5th
6th
7th

2000

1000

0
800

850

900

950

Frequency (GHz)

Figure 4.35: Typical Tsys at zenith with Band 10 for the first seven octiles of observing conditions at ALMA.
Note that the values for Tsys in the worst octiles, which should never be used for high-frequency observations,are off scale in this plot. Tsys was computed using only the receiver temperature values adopted in the OT andthe atmospheric contribution. No spill-over or background terms have been included. Temperature is given in
Kelvin.

Chapter 5

The Correlators
A correlator can be viewed as the virtual focal plane of an interferometer array where all voltage-based signals
from all individual antennas are processed to derive both the cross-correlation products from all independent
antenna pairs and the auto-correlation function of each antenna. It delivers complex fringe visibilities thatare used to synthesize astronomical images after calibrations in amplitude and phase,. Another function isspectroscopy by applying Fourier transform to the correlation products or the voltage-based signals. A correlator
tracks delay and phase to adjust the wavefronts of received signals in order to maintain the coherence of thecomplex visibilities. Walsh-switching modulations for sideband separation (90◦ phase switching) and spurioussignal suppression (180◦ phase switching) are demodulated in the correlator.1
All signals2 received by ALMA antennas are processed in one of two correlators: the 64-input Correlator(also known as the Baseline Correlator or BLC) and the ACA Correlator. The 64-input Correlator is usedprimarily for the main 12-m Array, while the ACA Correlator is used for the Morita Array comprised of the
ACA 7-m Array and the Total Power Array (i.e. single-dish), respectively3 . Both correlators run simultaneously
and independently. Thus, while the 12-m Array observes an object using the 64-input Correlator, the ACA
Correlator can work with the 7-m Array and/or the Total Power Array observing either the same or a different
object via a sub-array capability.
Celestial signals received by the antennas are down converted to lower frequency bands using a set of Local
Oscillators (LOs) and mixers as described in Appendix B. The outputs from the IF system form four BaseBands (BBs), each covering a bandwidth of 2 GHz in two orthogonal linear polarizations. These analog BB
signals are sampled at the sampling frequency of 4 GHz and quantized with eight quantization levels (3 bits per
sample) in digitizers, and then transferred via fiberoptic cable to one of the two correlators.
Both correlators generate auto-correlation and cross-correlation products at the same time. The autocorrelation is used not only for spectroscopic TP-Array observations but also for normalization of cross power
spectra and measurements of system noise temperatures (see Section 10.4.2). The cross-correlations are used
for interferometry with the 12-m Array and the ACA 7-m Array, and also for pointing and focus calibrations
for all Arrays.
This chapter addresses capabilities of the correlators to be offered for Cycle 8 observations. The specificationsof the correlators determine a lot of observational performance such as bandwidth, spectral resolution, time
resolution, and polarimetry. The phase tracking performance provides coherence and improves phase stability
in correlated data delivered to users. Imperfect correction for the non-linear response in the correlators invokes
systematic errors in complex visibilities. The response of digital signal processing is also presented in thischapter.
1 Some of these features can be employed outside the correlator. In the case of the ALMA correlators, the phase tracking istaken in the LO1 and LO2. The 180◦ phase switching is modulated in the LO1 and demodulated in the DTS transmitter after
digitization. See also Sections 5.5.4, B.4.4, and also Emerson 2005, ALMA memo No. 537.
2 Except total power (TP) continuum observations for solar observations (see Section 8.10.3) that employ square-law detectors(SQLDs).
3 Crossbar switching allows for some flexibility in this arrangement.

58

CHAPTER 5. THE CORRELATORS

Figure 5.1: The ALMA 64-input Correlator. This view shows lights glowing on some of the racks of thecorrelator in the ALMA Array Operations Site Technical Building and shows one of four quadrants of thecorrelator. Credit: ALMA (ESO/NAOJ/NRAO), S. Argandoña

5.1

The 64-input Correlator

The 64-input Correlator (Figure 5.1) employs a hybrid design, also known as the FXF4 system (Escoffier et
al. 2007, A&A 462, 801), that increases by a factor of 32 the spectral resolution of its traditional lag (XF)
part. It operates in two basic modes, Time Division Mode (TDM) – equivalent to an XF correlator with awide bandwidth and a coarse spectral resolution for mainly continuum observations, and Frequency Division
Mode (FDM) with fine spectral resolutions for spectral-line observations. A simplified overview diagram of
the 64-input Correlator is shown in Figure 5.2. It consists of four quadrants, all of which are available for
Cycle 8. Each quadrant can handle a 2 GHz dual-polarization BB for up to 64 antennas5 . The full set of four
quadrants is capable of accepting four BBs to cover a total 8 GHz bandwidth per polarization, that is 16 GHzof instantaneous bandwidth.

5.1.1

TDM mode

TDM is mostly used for continuum observations. Its simplicity, compared with FDM, offers advantages of alower data rate and better linearity. Therefore, it is used for standard setups such as pointing, focus, delay
calibration, system temperature measurements and sideband ratio measurements. TDM provides also a higher
time resolution capability as described in Section 5.5.3. The full 2 GHz BB is directly sent to the correlator bypassing the Tunable Filter Banks (TFBs). The correlator cuts off the least significant bit to reduce quantizationlevels from 3- to 2-bits per sample (Section 5.3).
The TDM mode provides a spectral window (spw)6 that consists of up to 256/Npol channels per BB, where
Npol is the number of polarization products per BB7 . As the full 2000 MHz BB is covered, this requires sometruncation of the band-edge channels in offline data processing yielding 1875 MHz of usable bandwidth – see
Section 6.4.
4 F, X and F stand for filtering, correlation and Fourier transform, respectively.
5 Nant (Nant − 1) = 2016 baselines and 64 auto-correlations for N
ant = 64.
2
6 An spw is a continuous spectrum composed of uniformly spaced frequency channels.

See also Chapter 6 about the relation
between BB and spw.
7N
pol = 2 for standard Stokes-I observations that employ XX and Y Y products, and Npol = 4 for full-Stokes observations.

59

5.1. THE 64-INPUT CORRELATOR

One quadrant to process

At antenna
POL 2

4 GHz Digitizer
4 GHz Digitizer
4 GHz Digitizer
4 GHz Digitizer
4 GHz Digitizer
4 GHz Digitizer
4 GHz Digitizer

DATA
Transmitter
DATA
Transmitter
DATA
Transmitter

12:1 Optical Splitter

4 GHz Digitizer

12:1 Optical Combiner

POL 1

DATA
Transmitter

Digitizes analog signals andapplies ultra fine delay

DATA
ReceiverTunable Filter Bank Card

DATA
ReceiverTunable Filter Bank Card

DATA
ReceiverTunable Filter Bank Card

DATA
ReceiverTunable Filter Bank Card

Three optic
carriers

Three optic
carriers

Tunable Filter Bank Card

Tunable Filter Bank Card

Tunable Filter Bank Card

Tunable Filter Bank Card
Fine delay andselects bandwidth

Station Card

Station Card

32-parallel outputs x 2-bits
per sample x 2-polarizaitons

Correlator station electronics one baseband, two polarizations

Station Card

Station Card

Bulk delay, re-orders
and packetizes samples

Correlator baseline electronics

32-parallel outputs x 2-bits
per sample x 2-polarizaitons
Antenna 0

Plane 31
Plane 2

Plane 1

Plane 032-parallel outputs x 2-bits
per sample x 2-polarizaitons
Antenna 63

Horizontal drive to correlator matrix

Correlator array(one of 4 quadrants in system shown)Long term
accumulator(LTA)

LTA-addertree

Intra-quadrant
results cross bar
and real timecomputerinterface

Real timecomputersystem

4 PCB
Vertical drive to correlator matrix

Figure 5.2: Overview diagram of the ALMA digitizers, data transmission system and 64-input Correlator(Escoffier et al. 2007, A&A 462, 801). The digitized data from the individual BBs are transferred to the
Tunable Filter Banks (TFBs) and station cards (top right) for the parallelization and processing required oneach antenna data stream. The correlator array (lower half) produces auto-correlations on the main diagonal
and cross-correlations elsewhere in the correlator matrix. The correlations are then integrated in the Long-Term
Accumulators (LTAs, lower right).

5.1.2

FDM mode

FDM is primarily used for spectral-line observations that require a spectral resolution higher than that of TDM.
Each 2-GHz BB in an antenna is processed in a TFB card, where digital filtering, a digital mixer and LO (LO4)
are implemented in a Field Programmable Gate Array (FPGA). A TFB consists of 32 independent 62.5-MHz
bandpass filters (sub-bands). To avoid edge artifacts, sub-band center frequencies are set such that their skirts
overlap and the effective bandwidth is thus reduced by a factor of 15/16 that yields 58.59375 MHz per subband. The correlator software then combines together contiguous sub-bands to output a seamless cross power
15
× 8192/Npol channels.
spectrum to form an spw with as many as 16
The number of channels in each spw can be reduced by averaging 2, 4, 8, or 16 channels into one toaccommodate the maximum data rate. Table 5.1 lists the spectral setups for Stokes I (Npol = 2) observations.
The number of valid sub-bands to form an spw is selectable from 32, 16, 8, 4, 2, or 1. That is, spw bandwidthsof 1875, 937.5, 468.75, 234.375, 117.1875, and 58.59375 MHz, respectively. It is possible to have multiple (upto 4) spws in the same BB. While different spectral setups can be set for spws in different BBs, all of spws in
the same BB must have the same channel spacing.
The center frequency of each spw can be tuned over the 2 GHz-wide BB using the digital LO (LO4) in the
TFB card. However, the edges of the full bandwidth of the sub-bands cannot fall outside the 2 GHz BB range,
and the frequency tuning is made in steps of 30.5 kHz set by the frequency resolution of the TFB digital mixer.

60

CHAPTER 5. THE CORRELATORS

See also Section 5.5.2 for details about spectral setting.
Correlator/ ModeBandwidth(MHz)

Num. of ch. per pol.
(in dual-pol.)Ch. spacing(MHz)

BLC/TDM
BLC/FDM
BLC/FDM
BLC/FDM
BLC/FDM
BLC/FDM
BLC/FDM
ACA
ACA
ACA
ACA
ACA
ACA

2000∗
1875
938
469
234
117
58.6
2000∗
1000
500
250
125
62.5

128
3840
3840
3840
3840
3840
3840
4096
4096
4096
4096
4096
4096

15.625
0.488
0.244
0.122
0.061
0.03050.0153
0.488
0.244
0.122
0.061
0.03050.0153

Table 5.1: Correlator modes and spectral performances per BB for dual parallel polarization (XX and YY).
∗
Usable bandwidth excluding band edges is ∼ 1875 MHz.

5.1.3

Correlation and Realtime Processing

The correlation cards perform the multiply-and-add operations to produce the correlation functions at a clock
rate of 125 MHz (4 GHz samples demultiplexed by 32). Four quadrants handle four BBs. A quadrant of
the correlator consists of 32 planes of 64 × 64 256-lag correlator circuits, and it yields auto-correlations andcross-correlations for 64 antennas. In FDM there are always 8192 spectral points per BB for both X andY polarizations, and higher spectral resolutions can be achieved by reducing the number of sub-bands (i.e.
bandwidth) used to form an spw. It is possible to set different modes in different quadrants (i.e. BBs);for example, while one BB is set in TDM, other BBs can be set in FDM. For spectral setup details, see
Chapter 6. The Long Term Accumulator (LTA; see Figure 5.2) takes short 1 ms or 16 ms integrations fromthe correlator circuits and provides longer term integration. Further time averaging through multiple dump
intervals is performed in the Correlator Data Processor (CDP) computers. See also Section 5.5.3 about time
resolution. Section 5.5 describes in detail the correlator data processing.

5.2

The ACA Correlator

The ACA Correlator (Figure 5.4) is dedicated to observations with the Atacama Compact Array that consistsof the 7-m Array with twelve 7-m antennas and the Total Power Array (TP Array) with four 12-m antennas.
The ACA Correlator is based on the FX8 design in which the incoming time-domain data stream is converted
into frequency-domain spectrum via an FFT (Fast Fourier Transform) module before cross multiplication toform the power spectrum. The FFT part always accepts a full 2 GHz bandwidth and outputs 524288 channel
spectra with a frequency resolution of 3.815 kHz (Figure 5.6). This design enables flexible spectral handlingas shown in Figure 5.3 producing multiple spws with different channel spacings by averaging multiple channels(spectral binning). Since the spectral resolution function is different from that of the 64-input Correlator, afrequency profile synthesis (FPS) is performed in the Correlator Data Processor computer so that the outputsof both correlators are matched (Kamazaki et al. 2008, ALMA Memo 580).
A detailed diagram of the signal processing in the ACA Correlator itself is shown in Figure 5.3. Similar to
the 64-input Correlator, each quadrant of the ACA Correlator processes a BB pair; so the complete system canprocess up to sixteen antennas independently from the 64-input Correlator.
8 F and X stand for Fourier transform and multiplication, respectively.

5.2. THE ACA CORRELATOR

61

Figure 5.3: Block diagram of the ACA Correlator. One of four quadrants is shown. Time-series data from eachantenna are divided in the time domain and processed in an 8-way parallel stream. FFT is performed in an
FPGA delivering signals in the spectral domain which are then multiplied. The auto and cross-correlation data
are then accumulated in time, and the parallel streams averaged together in the Correlation and Integration
Processor (CIP) module. The correlated spectra are then fed to the ACA-CDP for further accumulation andprocessing.
After receiving the digitized BB signals in the Digital Transmission System Receiver (DTS-Rx), the DTSRx and FFT Processor (DFP) modules compensate for geometrical delays between antennas and perform the
220 -point FFT that produces a 219 -point complex spectrum9 (hereafter, voltage spectrum) for every BB per
9 220 -point FFT produces a 220 -point complex voltage spectrum of a double sideband including the image sideband that will bediscarded.

62

CHAPTER 5. THE CORRELATORS

Figure 5.4: Two quadrants of the ALMA Compact Array (ACA) correlator installed in the ACA correlator
room. Credit : ALMA (ESO/NAOJ/NRAO), S. Okumura
antenna per polarization, with a channel separation of 3.815 kHz (= 2 GHz ÷ 524288 channels) in a 16-bit
complex integer form. The 16-bit complex voltage spectra are re-quantized into a 4-bit complex integer andsent to the Correlation and Integration Processor (CIP) modules.
The CIP module trims the required frequency range and multiplies the antenna-based voltage spectra to
generate baseline-based cross power spectra that correspond to cross-correlations. Antenna-based power spectra,
corresponding to auto-correlation, are also generated in the same way. Cross-polarization power spectra can be
optionally produced. The (cross) power spectra are channel-averaged and time-integrated as designated before
they are sent to the ACA-CDP computers in the Computing subsystem through optical fibers.
The ACA-CDP performs further spectral processing such as non-linearity correction (see Section 5.6.2), FPS
and temporal integration, before data are sent to the archive.
The overall hardware design of the ACA Correlator is shown in Figure 5.5. The ACA Correlator is equippedwith high-speed FPGA chips rather than Application Specific Integrated Circuit (ASIC) chips used in the
64-input Correlator. For technical details, see Kamazaki et al. 2012, PASJ 64, 29.

5.3

Digitizers

A digitizer is a device converting continuous voltage waveforms into quantized voltage levels, sampled at discretetimings, and encoded in a digital format. The ALMA digitizers are located in the antenna back ends (BEs)where they convert BB signals into the ALMA digital format (Recoquillon et al. 2005, ALMA Memo No.
532). The Digital Transmitter (DTX) on the BE transfers the digital signals through optical fibers to the data
receivers (DRXs) in the correlators.
Each antenna BE is equipped with 8 digitizers to accept 8 signal streams of 4 BBs × 2 polarizations.
To sample and quantize the 2-4 GHz BB signals, the ALMA digitizer samples at the Nyquist frequency of
4 GHz and uses 8 quantization voltage levels (3-bit per sample). However, the 64-input Correlator reduces
the quantization levels to 4 (2-bit). Signals through the TFBs are re-quantized in 4-bit before the correlation
process. The ACA Correlator handles 3-bit digital form in FFT and the spectrum is requantized in 4-bit before
cross multiplication. These quantization processes affect the sensitivity and linearity in the power spectra.
Compared to an ideal analog system, the 64-input correlator has a sensitivity loss of 12% (TDM) or 15.5%(FDM) due to the quantization including re-quantization. Similarly the ACA Correlator has a 4.8% sensitivity

5.4. OFFLINE WVR CORRECTION

63

Figure 5.5: Overview diagram of the ACA Correlator. The signals from the BackEnd Subsystem are processedin the DFP and CIP modules and the auto- and cross-correlation products are sent to the Computing Subsystem(see text and Figure 5.3 for details of these). The modules are controlled by the Monitor and Control Interface(MCI), which communicates with the correlator control computer (ACA-CCC). The DTS-Rx is connected withthe monitor and control computer (ACA-DMC) for the monitor and control compatibility with the 64-input
Correlator.

Figure 5.6: Data capture sequence of the ACA Correlator. The design enables output with multiple spws withdifferent channel spacings by averaging multiple channels (spectral binning). The frequency range of an spw isselectable from the 524288-point (512K) spectra across 2 GHz bandwidth.

loss. These numbers suppose that the digitizer input power is in the expected range and that the digitizer
adjustments are optimal. See also Section 5.6.1 about the quantization loss.

5.4

Offline WVR Correction

The Water Vapor Radiometer (WVR; see Appendix A.6 for technical description) is a device mounted on each of
the 12-m antennas to measure the amount of Precipitable Water Vapor (PWV) in order to correct for pathlength
fluctuations in the troposphere.
While the WVR data were previously recorded together with the visibilities, since Cycle 7 the online software
will only produce uncorrected visibilities, and the WVR correction will be applied offline in the CASA pipeline.
Recording both WVR corrected and uncorrected results impacted data rates and storage, and producing only
one data stream allows for shorter integration times.
The WVR correction will not be applied in the ACA Correlator because the array is so compact that PWVfluctuation is not significant.

64

CHAPTER 5. THE CORRELATORS

5.5

Capabilities of the Correlators

5.5.1

Polarization

Since Cycle 8, ALMA adds the full-polarization capability with the 7-m array as well as with the 12-m array.
However, polarimetry with the TP Array remain unavailable for Cycle 8.
Both correlators are capable to produce correlation pairs of hXX ∗ i, hXY ∗ i, hY X ∗ i, and hY Y ∗ i where X andY stand for two linear orthogonal polarization components. These correlations relate to the Stokes visibilitiesof I, Q, U , and V as





hXX ∗ i /(GX G∗X )
I
1
0
0
1
 Q  1  cos 2ψ − sin 2ψ − sin 2ψ − cos 2ψ   hXY ∗ i /(GX G∗ ) 
Y
,




(5.1)
 U  = 2  sin 2ψ
cos 2ψ
cos 2ψ
− sin 2ψ   hY X ∗ i /(GY G∗X ) VhY Y ∗ i /(GY G∗Y )0−ii0where GX and GY stand for complex antenna-based gains in X and Y polarizations and ψ is the parallactic
angle. This formulation doesn’t include cross talk, also known as ‘D-terms’, whose calibration will be discussed
in Chapter 10.
Both correlators form cross-polarization products of hXY ∗ i and hY X ∗ i only when polarimetry is required.
This is obtained at the expense of less spectral channels.

5.5.2

Spectral Setup

Both correlators are capable of accepting eight 2 GHz bandwidth signal streams consisting of four BBs and twopolarizations, and to be configured to have multiple spws within a BB.
Each spw yields a continuous spectrum composed of uniformly spaced spectral channels. Table 5.1 summarizes the maximum number of spectral channels and the channel spacing of the correlators in dual linear
polarization mode (XX and Y Y ). The maximum number of channels per spw would be doubled (and the channel spacing halved) for single polarization (XX) observations. Conversely, for full polarization observations(XX, XY , Y X, and Y Y ), the maximum number of channels is halved and the channel spacing correspondingly doubled as compared to Table 5.1. The bandwidth and the number of channels available from the ACA
correlator are identical through the application of FPS (Frequency Profile Synthesis). Note that the channel
spacing is not the same as the spectral resolution because of the effects of the applied weighting function, as
shown in Figure 5.7. See also Chapter 6 about multiple-spw setup.
The spectral profile which the correlators output is a convolution of the true spectrum with the spectral
resolution function shown in Figure 5.7. The spectral resolution function is given by the Fourier transform of
the weighting function applied to the correlation function in the lag domain. The spectral resolution is often
characterized by the FWHM (full width at half maximum) of the spectral resolution function.
Uniform weighting in the lag domain results in the sinc function with the FWHM of 1.21× the channel spacing
and yields spectral sidelobes. This ‘ringing’ phenomenon affects the spectra when a narrow line, interference
spike, or strong edge channels are present. Alternative weighting functions10 are applicable to suppress the
spectral sidelobes as shown in Figure 5.7. Note that the sidelobes do not matter in most of astronomical
observations where a line profile spreads over several spectral channels. The choice of a weighting function is atrade off between resolutions and sidelobes. The default weighting function is the Hanning function, which gives
the spectral resolution of 2 × the channel spacing and the maximum sidelobe level of −2.6%. A proposer may
request another weighting function if scientifically necessary and technically justified through the OT during
the Phase 2 validation stage. The proposer must contact their supporting ARC to make this change at Phase2.
Spectral channel averaging is available to bin or average spectral channels in the CDP. Channels can beaveraged together; factors of N = 2, 4, 8, or 16 are available. The main purpose is to reduce the data rate to
the archive and the total data volume. It also provides a broader spread of correlator functionality between
the current TDM (which has only 128 channels in dual polarization) and full FDM (with 3840 channels in dual
polarization mode). As such, spectral averaging is beneficial to those projects requiring more resolution thanTDM, but where the FDM channels at full resolution are unnecessary. Table 5.2 shows the resolutions (in kHz)
10 For a full description, see http://mathworld.wolfram.com/ApodizationFunction.html.

65

1.21
2.00
1.82
1.77
2.30
1.59

−0.217−0.026+0.007+0.047+0.001−0.086

0.6

Uniform
Hanning∗
Hamming
Bartlett
BlackmannWelchhalf maximum
0.4

Max
sidelobe

0.2

FWHM
(ch)

Uniform
Hanning
Hamming
Bartlett
Blackmann
Welch

-0.2

0.0

WeightingSpectral Response

0.8

1.0

5.5. CAPABILITIES OF THE CORRELATORS

-3

-2

-1

0

1

2

3

Frequency [channel]

Figure 5.7: (left table) Spectral resolutions (FWHM) and the maximum sidelobe levels for weighting functions.
ALMA employs the Hanning window in default. (right figure) Spectral resolution functions corresponding tovarious weighting functions
for different values of N , using Hanning weighting, in the different bandwidth modes. The channel spacings arein parentheses.
Note that the default Hanning window function gives a resolution 2 times the channel spacing, so using N = 2(cutting the number of spectral channels from 3840 to 1920) results in negligible loss of final resolution. It is
recommended, unless the maximum spectral resolution is required by the observations, to reduce the numberof channels when feasible. However, note that this is a non-reversible operation. For Cycle 8, the default value
for spectral averaging will be N = 2. The proposer must specifically request and justify the use of N = 1 forspectral averaging.
The ACA Correlator is an FX correlator where the uniform weighting in the FFT segment is equivalent to
the Bartlett weighting in the lag domain. FPS in the CDP can be applied to match the spectral resolutionfunction to that of the 64-input Correlator. The bandwidth and the number of channels in the ACA correlator
remain unchanged through FPS since Cycle 4.

5.5.3

Time Resolution

As shown in Figure 5.8 there are three stages where correlated data are accumulated or averaged within acorrelator sub-system:
1. Accumulator#1: implemented in the correlator itself. Data are accumulated without applying a proper
averaging factor. The accumulation period is called dump duration.
2. Accumulator#2: implemented in the CDP, this stage first truncates ∼ 5% band edges for each spw andthen averages the whole spectral channels into one. Those channel averages are then further averaged intime during a number of dump duration periods. This average period is called channel average duration,
which must be an integer multiple of the dump duration.

66

CHAPTER 5. THE CORRELATORS

Usablebandwidth(MHz)Spectral resolution (channel spacing) [kHz]
1
2∗
4
8
3840
1920
960
480

N=
Channels =

1875
937.5
468.8
234.4
117.2
58.6

977 (488)
488 (244)
244 (122)
122 (61)
61 (31)31 (15)1129 (977)564 (488)
282 (244)
141 (122)
71 (61)35 (31)

1938 (1953)
969 (977)
485 (488)
242 (244)
121 (122)
61 (61)3904 (3096)
1952 (1953)
976 (977)
488 (488)
244 (244)
122 (122)

16
240
7813 (7812)
3906 (3906)
1953 (1953)
977 (977)
488 (488)
244 (244)

Table 5.2: Spectral resolution and channel spacing (in parentheses) in kHz for different correlator bandwidthmodes (left column) and for different spectral channel averaging factors (columns, N = 1 to 16), using Hanningsmoothing. The number of channels can be reduced from 3840 (for the unaveraged case, N = 1) down to 240(for N = 16). As N increases, the spectral resolution functions of adjoining channels are combined and then the
spectral resolution approaches the channel spacing. Values are given for the dual polarization case. For Cycle
8, the default value for spectral averaging will be 2.

Correlator
Accumulator#1

WVR data
every 1.15 second

Transfer data
every dump time

CDP
Accumulator#2
Truncate channels,
take average
BDF
Transfer data every
channel-average duration
Channel-averaged data

WVR correction

Accumulator#3
BDF
Transfer data every
integration duration
Spectral data

Archive

BDF
Transfer data every
integration duration
WVR-corrected spectral data

WVR data

Figure 5.8: Basic data processing and accumulation/averaging steps between the correlator and archive. The
CDP applies channel truncation, spectral averaging, and time averaging for the channel-averaged data. It also
applies online WVR correction to produce the WVR-corrected spectral data. They are packed in Binary Data
Format (BDF) and are archived together with the WVR data.

5.5. CAPABILITIES OF THE CORRELATORS

67

3. Accumulator#3: implemented in the CDP, this stage averages full resolution spectra during a number ofof dump duration periods. This average period is called integration duration, which must be an integer
multiple of the channel average duration. This also outputs WVR-corrected spectral data.
Most of the data produced by the correlator corresponds to full resolution spectra, and its data rate can beapproximated by the following expression:2
Rint = Nant
× NBB × Nch × Npol × Nbyte /Tint , (bytes/sec)(5.2)

where Nant , NBB , Nch are the number of antennas, BBs, and total number of spectral channels, respectively.
Npol = 1, 2, and 4 for single, dual and full polarization products, respectively. Nbyte (bytes/visibility) is the byte
size of the real or imaginary part of a visibility, and Tint is the integration duration in the Accumulator#3. For
example, an array configuration with Nant = 43, a spectral setup with NBB = 4, Nch = 3840 × 2 polarization
products (XX and Y Y ), Tint = 6 sec, and assuming Nbyte = 2 yields a data rate of 18.9 MB/sec.
In Cycle 8, ALMA regulates Rint at 70 MB/sec. The ALMA Observing Tool (OT) estimates the data rate
for each science goal and warns if it exceeds the limit. In this case, it is required to consider the optimal
trade between time and spectral resolutions, number of polarization products, number of BBs, and number ofantennas in the array.
Some specific considerations about different time duration follows:• Integration duration of spectral data with the 64-input Correlator
The basic integration time of the 64-antenna Correlator is 16 and 1 ms for cross- and auto-correlation,
respectively. The correlator integration duration can be, in TDM and FDM, any value that would keep
the integration data rate Rint under the regulated limit for a given science cycle. Note that the 64-input
Correlator sets Nbyte = 2 in real-time, based on the actual magnitude of the data produced (correlation
regime). For validation purposes, and only in FDM, a favorable condition of Nbyte = 2 is assumed.
• Integration duration of spectral data with the ACA Correlator
The ACA Correlator uses Nbyte = 4 and its dump time is a multiple of 1 ms and 16 ms for autocorrelation and cross-correlation, respectively. The maximum data rate from the ACA Correlator is 3.6
MB/s, independently of the number of antennas. However, the average data rate to the archive will belower during typical observing modes, because of overheads and the use of TDM in calibration scans.
• Channel-averaged duration
The average power spectra across the whole bandwidth, in each spw, can be recorded in an independent
spw consiting of only one spectral channel. This single channel spw, without bandpass calibration, is not
used for astronomy, but for recording phase and amplitude variations through the observing time. Its
duration should normally be equal to or shorter than the WVR integration duration.
Time-domain observing mode
A time-domain observing mode is dedicated for observing time-variable objects such as pulsars and transients.
This capability is offered starting Cycle 8, using the 64-input correlator, as described in Section 8.11.4. For
Cycle 8 this mode is limited to Band 3 only. This mode employs the VLBI phased array capability whereby
signals from individual antennas are summed up after phase alignment (phasing) through adjustment of the
TFBs. The phased sum signal is converted to VDIF format and recorded onto Mark 6 VLBI recorders. The
disk modules containing the recorded baseband data will then be shipped to the VLBI correlation facility at the
Max Planck Institut für Radioastronomie for playback and generation of PSR-FITS format data appropriate
for timing and search analyses. The PSR-FITS file will have a user-specified time resolution of up to 8 µs anda spectral resolution of 32 channels/BB. See Section 8.11.4 for additional information. Beside generating thephased sum signal, the correlator also produces an ASDM data set that contains the standard interferometry
visibilities from the array with a standard time resolution.

68

5.5.4

CHAPTER 5. THE CORRELATORS

Phase Switching

The 180◦ phase switching capability is implemented to suppress spurious signals and IF cross talk between the
LO1 and the digitizers11 . The 90◦ phase switching capability is offered to separate, in real-time, upper andlower sidebands of DSB receivers (Bands 9 and 10). The expedient is based on 90◦ phase switching at the LO1,
and accumulation in different memory areas (bins) in the correlator12 . Walsh function series are employed tomake antenna-based switching patterns orthogonal to each other. The Walsh sequences permutes every 16 ms,
and the full cycle completes after 2048 ms to achieve orthogonality for all antennas in the array. The dump
duration, during a side band-separation observation, must be an integer number of the complete Walsh cycle.
See also Appendix B.4.3.
The 180◦ phase switching
The phase switching capability (see principles in Figure 5.9) is realized by phase modulation in the LO1 anddemodulation in the DTS transmitter module after digitization.
State

Ant.

LO phase

IF signal

Demod.

1
2

φLO
φLO

−iφLO

0
1

+N
S1 e
S2 e−iφLO + N

00hS1 · S2∗ i + hN · N ∗ i

1
2

φLO
φLO + πS1 e−iφLO + N
S2 e−i(φLO +π) + N

0πhS1 · S2∗ i − hN · N ∗ iaverage

Cross Corr.

hS1 · S2∗ i

Table 5.3: Cross correlation of a baseline under 180◦ phase switching. The received signal of antenna 2, S2 , ismodulated by 180◦ by the LO1 and demodulated in the DTS transmitter module at each antenna. Spurious
signals, N , in the IF or cross talks are not modulated via the LO1 and thus are canceled via demodulation andaccumulation of data in states 0 and 1.

The 90◦ phase switchingThis function aims to separate sidebands for the DSB receivers of Bands 9 and 10. When the LO phase ofantenna 2 is offset by 90◦ , the phases of USB and LSB signals in IF will be −φLO − π2 and φLO + π2 , respectively.
The 90◦ -demodulation is taken by swapping real and imaginary parts of the cross-correlations in the CDP.
11 Note that this scheme doesn’t work for auto-correlations.
12 See Thompson, Moran, and Swenson, “Interferometry and Synthesis in Radio Astronomy (2nd edition)”, §6.1 and §7.5.

Walsh series
S1

mod

LO

mod

S2

corr
demod

demod
accum

Figure 5.9: Schematic diagram of phase switching. The LO1 signal phase is modulated with the the Walshseries pattern and demodulated in the DTS before cross-correlation. The Walsh function series are employed
to generate switching patterns that are orthogonal to each other.

69

5.6. PRACTICAL PERFORMANCE

After demodulation, the sign of LSB correlation will be inverted with respect to USB. Thus, the average andthe difference of cross-correlations in two states gives the USB and the LSB visibilities, respectively.
State

Ant.

LO phase

0

1
2

φLO
φLO

1

1
2

φLO
φLO + π2

IF signal

Demod.

S1,U e+ S1,L e
S2,U e−iφLO + S2,L eiφLO

00S1,U e−iφLO + S1,L eiφLOπ
π
S2,U e−i(φLO + 2 ) + S2,L ei(φLO + 2 )

0

−iφLO

(State 0 + State 1)/2
(State 0 − State 1)/2

iφLO

π
2

Cross Corr.
∗∗
S1,U · S2,U
+ S1,L · S2,L∗∗
S1,U · S2,U
− S1,L · S2,L∗
S1,U · S2,U∗
S1,L · S2,L

Table 5.4: Cross correlation of a baseline under 90◦ phase switching. The suffixes of 1, 2, U, L stand for antenna 1
and 2, and USB and LSB, respectively. The LO phase of antenna 2 is modulated by 90◦ . After 90◦ -demodulationand correlation, the cross-correlations of USB and LSB have opposite signs. Thus, the average and the differenceof cross-correlations in two states gives the USB and the LSB visibilities, respectively.

5.6

Practical Performance

5.6.1

Sensitivity

A digitizer adds quantization noise to its input analog signal, with a consequent signal-to-noise reduction or
sensitivity loss. The ALMA digitizer employs 3-bit (8-level) quantization13 , and additional re-quantization
processes are applied in the correlators.
In Cycle 8, the 64-input Correlator TDM mode makes use of 2-bit quantization that yields a quantization
efficiency of ηQ = 0.88. In the FDM case, digital filtering is applied to 3-bit quantized signals followed by 2-bit
re-quantization. The two stages of quantization would cause the net quantization efficiency of ηQ = 0.96×0.88 =0.85 if they were independent (see mode chart tables of Escoffier et al., ALMA Memo 556), nevertheless, thereal efficiency can be slightly better than the multiplication (Iguchi et al. 2005, PASJ 57, 259)14 .
The ACA Correlator feeds 3-bit quantized signals into the FFT processors where butterfly arithmetic is
performed with 16-bit precision. The FFT output spectrum is re-quantized into 4-bit (16 levels) before crossmultiplication. The combination of these quantizations results in a loss of 4.8% (i.e. ηQ = 0.952; Kamazaki etal. 2012, PASJ 64, 29).
The quantization efficiencies above are theoretical values under optimal conditions of the input signal level
and threshold voltages. Although the signal level is adjusted for every scan, significant variation of power level(e.g. observation of strong sources, unstable weather, or a frequency band near atmospheric absorption lines)
can violate the conditions required to optimize the quantization efficiency.

5.6.2

Linearity

Digital quantization also causes non-linearity in the visibility measurements. The relationship between thecorrelation coefficient of quantized signals with that obtained for analog signals (i.e. infinite quantization levels)
is known as the Van Vleck relationship, which is used for the non-linearity correction.
Figure 5.10 shows the Van Vleck relationships in 2-, 3-, and 4-bit quantizations. The correlation coefficientsof quantized signals keep adequate linearity for small correlation coefficients15 . This indicates that for mostsources the cross-correlation response is effectively linear.
However, auto-correlations are affected by the non-linearity because the correlation coefficient at zero lagmust be unity by definition. The non-linearity in auto-correlation power spectra influences system temperature
13 The quantization efficiency would be η = 0.96 if optimal signal levels, threshold voltages, and perfect signal processing wereQ
performed (Thompson 1998, MMA Memo 220).
14 It is reported that the combination of 2-bit quantization, digital filtering, and 2-bit re-quantization yields η
Q = 0.81, better
than 0.88 × 0.88 = 0.77.
15 The departure from linear relation is δρ/ρ < 10−3 for ρ < 0.2

70

CHAPTER 5. THE CORRELATORS

Optimal Threshold Level
0.12

1.0

Optimal Threshold Level

0.08
0.06
0.04

Departure from Linear Relation

0.0

0.00

0.02

0.8
0.6
0.4
0.2

Digital Correlation Coefficient

2−bit
3−bit
4−bit

0.10

2−bit
3−bit
4−bit

0.0

0.2

0.4

0.6

0.8

1.0

Analog Correlation Coefficient

0.0

0.2

0.4

0.6

0.8

1.0

Analog Correlation Coefficient

Figure 5.10: Van Vleck relationship of 2-, 3-, and 4-bit quantizations at the optimal signal power level andthreshold voltages. (Left): Correlation coefficient of digitized signals as a function of analog correlation coefficients, ρ. (Right): Departures of the Van Vleck relationship from linear relation using the single factors ofη4 = 0.881, η8 = 0.963, and η16 = 0.988 for 2-, 3-, and 4-bit quantizations, respectively.
measurements and the TP Array observations. In both correlators, the CDPs measure total power of digitizedsignals and determine the Van Vleck relationship to correct the (cross) power spectra.

5.7

Final data product - the ASDM

The final product from each observation in the archive is known as the ASDM (the ALMA Science Data
Model), each of which has an unique hexadecimal name (e.g. uid://A002/X2fed6/X3f). The ASDM contains
the metadata (headers, descriptions of the observation setup, ancillary data, etc), and the binary data (the raw
data itself), and is described in more detail in Section 12.2. The following describes the spectral data in the
ASDM and how its related to the correlator output.
In the ASDM, the binary data are saved in a structure of spws. All of the data in a single spw must sharethe same frequency setup, including the number and width of spectral channels, and the integration time. The
observed spws will be a combination of the science spws set up by the proposers in Phase 1 of the OT, andadditional spws from observations needed for calibration (pointing, and sometimes system temperature) set
up during Phase 2. Additionally, the WVR data are stored in a spw with 4 channels around the water line
at 183 GHz. In the ASDM, except for the WVR spw, each requested spw maps into two output spws in thedata: one with the requested dimensions of N channels per polarization product (for example 128 or 3840),
and a second channel averaged version with one channel per polarization product (this averaging is done in
the correlator). The channel averaged data are used by the online telescope calibration system (TelCal) andfor realtime diagnostic purposes (QuickLook), and are typically not used downstream in the data reduction.
Overall, this can lead to ASDMs with a large number of spws. For example, a typical science observation in
FDM mode can have more than 25 spws. Every scan/spw combination has an associated “intent” that indicatesits purpose (pointing, system temperature, science, etc). The intent can be used in CASA to determine how toutilize each spw in the data reduction process.

Chapter 6

Spectral Setups
This chapter describes the frequency setup of ALMA. In particular it shows how spectral setups are defined fromthe user viewpoint and how these then set up the ALMA hardware. It summarises the functions and operationof the local oscillator (LO) and Intermediate Frequency (IF) systems, as well as outlining some of the otherpoints pertaining to the frequency setup. For those interested in more details of the LO and IF components
and how the hardware works, please see Appendix B.
To the ALMA system, a spectral setup includes the hardware LO, IF and correlator settings, such thateach spectral window (spws) covers the desired lines and/or continuum frequencies. To the user, however, thespectral setup is normally defined in the Observing Tool (OT) just in terms of the desired lines or observing
frequencies, spw bandwidths and spectral resolutions: there is normally no need for the user to worry about thedetails of each hardware setting. For full details of the OT and how to use it, see the user manual and reference
manuals, available from the ALMA website1 (and also in the OT itself). In this chapter, we try to reconcile
these two viewpoints.

6.1

Introduction

ALMA uses two stages of heterodyne conversion to shift the signals from the sky or observing frequency down
to a range where electronics can be used to perform the digital sampling and cross-correlations. In general, thesignals of observing frequency fsig are mixed to IF signals of frequency fIF using a narrow Local Oscillator
signal (LO, at fLO ). fIF is the difference frequency between fLO and fsig , where fIF is always, for ALMA,
much lower than fsig . The output signal is split into two separate sidebands at frequencies offset from fLO ,known as the upper and lower sideband (USB or LSB) .
Figure 6.1 illustrates the ALMA signal path and basic principle of operation. The first heterodyne stage
uses the SIS mixer and LO1 to mix (or downconvert) the astronomical signal to 4 GHz- to 8 GHz-wide IF
bands, giving both USB and LSB. Up to four 2 GHz wide basebands (or BBs) can be placed in the available
IF range in either or both the USB or LSB IFs using the second stage of downconversion. Within each of thesebasebands it is possible to place up to four spws. Each spw forms a final contiguous spectrum, with bandwidths
from 58.594 MHz up to 1.875 GHz wide (see Section 6.3).
Using the OT during both the proposal preparation (Phase 1) and scheduling block (SB) creation (Phase2), the user adds spws to each baseband by choosing the frequencies (or spectral lines) to be observed in theBB, along with the required bandwidth or spectral resolution. During the subsequent spectral tuning, there are
effectively four different LOs set up by the system (Figure 6.1):• LO1 which sets the frontend tuning frequency. This has continuous coverage.
• LO2 which positions the basebands within the frontend receiver IF (each baseband uses a different LO2,
hence there are four LO2s). This does not have continuous frequency coverage, as it is generated by a 125
MHz frequency comb plus a 20–42.5 MHz continuous frequency synthesizer.
• LO3 which is the clock frequency of the digitizers (fixed at 4 GHz),
1 http://almascience.org/documents-and-tools/

72

CHAPTER 6. SPECTRAL SETUPS• LO4 (also known as the tunable filterbank LO, or TFB LO), which is a digital LO synthesized in thecorrelators allowing positioning of the spws within each baseband. Each spws has effectively a separate
LO4.

Figure 6.1: Summary block diagram of ALMA signal path and LO system for one spw, one baseband, one
polarization. The Backend IF system is located in each antenna, and the digitized signal for each baseband/polarization is fed to the correlator in the central technical building through buried optical fibers. See
Appendix B for a more detailed description of the components and the other tasks that the LO systems perform.
The OT and the real-time system have a tuning algorithm that attempts to find the best tuning solution for
LO1, LO2 and LO4 based on the requested observing frequencies. Because the LOs themselves are generated
by combinations of frequency synthesizers, several different tuning solutions may be possible, and the algorithm
performs the requisite optimization.2 If no solution is possible, the OT will notify the user. A more detailed
description of the LO operation is given in Appendix B.2.
There are has similar restrictions on the spectral setups and tuning as in recent cycles (see Table 6.2 in
Section 6.8). The main limits are that the edges of the 2 GHz-wide basebands cannot lie outside the receivertuning range listed in Table 4.1, and the edges of the (untruncated) spws cannot lie outside the individual 2
GHz-wide basebands. In addition, the OT will give validation warnings if a) any part of a spw is closer than 30
MHz to the baseband edge or b) more than half of the spw is within (30 MHz + the line width) of the baseband
edge.
The settings of each baseband in the correlator are independent, so the bandwidth, resolution and correlator
mode as well as the value of LO4 can be different for each baseband. For example, it is possible to have a 58
2 Note that with tuning setups having multiple basebands, only the hardware LO1 and LO2, the requested frequencies may notappear in exactly the center channel in all the spws, because of the non-continuous coverage of LO2. Normally the tuning algorithm
will use LO4 to compensate for this and re-center the lines. However in the widest bandwidth modes (FDM 1875 MHz and TDM)
the spws cannot be shifted using LO4. Then the sum of the absolute frequency offsets in all basebands can be as much as 26.38
MHz for 4-baseband setups, giving a worst-case average baseband offset of 6.6 MHz; this is considered small compared with the
bandwidth (and the frequency labelling will still be correct). See Section B.2 and “ALMA LO System Setup Algorithms” (Scott,2009) for more details.

73

6.2. FREQUENCY DEFINITIONS

MHz-wide spws centered on a particular line in baseband 1, and simultaneously use a broadband time divisionmultiplexing mode (or TDM mode - see Chapter 5) for all the other basebands. It is possible to have multiple
FDM spws within each baseband, described in Section 6.3.2 below; however, currently the underlying resolutionof all spws within the same baseband has to be equal. Different spectral averaging is allowed however within the
spws. The spectral setups of the ACA Correlator and the 64-input Correlator are - to the user - effectively thesame, with the ACA Correlator having the same allowable spectral functions as the 64-input Correlator.

6.2

Frequency Definitions

There are several frequency definitions used in the ALMA system, in the OT Phase 1 and Phase 2. Most
important to the user are:Center Frequency (Rest) (fspws ) This is set by the user in the OT Phase 1, and is the central frequency ofthe spws in the requested rest frame of the source. Note that the source rest frame is selectable, but iscommonly set to the local kinematic standard of rest (LSRK), which is the conventional local standardof rest based on the average motion of the Sun with respect to the solar neighborhood (see Section 6.8).
Note it is strongly recommended that the user input the appropriate source velocity or redshift in the
Field Setup tab of the OT (Chapter 9).
Center Frequency (Sky) This is seen in the OT Phase 1, and is the actual central frequency of the spws in
the local ALMA (i.e. sky) velocity frame, after including the velocity of the source. However, it does notinclude the velocity shift of the chosen coordinate frame with respect to ALMA (i.e. the extra velocity
from Earth rotation and orbit) as this is not known until actual runtime.
Baseband desired Center Frequency (fBB ) This is the frequency center of the baseband, shown in OT
Phase 2. Both the Sky and Rest Baseband center frequencies are seen. If the spws are centered on the
basebands, these will be the same as the Phase 1 Center Frequencies (above). Otherwise they can bedifferent because of the TFB LOs (see below).
Center Offset Frequency (fof f set ) Used in the OT Phase 2, this is the offset due to the TFB LO. The center
frequency of the spws, fspws , is given in terms of this and Baseband Center Frequency by:fspws = fBB ± (fof f set − 3.0GHz)(6.1)

where the sign depends on the observing sideband.

6.3

Spectral Setups

The wide IF bandwidth and tuning ability allows for routine simultaneous imaging of multiple lines at different
spectral resolutions in different basebands. Some examples (with the approximate line frequencies in GHz) are
shown in Table 6.1 (for a source of redshift zero). Note that in many cases the lines will not necessarily appear
in the center of the spws (for example, in the Band 6 combination 6b). When <4 spws are required for the
primary lines, the other BBs can be set up to cover fainter lines or to observe the continuum, potentially in TDM
mode. If lines are the main goal in one spw, the other continuum spws frequencies need to be setup manually;
one method of doing this is described in the next section. The selection of secondary lines to be observed
can be done using the OT spectral interface. In the case of continuum spws, to maximize the sensitivity, thewidest bandwidth mode should be chosen (i.e. in TDM, or 1.875 GHz in FDM - preferably with some channelaveraging, see Section 6.4). Also the continuum spws should cover as much of the IF band as possible. Not
only will this maximize the continuum SNR on the science target, but these continuum data can be used to
improve phase and amplitude calibration. For this reason it is recommended that all four available basebands
be used in all observations. Note that there is no gain in sensitivity by overlapping spws in frequency, since
the input signal is the same in the overlap region; the OT uses the unique aggregate bandwidth in calculating
the sensitivity, taking any spw overlap into account. However, for sources with known high line density (onespectral feature per 10 MHz), PIs are encouraged to set up all the spws in FDM mode. This will allow a morerobust determination of the line-free channels used to form the aggregate continuum during data processing andimaging.

74

CHAPTER 6. SPECTRAL SETUPS

6.3.1

Observing Frequencies for Continuum

For optimum sensitivity, continuum spws should be set to the frequencies with the lowest system temperature.
Because the mixer frequency responses are fairly flat, normally this corresponds to the best atmospheric transmission. For full continuum observations (without any required lines, or with only low resolution) the OT has
standard optimized frequencies for each band which are used in the OT Phase 1 when Single Continuum isselected; these are noted in Table 6.1 and illustrated by the red in Figure 6.2.

Figure 6.2: ALMA bands available in Cycle 8 (Bands 3 - 10), showing the frequency of the standard continuum
settings as red shading. This gives the coverage of both USB and LSB, except for Bands 9 and 10, which have
8 GHz of bandwidth using the USB only. The available frequency coverage of each band is shown by the grey
shading, and atmospheric transmission for 0.6 mm of PWV is given by the blue line.
If mixed line+continuum operation is desired, for example with a single line in BB1 observed at frequency
f (GHz), the other BBs (2-4) can be set up for continuum observing using TDM mode3 . For 2SB receivers,
typically this would have BB2 in the same sideband (offset by 2 GHz from f ) and BB3 and BB4 in the opposite
sideband (offset from BB1 and BB2 by the front end center IF frequency, fIF ). To maximise sensitivity
the continuum BBs should cover the maximum aggregate unique bandwidth, i.e. they should not overlap infrequency. If sb is the sign of the sideband of BB1 (sb = +1 for USB, sb = −1 for LSB), then the four BBs
could be set up as follows:• BB1: f (BB covering the primary line)
3 Note - this case assumes one spws per BB

75

6.3. SPECTRAL SETUPS

Band/setup
3a
3b*
3c*
4a
4b
5a
5b
6a
6b*
7a
7b*
7c
8a
8b
9a
9b
10 a
10 b *-

Species/transition
Standard cont.
HCO+ (1-0)
HCN (1-0)
CH3 OH (7(-2,6)-7(1,6))
H2 CO (6(1,5)-6(1,6))
continuum spws
CO (1-0)
CN (N=1-0)
C17 O (1-0)
continuum spws
continuum spws
Standard cont.
CS (3-2)
DCO+ (2-1)
SO2 (4(2,2)-4(1,3))H2 CO (2(0,2)-1(0,1))Standard cont.
H2 O (3(1,3)-2(2,0))
continuum spws
H2 S (1(1,0)-1(0,1))
continuum spws
Standard cont.
12
CO (2-1)
continuum spws
C18 O (2-1)
13
CO (2-1)
continuum spws
Standard cont.
continuum spws
12
CO (3-2)
HC15 N (4-3)
H13 CN (4-3)
HCN (4-3)
HCO+ (4-3)
NHD2 (2(2,0)-2(1,2))
12
CO (3-2)
continuum spws
13
CO (3-2)
continuum spws
Standard cont.
CI (3 P1 - 3 P0 )CS (10-9)
continuum spws
continuum spws
Standard cont.
12
CO (6-5)
CS (14-13)
H2 S (2(0,2)-1(1,1))
C17 O (6-5)
Standard cont.
CO (7-6)
HCO+ (9-8)
continuum spws
continuum spws

Freq. (GHz)1

97.5
89.18888.632101.293101.333
101.3
115.271113.499112.359102.5
100.5
145.01146.969
144.077
146.605145.603
203.0
183.31
181.4
168.763170.8
233.01230.538234.0
219.560
220.399216.5
343.51343.0
345.796344.200
345.340354.505356.734
356.230
345.796344.8
330.588331.6
405.01492.160
489.751
477.5
479.5
679.0
691.472685.436687.303674.009875.0
806.652802.458805.5
803.65

Sideb.

bandwidth

dual
LSB
LSB
USB
USB
USB
USB
USB
USB
LSB
LSB
dual
LSB
LSB
LSB
LSB
dual
USB
USB
LSB
LSB
dual
USB
USB
LSB
LSB
LSB
dual
LSB
LSB
LSB
LSB
USB
USB
USB
USB
USB
LSB
LSB
dual
USB
USB
LSB
LSB
USB
USB
USB
USB
LSB
USB
LSB
LSB
USB
USB

TDM
58 MHz58 MHz
125 MHz
125 MHzTDM
58 MHz58 MHz117 MHz
TDM
TDM
TDM
117 MHz117 MHz117 MHz117 MHzTDM
250 MHzTDM
250 MHz
TDM
TDM
937 MHzTDM
937 MHz937 MHz
TDM
TDM
TDM
469 MHz234 MHz234 MHz469 MHz117 MHz234 MHz58 MHzTDM
58 MHzTDM
TDM
117 MHz117 MHz
TDM
TDM
TDM
469 MHz117 MHz234 MHz469 MHzTDM
469 MHz117 MHz
TDM
TDM

BB

spws

1
2
3
3
4
1
1
2
3
4

1
1
1
1
1
1
2
1
1
1

1
2
3
4

1
1
1
1

1
2
3
4

1
1
1
1

1
2
3
3
4

1
1
1
2
1

1
2
2
2
3
4
4
1
2
3
4

1
1
2
3
1
1
2
1
1
1
1

1
2
3
4

1
1
1
1

1
2
3
4

1
1
1
1

1
2
3
4

1
1
1
1

Notes
LO1=97.5
HCO+ /HCN/H2 CO

CO/CN/C17 O

LO1=145.0
CS/DCO+

LO1=203.0

LO1=233.0
J=2-1 CO isotopes

LO1=343.5
CO/HCO+ /HCN
1/2-corr
1/4-corr
1/4-corr
1/4-corr
1/2-corr
J=3-2 CO/13 CO

LO1=405.0
CI/13 CI

LO1=671.0
CO/CS

LO1=867.0
CO/HCO+

Table 6.1: Examples of spectral setups possible with the existing hardware and software. This includes thestandard continuum-only setups for each band, and some multiple line/continuum configurations. Notes: 1.
Frequency for standard continuum setups are the mean observing frequency of all spws, ≈LO1 in dual-sideband(2SB) receivers, this frequency isn’t actually covered if both sidebands are used. See Figure 6.2.

76

CHAPTER 6. SPECTRAL SETUPS• BB2: f − 2.0 (continuum BB in the same sideband, 2 GHz below the primary line)• BB3: f − (2.sb.fIF ) (continuum BB in the opposite sideband)• BB4: f − (2.sb.fIF ) − 2.0 (continuum BB in the opposite sideband)
where fIF is the front-end IF frequency (6.0 GHz for Bands 3, 4, 5, 7 and 8, and normally 8.0 GHz forBands 6, 9 and 10). For DSB receivers, it is common to keep all the BBs in the same sideband, so BB3 and BB4
would be at f − 4.0 GHz and f − 6.0 GHz. Note that this is an approximate rule and for the DSB receivers,
the image sidebands are now turned on by default providing the added sensitivity for continuum observations(Section 6.3.4). When at all possible, adjustments of the continuum BBs (for example, choosing whether the
opposite sideband is LSB or USB) should be done using the OT spectral display, to avoid deep atmosphericabsorption features. This is particularly important at Bands 8, 9 and 10, and near the water lines around 183
GHz in Band 5 and 325 GHz in Band 7 (see Figure 6.2). Also, if contiguous spectral coverage of the continuum
is desired, the BBs should be offset by 1.875 GHz rather than 2.0 GHz as suggested above. Adding TDM spws
in otherwise unused BBs (at non-overlapping frequencies) will improve the overall sensitivity for calibration and
it is recommended to use all four BBs whenever possible.

6.3.2

Multiple Spectral Windows in the Same Baseband

The system allows the capability to have up to four spws in each baseband, and each baseband can have completely different setups. This is useful for projects where several lines need to be observed simultaneously athigh spectral resolution. However, in cases where four lines or fewer are observed in total, if the full bandwidth/resolution is needed for each line and they are well-separated, it may be preferable to place each ina different baseband. Alternatively, in cases where the lines are close to one another, or less spectral resolution/bandwidth is acceptable, it may be better to include multiple lines in the same baseband or even in
the same spws, and use the other basebands in TDM mode to maximize the total (aggregate) bandwidth forcalibration. An example of this is shown in Table 6.1 for spectral setup 6 b, where both C18 O and 13 CO areobserved in the same baseband (3.1 and 3.2). Channel-averaging can be applied to each spws, which simply
bins spectral channels together in the correlator data processing (see Section 6.5).
Multiple spws per baseband does have some restrictions: each spws within the same baseband must have thesame correlator channel width (i.e. before channel-averaging)4 , and the sum of the correlator resources in eachbaseband should add up to 1.0 (or less). Given these restrictions, it is possible to set up different bandwidths
and/or different channel-average values for each spws. Multiple spws are set up in the Phase 1 OT simply byadding more spectral lines in the same baseband, and setting the spws to have a correlator fraction less than
1.0 (so for 4 spws, each has a correlator fraction of 1/4). There may be up to 4 spws per baseband, however,
the total number of spectral channels in each baseband is limited by the correlator resources. So doubling thenumber of spws in one baseband will result in half the number of channels per spws, i.e. a lower resolution.
Figure 6.3, which is adapted from the Phase 2 Spectral Editor of the Observing Tool (OT), illustrates a more
complex spectral setup with multiple spws and basebands. The lines observed are given in Table 6.1, example
7 b. In this case, the frequency of LO1 is 350.0 GHz, and the upper and lower sidebands of the Band 7 receiverare shown as green shaded areas. The four basebands, illustrated in this case by the red horizontal bars, canbe moved around, but only within the two sidebands. The spws are also shown, labelled by the name of the
primary spectral line or continuum. In this example, baseband 1 is set for a TDM spw covering the whole 2
GHz baseband for a continuum measurement, whereas in other basebands, FDM is used. Baseband 2 has three
spws with 0.56 MHz resolution and channel-average of 2; two of 234 MHz bandwidth and 1/4 of the correlator
resources per spw, and one with 469 MHz and 1/2 of the correlator resources. At the same time, in BB3 oneline is observed with 469 MHz bandwidth and 0.49 MHz resolution (with a factor of 4 channel-averaging). In
BB4, one spw has 234 MHz bandwidth and 0.28 MHz resolution (with 2 channel-average) and one spw has
117 MHz bandwidth and 0.48 MHz resolution (with 4 channel-average). Basebands (and spws) are allowed topartially overlap, although the overlapping region only counts once in the aggregate bandwidth and estimateof continuum sensitivity. So it may be preferable to observe closely-spaced lines with a single baseband (e.g.
C18 O and 13 CO in example 6 b above) or better, with a single spw, as this can free an additional TDM spw for
improved continuum sensitivity. Many combinations of spws and basebands can be set up in this way.
4 although, as before, spws in different basebands can have different channel widths

6.3. SPECTRAL SETUPS

77

Figure 6.3: Illustration of a frequency setup, based on the OT spectral display. Green areas are the IF ranges,
horizontal red bars are the 2 GHz-wide basebands (BB1–BB4), and smaller horizontal lines represent the spws
(up to 3 per baseband in this example). The frequency of LO1 is shown by the central vertical line. The blue
hashed area represents the tuning range of the front end (in this case a section of Band 7), and the curved
line represents the nominal atmospheric transmission for the chosen PWV. The bandwidths of the spws areillustrated by the widths of the horizontal lines. The lines observed are given in example 7 b in Table 6.1.

6.3.3

Spectral Setups for Lines near the Edge of the Bands

The restriction that the baseband coverage cannot fall outside the maximum or minimum tuning range of thereceiver is an issue for certain lines at the edge of the tuning range. One obvious example is the 12 CO(J=1-0)line at a redshift of zero (rest frequency of 115.271 GHz). This is close to the maximum tuning range of Band 3(116.000 GHz, see Table 6.1). A setup using the wide bandwidth modes (TDM or FDM/1875 MHz) centered at
the line frequency with zero redshift will not validate in the OT, because some of the basebands will fall outside
the maximum Band 3 frequency (116.0 GHz). Narrower modes will not go over the edge and are allowed.
There are two possible solutions: If the full bandwidth is absolutely required, the center rest frequency canbe set to the closest valid frequency, resulting in an offset of the line from the spws center (in this case, set to115.0 GHz and the line will be offset by 0.271 GHz). Another solution is to choose a narrow spws bandwidth(e.g. 1 GHz or less); in this case the spws will be offset from the center of the baseband, and the line will be at
the center of the spws.

6.3.4

Spectral Setup in Bands 9 and 10: DSB Considerations and 90-degree Phase
SwitchingBands 9 and 10 use double-sideband (DSB) receivers. If only one sideband is required (the so-called ’signal’sideband) the other sideband (known as the ’image’ sideband) can either be suppressed using LO offsetting(currently using LO1 and LO2). Alternatively, both sidebands can simultaneously be recorded using 90-degree
phase switching, although this can only be used in interferometric mode and is now the default - see Section B.4.2.
Observing a single sideband
The choice of which sideband a particular baseband is configured to observe (and which sideband is suppressed)
depends only on the relative sign of the LO1 and LO2 offset. This can be arbitrarily different for different
basebands. So it is possible to set up two basebands at approximately the same LO1/LO2 frequency, but

78

CHAPTER 6. SPECTRAL SETUPS

observe one line in the upper sideband in one baseband, and another in the lower sideband using the next
baseband, just by having different signs in the LO2 offsetting. However, in this case it might be better to use
90-degree switching (see next section) to record both using the same baseband. Note that different spws in thesame baseband must have the same sideband, as image suppression uses LO2, which is common to the whole
baseband.
Observing both sidebands - 90-degree switching
Starting in Cycle 6, it was possible to double the continuum bandwidth by simultaneously recording bothsidebands from the DSB receivers using 90-degree phase switching. This is enabled by phase modulation of
LO1, with ±90 degree demodulation in the correlator, controlled with a Walsh sequence (see Chapter 5; also
ALMA Memo 287). It has the advantage of doubling the continuum bandwidth to a nominal 16 GHz perpolarization (2 × 2 GHz per baseband × 4 basebands)- particularly helpful in these high-frequency bands as√
it can improve the continuum sensitivity by ∼ 2, as well as making lines available in the opposite sideband.
The actual improvement however, depends on the atmospheric transmission in the opposite sideband, whichin Bands 9-10 can result in image system temperatures 20% (or more) higher or lower than the main signal
sideband. Even though this doubles the number of spws there is no loss of correlator spectral resolution, so thecorrelator data rate is doubled. In rare cases, this may cause correlator data rate limitations in FDM mode,
which could be mitigated by longer integration times, lowering resolution by increasing the channel-averaging
factor, and/or using TDM in the continuum-only basebands. For Cycle 8, there is a restriction that this mode
can only be used with TDM or the maximum bandwidth (1875 MHz) FDM configuration, and the spws canonly be centered on each baseband even when the spectral scan mode is selected (Section 6.6). It also requiresthat the integration duration should be a multiple of 2048 ms.

6.4

Usable Bandwidth

The IF system contains an anti-aliasing filter which limits the bandwidth of the basebands. Nominally this filter
has -1 dB points at 2.10 and 3.90 GHz, giving a maximum bandwidth of 1.8 GHz. However, the IF response issuch that the usable bandwidth is slightly wider – i.e. closer to 1.9 GHz. In FDM mode, the correlator outputs
a maximum bandwidth of 15/16 of the nominal bandwidth, and reduces the number of channels by the same
factors, from 4096 to 3840 (or 2048 to 1920 after the default channel-average factor - see Chapter 5). So, for anominal 2 GHz spectral setup, the correlator outputs a bandwidth of 1.875 GHz. Thus in FDM wide-band, thefilters do not truncate the spectrum, and the full available correlator bandwidth in wide-band mode can be used.
In TDM the correlator outputs a bandwidth of 2.000 GHz, but typically the edges of the spectra are affected by
low power due to this filter and some ringing effects (see upper panel in Figure 6.4). It is recommended that 4(in double-polarization) or 8 (single-polarization) channels are removed or flagged manually offline. This results
in approximately the same usable bandwidth in both TDM and FDM modes and is illustrated in Figure 6.4.
Note that if the centers of two basebands are separated by 1.875 GHz it is possible to set up spws that can bejoined in data reduction to yield a contiguous 3.75 GHz spectrum.

6.5

Spectral Resolution and Channel-averaging

The spectral resolution of each spws is set by a combination of the inherent resolution/bandwidth setup in thecorrelator, the correlator weighting function (also known as the smoothing function) and the channel-averaging(also known as spectral-averaging) factor (which is carried out at a late stage of processing in the correlator).
This is described in Section 5.5.2. The default FDM setup from the OT in Cycle 8 uses Hanning smoothing witha channel-averaging factor of N=2 (see Section 5.5.2). Hanning smoothing plus a channel average of 2 results
in a spectral resolution equal to the final channel spacing x 1.15 - only ∼15% worse than Hanning without
channel-averaging but has the advantage of halving the data rate. If the line is well resolved, with ≥3 channels
covering the linewidth, then this will not cause a problem. However, marginally resolved lines should keep the
maximum resolution. If possible it is recommended to use this default in order to reduce the data rate and sizeof the final product. If the extra 15% resolution is required or the line is expected to be marginally resolved, ajustification for using a channel average of N=1 should be made. Note that for TDM mode, Hanning smoothing
without channel averaging (N=1) is the default.

6.6. SPECTRAL SCANS

79

Figure 6.4: Comparison of TDM (left) and FDM (right) auto-correlation bandpass showing the dropoff in total
power at the edges in the two modes. Colors represent the two polarizations from the example antenna. In
TDM, 128 channels covering 2.0 GHz bandwidth are displayed, which illustrates the drop in power in the upperand lower ∼4 channels due to the anti-aliasing filter. In this case the FDM spectrum has 3840 channels covering
only the central 1.875 GHz, and the drop in power at the edges of this bandwidth is negligible (and comparablewith the variations in the bandpass). (The narrow spike in the center of the FDM data is a test signal).

6.6

Spectral scans

For coverage of frequency ranges greater than the IF bandwidth, a spectral scan observing mode is available.
If spectral scan is selected in the OT, this will observe up to 5 different LO1 frequency tunings to cover therequested range, using all four BBs in USB and LSB. Tunings will be programmed to include an overlap between
each setting to avoid issues with edge channels. Band 9 and 10 will also use the 90-degree phase switching todouble to effective bandwidth per tuning only if the TDM or the maximum bandwidth (1875 MHz) FDM
configurations are selected. If more than 5 tunings are required to cover the range, additional science goals need
to be created.
Spectral scans are now observed more efficiently by using the bandpass calibrator as the flux density calibrator. This change, along with all tunings of a calibrator now being observed immediately after each otherwhich reduces the amount of pointing calibrations considerably, should also make spectral scans more efficient.
It is recommended that the user selects System-defined calibration in the Calibration Setup in the OT whenchoosing spectral scan mode. However, the user can select a separate flux calibrator from a solar system object
if necessary. It is also possible to now set up a spectral scan observation on ACA only observations.

6.7

Spurious Signals

Most spurious signals in the cross-correlation data are suppressed using a combination of 180-degree phasemodulation of LO1 and using different LO offsets for different antennas, both indexed with a Walsh pattern(see Section B.4.4). Not only does this effectively suppress signals generated after the front ends, but it also
improves the image sideband rejection for 2SB receivers by an additional factor of ∼20 dB. However, it does not
reduce spurious signals coming in at the observing frequency. Results from tests using these Walsh functions
show very few remaining spurious signals, and these are further reduced by the fringe tracking. However,
harmonics of the LO in the WVRs (ie 91.66, 183.32, 274.98, 366.64, 458.3 ... GHz) are very bright and cannot
be removed through these methods5 . These are very narrow and may require a few spectral channels to be
5 Although the WVR LOs have small offsets which are different for each antenna, which helps to reduce their cross-correlated
signal80

CHAPTER 6. SPECTRAL SETUPS

flagged out during data reduction. Observing lines at these frequencies should be avoided if possible.

6.8

Doppler Setting and Velocity Reference Frames

In most cases the system will be set up to provide online correction for the science target velocity in a particularreference frame and the Earth motion in that frame. The primary velocity reference frames recommended foruse in ALMA are:
Topocentric In this case no correction for the source or Earth motion is made. The Center Frequency (bothRest and Sky) will be identical.
Barycentric This is with respect to the center of mass of the Earth-Sun system, and is very close to theheliocentric frame.
LSRK Velocity with respect to the Kinematic local standard of rest, at 20.0 km/s in the direction 18h , +30o
[B1900.0]. This frame is based on the mean velocity of the stars in the Solar neighborhood.
If a target velocity and reference frame other than topocentric is selected in the OT, at the start of theobservation, the velocity of the science target in the chosen reference frame and the velocity of the observatory
relative to the chosen reference frame are used to set the center frequencies of the science spws6 . For example,
for a source of radial velocity 100 km/s in the LSRK frame, the difference between rest and sky frequency in
the OT will be the equivalent of 100 km/s. At run-time, the extra velocity from the Earth orbit and rotation(up to ±30.3 km/s and ±0.46 km/s), plus the motion of the LSRK (20.0 km/s toward RA=18 hrs, δ =30◦ forepoch 1900.0) will be included. This means that the LO solutions are slightly different at run-time comparedwith those from the OT, although this is normally transparent to the user7 . It is also possible to just make thecorrection for the motion of the observatory relative to the chosen reference frame, ignoring the source velocity
in that frame. The frequency setting for the science target will normally also be used in the same execution forboth the bandpass and amplitude calibration.
For sources with an external ephemeris file, the rate of change of distance between the target and theobservatory taken from the ephemeris is used to compute the source velocity at the start of the execution. Thisvelocity is used throughout the observation (like non-ephemeris observations, the velocity from the ephemeris
is not updated). Combining executions with different velocities must be done in CASA offline.
The user can specify either the velocity or the redshift of the target. Again, it is strongly recommended thatthe user input the appropriate source velocity or redshift and reference frame in the Field Setup tab of the OT(Chapter 9). Note that velocities can be defined in three different ways, resulting in different conversions tofrequency. These differences only become significant at high velocities.
The velocity formulae are:Radio v = c(fo − f )/fo . This is the default.
Optical v = c(fo − f )/f
Relativistic v = c(fo2 − f 2 )/(fo2 + f 2 ).
In these equations, v is the source velocity, and f and fo are the observed and the rest frequencies of theline. If a redshift z is specified, the conversion to frequency uses z = (fo − f )/f . For further details, see theKnowledgebase article “What are the frequency reference frames in CASA?"

6 Note that ALMA does not do Doppler tracking, where the frequency would be continuously updated for Earth motion during
the observation. Doppler corrections are only set once at the start of each execution. Compensation for the small changes during
an observation (<0.1 km/s for an execution lasting 2 hours) are made during CASA offline reduction.
7 The system allows for a small (< 1 MHz at Band 6) overhang of the spws outside the 2 GHz-wide basebands at runtime, toallow for the very slightly different Doppler corrections in different spws, which will shift the spws with respect to one another.

6.8. DOPPLER SETTING AND VELOCITY REFERENCE FRAMES

Rule

Description

1.
2.

LO1 must lie within the LO tuning ranges given in Table 6.1.
No part of the 2.0 GHz-wide basebands can extend over the edge of the IF passband. So, thebaseband centers cannot be closer than 1.0 GHz to the IF passband edge. For example, with a
4.0–8.0 GHz IF range, the baseband center frequency must lie between 5.0–7.0 GHz. The system
actually does allow a small extension of the edges of the basebands over the IF edges, to cope withthe differential Doppler shifts in the different basebands, but this is small (< 1 MHz at Band 6)
and is transparent to the OT user (see Section 6.8).
For 2SB receivers (Bands 3–8), the number of basebands in one sideband can only be 0, 1, 2, 3 and4. However, note that three basebands in one sideband and one baseband in the other sideband
is not allowed whereas the combination three-zero is. For DSB receivers (Bands 9 and 10), there
is no such restriction (the number can be 0, 1, 2, 3 or 4).
For > 2 basebands, BB1 and BB2 should be in the same sideband, as should BB3 and BB4.
No part of the full nominal bandwidth of the spws can extend over the edge of the 2 GHz-wide
baseband. For a mode with nominal bandwidth B (e.g. 62.5 MHz), that means the spws centerIF frequency (a.k.a. Center Offset Frequency in the OT, Phase 2) must be >(2000+B/2) and<(4000-B/2) MHz. The current version of the OT forces this restriction. For 2 GHz FDM andTDM modes, this means that the spws must be at the center of the baseband. However there isa further restriction on this, as noted in the next rule.
The spws usable bandwidth (ie 15/16 of the nominal spws bandwidth of a multiple of 62.5 MHz)should be in an allowed region of the baseband. This is in addition to (5). In practice this meansthat the required range of the spws should normally be inside the range ∼2050 - 3950 MHz (i.e.
>50 MHz from the edges of the 2–4 GHz second IF) to ensure that the edge of the anti-aliasing
filter does not significantly affect the IF power. In practice it is possible to extend some fractionof the spws to <50 MHz of the IF edges (although this is no longer so critical for the Band 6 setup
6 b in Table 6.1, as the allowable IF range has been extended down to 4.5 GHz).
The line frequency does not need to be in the center of the spws in Phase 1 of the OT: if a line
like 12 CO 1-0 is requested, it will generate an SB with the correct TFB LO offset, as long as rule 5
is obeyed (which may require using a narrower spws). This is mentioned in more detail in Section
6.2
Only 2-bit, Nyquist sampling is allowed in the correlator.
It is possible to have multiple targets with different redshifts within the same Science Goal in the
OT. For SGs including sources with more than one redshift, all the observations must be achievableusing five or fewer tunings within the same receiver band, considering the source redshifts and, inthe case of spectral lines, the line widths and configuration of spws.
The number of spws per baseband can be 1, 2, 3 or 4. For 3 spws, the correlator resources per
spws should be set to 1/4, so only 3/4 of the available resources are used in this case.
All the spws within the same baseband are required to have the same correlator channel width(before channel-averaging). An individual spws within a baseband may occupy 1, 1/2 or 1/4of the resources available in the baseband and the sum of the fractional resources within one
baseband must be ≤1. The correlator resources are proportional to the number of correlator
spectral channels.
With DSB receivers (Band 9 and 10), 90-degree phase switching is allowed, giving both sidebands
simultaneously. This is only available for TDM and FDM 1875 MHz bandwidth modes.

3.

4.
5.

6.

7.

8.
9.

10.
11.

12.

Table 6.2: Rules for spectral setups.

81

82

CHAPTER 6. SPECTRAL SETUPSChapter 7

Imaging with ALMA
7.1

Introduction

Imaging ALMA data consists of Fourier transforming calibrated interferometric visibilities from one or more
configurations or arrays; de-convolving the interferometer point spread function (PSF); and, if Single-Dish data
have been collected, merging them with the interferometric image or cube. We describe in this chapter some of
the key considerations of this process that should be taken into account in order to obtain the best results from
ALMA observations.
As described in Chapter 3, the van Cittert-Zernike theorem is the mathematical foundation of synthesis
imaging. It describes a fundamental relationship between the sky brightness distribution (I), the beam pattern(A) and the visibility distribution V:
Z Z
A(l, m)I(l, m) =V(u, v)e2πi(ul+vm) dudv
(7.1)
A more detailed discussion of the van Cittert-Zernike theorem can be found, e.g., in Rohlfs & Wilson(2004). An interferometric observation can be represented by N discrete points in the uv plane Vk (uk , vk )where k = 1, . . . , N . The variables uk and vk represent the x and y components of a a specific k th baseline
between a pair of antennas, measured in wavelengths λ. There are in general Nant (Nant − 1) × 0.5 distinct
baselines; factoring in distinct frequency channels and temporal integrations, N can reach a few million ormore for ALMA. One implication of the van Cittert-Zernike theorem, which will be discussed in more detailelsewhere in this chapter, is that the interferometer point-spread function (PSF) is the Fourier Transform of
the set of (uk , vk ) points measured. In the parlance of radio astronomy this set of (u, v) points is often called
the “uv-coverage” of an observation, and the PSF is called the “synthesized” or “dirty” beam. In practice it isoften useful to define a weighted visibility function V W (see Briggs, Schwab & Sramek, 1999) that enables theproperties of the synthesized beam to be controlled to some extent, often at the expense of sensitivity. The
weighted visibility function can be represented as:
V W (u, v) =N
X

Rk Tk Dk δ(u − uk , v − vk )Vk (uk , vk ).

(7.2)

k=1

In Equation 7.2, Rk , Tk and Dk are weights which control the relative weighting of individual visibilities inimaging. Rk is a noise-variance weight derived from the sensitivity of the k th visibility measurement. It
accounts for variables such as the integration time, the system temperature, and the bandwidth. These factors
are determined by the instrument, technical set-up, and observing conditions, and are not controlled by theimaging process. Tk is a “taper” weight— usually taken to be a multiplicative, Gaussian factor in the uv
plane— that can be used to down-weight the longest baselines, suppress small-scale sidelobes, and increase thesynthesized beam width and surface brightness sensitivity. Finally, Dk is a uv “density” weight that can be used
to offset the high concentration of measurements near the center of the uv plane, typically increasing angularresolution and reducing the large-scale sidelobes caused by abrupt gaps in the uv-coverage density.
The following sections describe: the ALMA configurations (Section 7.2); the effects of antenna shadowing(Section 7.3); the factors that affect angular resolution and beam shape (Section 7.4); the special case of

84

CHAPTER 7. IMAGING WITH ALMA

short “snapshot” observations (Section 7.5); the large spatial scale response of ALMA (Section 7.6); mosaicing(Section 7.7); multi-array and multi-configuration ALMA observations (Section 7.8); and, finally, multi-arrayand multi-configuration imaging (Section 7.9).

7.2

Configurations

Depending on the range of angular scales required, an ALMA Science Goal will obtain data from either: a single
12-m Array configuration; two 12-m Array configurations; one or two 12-m Array configurations plus the 7-m
Array; or one or two 12-m Array configurations plus the 7-m and Total Power (TP) Arrays1 . The detailed logic
by which specific combinations are chosen based on the PI Science Goals is described in Section 7.8. Generally,
the PI’s desired angular resolution determines the most extended array, while the largest angular scale of interest(or LAS) determines the most compact array— whether that is a second 12-m Array, the 7-m Array, or the
Total Power in order of progressively larger spatial scales. Intermediate configurations or arrays are added toconnect these spatial scales as required. Note that, at present, total power continuum observations are notoffered, limiting the largest angular scale of ALMA continuum observations to that provided by the 7-m Array.
During Cycle 8, the 12-m Array will be arranged in eight different configurations. As discussed below,
operational factors impact the actual configuration achieved for a given observation, so the configurations
presented in this chapter that are to be used for simulations or project planning are referred to as “notional
configurations”. These notional imaging configurations of 43 12-m antennas (C43-X) are available on the Science
Portal and in CASA. In real operations, configurations of all 50 antennas are used, out of which at any given
time, and depending on the requested band, a number of antennas may not be available for observations. Thesenotional configurations are identical to those used since Cycle 5. ALMA is committed to providing at least
43 antennas for each 12-m Array observation and on average provides more than 43 antennas; in exceptional
circumstances, observations may occasionally be made with an array with up to two fewer antennas. In Cycle
8, the two most extended configurations (C-9 and C-10) are not offered. The two most extended configurations
offered in Cycle 8 will be C-7 and C-8; the longest baseline offered will be 8.5 km for Bands 3-7 and 3.6 km forBands 8-10. The 7-m Array will be available in only one configuration of twelve antennas, where ten antennas
should be provided in practice, except in exceptional circumstances where observations may be carried out witheight or nine antennas.
Tables 7.1 and 7.2 give the basic properties of the 12-m Array and 7-m Array configurations. These properties
are based on simulations which use the notional antenna configurations described above (i.e., for the 12-m Array
the C43-X configuration files available on the Science Portal were used). Each configuration is characterized bya maximum recoverable (spatial) scale θM RS and an angular resolution θres . Generally, these are taken to be
determined by the shortest and longest baselines in the configuration, respectively. As discussed in Sections 7.4
and 7.6, ALMA uses the somewhat more robust 5th and 80th percentile baseline lengths instead. Figures 7.2
and 7.3 show the notional configurations of the 12-m Array, which are the 43 pads in each configuration thathave the highest operational priority in terms of antenna availability. Figure 7.4 shows the notional 10-antennaconfiguration of the 7-m Array. The three TP Array single-dish 12-m antennas will be in fixed positions,although their relative spatial locations do not substantially affect their imaging characteristics.
12-m Array configurations in particular are impacted by a variety of “real-world” factors including, but notlimited to, the availability of specific antenna pads2 , and necessary, ongoing antenna relocations. The Schedulingsubsystem takes these changes into account alongside the performance margins that the ALMA QA2 process
allows. Thus, from the user’s point of view, configurations are not directly selected: instead, the required
angular resolution (θres ) and largest angular scale (θLAS ) are specified in the ALMA Observing Tool (OT), andprojects are observed using array configurations that will achieve the specified science goals. Since Cycle 5 it
has also been possible for PI’s to specify an acceptable range of θres . More details about array combinations
are provided in Section 7.8.
As mentioned above, the antenna configurations used in real operations (denoted C-X) can differ from theC43-X notional configurations, and not all 50 antennas may be available for operations at any given time.
These real-world configurations often use pads of the next more compact C43-X configuration and typically
1 The combination of the 7-m Array and the Total Power Array constitutes the ALMA Compact Array (ACA). The ACA is also
known as the Morita Array in honor of Prof. Koh-ichiro Morita.
2 ALMA’s 54 12-m antennas can be distributed among 192 “antenna pads” which provide power, IF signal & network connections,and a structurally stable foundation.

7.2. CONFIGURATIONS

85

Figure 7.1: ALMA’s high resolution images of nearby protoplanetary disks, which are results of the Disk Substructures at High Angular Resolution Project (DSHARP). The data provided by the observing team are available at https://almascience.org/almadata/lp/DSHARP/ Credit: ALMA (ESO/NAOJ/NRAO), S. Andrews etal.; NRAO/AUI/NSF, S. Dagnello

86

CHAPTER 7. IMAGING WITH ALMA

Config.
7-m
C-1
C-2
C-3
C-4
C-5
C-6
C-7
C-8
C-9
C-10

Band
Frequency (GHz)

3
100

4
150

5
185

6
230

7
345

8
460

9
650

10
870

θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)
θres (arcsec)
θM RS (arcsec)

12.5
66.7
3.38
28.5
2.30
22.6
1.42
16.2
0.918
11.2
0.545
6.7
0.306
4.11
0.211
2.58
0.096
1.42
0.057
0.814
0.042
0.496

8.35
44.5
2.25
19.0
1.53
15.0
0.943
10.8
0.612
7.5
0.363
4.47
0.204
2.74
0.141
1.72
0.064
0.947
0.038
0.543
0.028
0.331

6.77
36.1
1.83
15.4
1.24
12.2
0.765
8.73
0.496
6.08
0.295
3.62
0.165
2.22
0.114
1.4
0.05190.768
0.03080.44
0.0227
0.268

5.45
29.0
1.47
12.4
0.999
9.81
0.615
7.02
0.399
4.89
0.237
2.91
0.133
1.78
0.09171.12
0.04170.618
0.02480.354
0.0183
0.216

3.63
19.3
0.98
8.25
0.666
6.54
0.41
4.68
0.266
3.26
0.158
1.94
0.08871.19
0.06120.749
0.02780.412
0.01650.236
0.0122
0.144

2.72
14.5
0.735
6.19
0.499
4.9
0.308
3.51
0.2
2.44
0.118
1.46
0.06650.892
0.0459
0.562
-

1.93
10.3
0.52
4.38
0.353
3.47
0.218
2.48
0.141
1.73
0.08381.03
0.0471
0.632
0.0325
0.398
-

1.44
7.67
0.389
3.27
0.264
2.59
0.163
1.86
0.106
1.29
0.06260.77
0.03520.472
0.0243
0.297-

Table 7.1: Resolution (θres ) and maximum recoverable scale (θM RS ) values for different 7-m Array and 12-m
Array configurations are shown for one representative frequency in each ALMA receiver band. The value ofθM RS is computed using the 5th percentile baseline (L05) from Table 7.2 and Equation 7.7. The value of θres is
the mean size of the interferometric beam obtained through simulations with CASA. Computations were done
for a source at zenith; for sources transiting at lower elevations, the North-South angular measures will increase
proportional to 1/sin(elevation). Calculations are based on the notional C43-X and 7m configurations. Notethat C-9 and C-10 are not offered in Cycle 8.
have +4.3% (+/- 1.4%) larger beams than the notional configurations, apart from C-8 (+10.4%) and C-9 (7.1%). A priority is set for the availability of the outer antennas defining the resolution. In practice, the actual
configurations have a spread of resolutions (5-10%). The final beam resolution of a data set is further affectedby the projected baselines during an observation, 1/sin(elevation) and the uv-weighting applied during data
reduction, e.g. choice of the Robust parameter (20-40%). Both the OT and scheduling system take the effect ofprojected baselines on resolution into account, with the OT assuming a nominal elevation and the schedulingsystem using the actual parameters at the time of observation. Although the 7-m Array is not subject to all ofthese constraints, its configuration is typically somewhat elongated North-South to facilitate observing targets
at a range of Declinations without excessive shadowing (§ 7.3).
In Table 7.1, angular resolutions for the 12-m array are calculated using the notional C43-X antenna configurations for a 2-hour observation centered on transit (at zenith) with Robust = 0.5 and imsize = 100. For
the 7-m Array, imaging parameters are the same but angular resolutions are calculated using the notional
10-antenna 7-m Array and a 20-minute track centered on zenith.

7.3

Shadowing

During interferometric array observations at low elevations — particularly in compact configurations — one
antenna’s view of the source can be partially blocked by another antenna, corrupting data from the first antenna.
This phenomenon is known as shadowing. Given ALMA’s location (latitude=−23.02917◦ ), targets as far North

87

7.3. SHADOWING

1000

C43-1

500

500

0

0
Y (meter)Y (meter)

1000

500
1000

1500
1000

500

0
X (meter)

500

1000

1500

1500

500

500

0

0

500

1000

1500

1500
1000

500

0
X (meter)

500

1000

1000

1500

1500

0
X (meter)

500

0

0
Y (meter)

500

500
1000

1000

1500

C43-4

1000

500

0
X (meter)

500

1000

C43-5

500

1000

1500

C43-6

500
1000

1500
1500

500

500

1000

1500

1000

1000

C43-3

Y (meter)Y (meter)

1000

Y (meter)

500
1000

1500
1500

C43-2

1500
1000

500

0
X (meter)

500

1000

1500

1500

1000

500

0
X (meter)

500

1000

1500

Figure 7.2: Notional (C43-X) 12-m Array compact configurations available for running simulations and planningobservations. The actual array configurations available during a Cycle can be different than these notional
configurations.

88

CHAPTER 7. IMAGING WITH ALMA

Configuration
Minimum baseline (m)5th percentile or L05 (m)80th percentile or L80 (m)Maximum baseline (m)

7-m
8.7
9.1
30.7
45.0

C43-1
14.6
21.4
107.1
160.7

C43-2
14.6
27.0
143.8
313.7

C43-3
14.6
37.6
235.4
500.2

C43-4
14.6
54.1
369.2
783.5

C43-5
14.6
90.9
623.8
1397.9Configuration
Minimum baseline (m)5th percentile or L05 (m)80th percentile or L80 (m)Maximum baseline (m)

C43-6
14.6
148.6
1172.52516.9

C43-7
64.0
235.2
1673.13637.8

C43-8
110.4
427.3
3527.38547.7

C43-9
367.6
746.9
6482.613894.2

C43-10244.01228.18685.916194.0

Table 7.2: Basic parameters of the notional 7-m Array and 12-m Array configurations. The baselines areprojected for a source transiting at zenith.
10000

10000

C43-7

5000
Y (meter)Y (meter)

5000

0

5000

10000
10000 8000

6000

4000

2000 0X (meter)

2000

4000

10000
10000 8000

6000

6000

4000

2000 0X (meter)

2000

4000

10000

C43-9

6000

C43-105000
Y (meter)5000
Y (meter)

0

5000

10000

0

5000

10000
10000 8000

C43-8

0

5000

6000

4000

2000 0X (meter)

2000

4000

6000

10000
10000 8000

6000

4000

2000 0X (meter)

2000

4000

6000

Figure 7.3: Notional (C43-X) 12-m Array extended configurations available for running simulations and planningobservations. The actual array configurations available during a Cycle can be different than these notional
configurations.
as declination +47◦ can in principle be observed, corresponding to a maximum source elevation at Chajnantorof ∼ 20◦ . However, shadowing by adjacent antennas can be a significant problem at such low elevations.
Figure 7.5 shows the fraction of data that will be shadowed (i.e., the “shadowing fraction”) when sources ofvarious declinations are observed with the most compact 12-m notional ALMA configurations (C43-1 and C432) and the 7-m Array. As can be seen, the shadowing fraction can be as large as 55% for sources observed withthe most compact 12-m Array configuration. Image quality and time on source will necessarily be limited forsuch northern sources. Given the short baselines in the 7-m Array, sources with declinations less than −70◦ or7.3. SHADOWING

89

Figure 7.4: Notional 7-m Array configuration available for running simulations and planning observations.

greater than +25◦ are subject to significant shadowing. For the 12-m Array, shadowing becomes significant (>5 %) in the most compact configuration for sources with declination lower than −65◦ or higher than +20◦ .
Note that independent of shadowing, observations at low elevation often result in elliptical uv-coverage
and, therefore, elliptical synthesized beams. The OT will provide an estimate of the beam ellipticity for thoseobservations requesting low elevation targets in order for the PI to properly plan these types of observations
and anticipate the data products that will be provided given such an elliptical beam.

Figure 7.5: Shadowing fraction (%) for the most compact configurations as a function of declination (for a
1-hour observation at transit).

90

CHAPTER 7. IMAGING WITH ALMA

7.4

Angular Resolution and Beam Shape

7.4.1

Definition of angular resolution

The angular resolution θres of an array can in general be estimated with the following equation:
θres =

kλ[radians]
Lmax

(7.3)

where θres is the FWHM of the main lobe of the synthesized beam; k is a factor that depends on the uv plane
weighting function; λ is the observing wavelength in meters; and Lmax is the longest baseline in meters. For
commonly used weighting schemes, k is typically in the range 0.7 < k < 1.2. Since uv-coverage is in general
non-uniform, however, the longest baseline is often not a representative value for the largest distance at which
there is significant uv-coverage. Thus Lmax is a somewhat fragile indicator of angular resolution and ALMA
uses the 80th percentile of the uv distance as a more robust proxy for angular resolution. Via simulations using
the ALMA notional configurations, the following equation was empirically determined:θres ≈

0.574λ[radians]
L80

(7.4)

where again λ is the observing wavelength in meters, and L80 is the 80th percentile of the uv distance in meters(see also Table 7.2).

7.4.2

Effects of weighting scheme

As shown in Equation 7.2, the synthesized beam is affected by uv plane weights, including the user defined taper
weights Tk and density weights Dk . Taper weighting schemes generally take the form of a Gaussian envelope
function in uv distance, and are not used within the ALMA pipeline. Two commonly used, limiting forms ofdensity weighting are natural weighting and uniform weighting:• Dk = 1 is called natural weighting, and results in maximum sensitivity but a relatively large synthesized
beam due to the typically high density of points in the inner region of the uv plane.
• Dk = Ns1(k) is called uniform weighting, where Ns (k) is the number of visibilities in a region centeredon the k th visibility3 . It removes the dependence of spatial-scale sensitivity on the density of visibilities(samples) in the uv plane. Uniform weighting increases angular resolution at the expense of sensitivity.
To bridge the extremes of natural and uniform weighting, Briggs (1995) defined a continuous scheme thatuses a “robustness” parameter R (called robust in CASA). In CASA, uniform weighting is close to robust = −2
and natural weighting is close to robust = 2. Figure 7.6 shows the angular resolution achieved for an observation
with the notional C43-4 configuration at 100 GHz using robust values between −2 and 2. As can be seen, theangular resolution varies from 0.700 (robust = −2) to 1.200 (robust = 2). Unless otherwise specified, the angularresolutions and time ratios presented in this chapter were computed using CASA simulations with Briggs
weighting and robust = 0.5. The ALMA OT also uses the C43-X configurations and Briggs weighting withrobust = 0.5 for calculations of angular resolution and sensitivity. Real observations are processed in the ALMA
Pipeline with an initial default of robust = 0.5 for 12-m Array observations, but a range of values between 0
and 2 are additionally considered and the value which best meets the desired θres and sensitivity is used. A
value of robust = 0.5 is always used when processing 7-m Array observations.
It is important to note that the degree of impact that a given robust value has on the final beam size isdependent on the uv-coverage of the gridded data to be imaged. Snapshot data will have less uv-coverage thanlonger integrations, as will single channels of an image cube compared to continuum MFS images. When thefractional bandwidth of a spectral window being imaged is high enough, the full set of channelized visibilities
from a given baseline in dense inner region of the uv plane may fall within a single grid cell, but span multiple gridcells in the outer regions of the uv plane. Thus, the gridded Ns (k) used in calculating Dk will change dependingon this fractional bandwidth and affect what resolution uniform weighting yields (along with the entire robust
3 In gridded imaging such as that used by CASA, uniform weighting is normalized by the number of visibilities in a given gridcell, rather than a region directly centered on each visibility. This is the origin of the effects discussed for the perchanweightdensity
parameter.

7.4. ANGULAR RESOLUTION AND BEAM SHAPE

91

Figure 7.6: Angular resolution achieved using different values of the CASA robust parameter for a 1-hourobservation at 100 GHz and a declination of -23 deg in the notional C43-4 configuration. Note that robust = −2
is close to uniform weighting and robust = 2 is close to natural weighting. The dotted line corresponds to k = 1.
trade-off curve). Similarly, the image size (imsize in CASA) can also have a few to 10% effect since the finer uv
gridding associated with a larger field-of-view and number of image pixels changes the weighting scheme andits effect on the synthesized beam.
Additionally, the exact method used for the uniform weighting normalization has an impact on the resultant
resolution for spectral cubes. CASA versions prior to 5.6 had historically used a method in which the full dataset
was used to calculate Ns (k), and then these weights were applied to the data in each channel. As the Ns (k)calculated for the full dataset is a less good descriptor of the uv density distribution for edge channels than it
is for central channels (due to the to fractional bandwidth effects described above), this results in a ‘spectral
curvature’ where edge channels have a different beam size and RMS noise compared to central channels.
In CASA 5.6, a new parameter perchanweightdensity was introduced to TCLEAN to alleviate this spectral
curvature. The old behavior is equivalent to perchanweightdensity = F alse, while perchanweightdensity =T rue forces Ns (k) to be calculated on a per channel basis. This removes the spectral curvature, but dramaticallylimits the effective range of beam sizes that Briggs weighting can provide and shifts the beam sizes for a given
value of robust closer to naturally weighted beam. In CASA 5.6 and above, perchanweightdensity is set to
T rue as the default. The ALMA project has retained perchanweightdensity = False for QA2 until such a timeas the impact of setting it to True can be properly accounted for in all subsystems since it changes the beam
size in a way that depends upon the uv-coverage and correlator configuration, and reduces the extent to whichchanging robust can mitigate mismatches between the achieved beam and the PI requested AR. It is important
to note that in order to achieve similar results between the OT and simulations with CASA ≥5.6, perchanweightdensity must be explicitly set to F alse.

7.4.3

Other factors affecting beam size and shape

Source declination directly impacts uv plane sampling during the observation(s), and thus the beam shape. In
addition to shadowing, sources that must be observed at low elevations also have shorter projected North-Southbaselines, causing the shape of the uv plane sampling distribution and the beam shape become more elliptical.
For example, Figure 7.7 shows the different beam shapes for sources observed at declinations of −70◦ (similar
to the SMC and LMC) and −30◦ . Figure 7.8 shows the uv-coverage for these sources, revealing the projection

92

CHAPTER 7. IMAGING WITH ALMA

Figure 7.7: Beam shape for notional configuration C43-1 with a 2-hour observation of a transiting source at a
declination of either −70◦ (left) or −30◦ (right).
and subsequent ellipticity of the uv plane sampling distribution, together with the large fraction of shadowing,
for the more southern sources. To mitigate this effect, one can convolve the resulting images to a more circular(albeit larger) beam after deconvolution.
To demonstrate the range of these effects across the declinations observable with ALMA, Figure 7.9 shows
the minor and major axes of the synthesized beam widths (θres ) for each notional array configuration as afunction of source declination for a 2-hour observation at 100 GHz, imaged with robust=0.5. Figure 7.10 shows
the geometrical mean of the major and minor axes of θres at the same frequency. The beam width scales with λ,but bear in mind that not all configurations can be used with the higher-frequency bands. Also, note that thesevalues are given for the notional configurations. As discussed in Section 7.2, the C-X configurations generally
result in ∼4% larger beams than the notional C43-X configurations, with real operations falling between these
two limiting cases.
If the imaging requirements of a project are particularly scientifically critical, then for purposes of proposal
preparation it is advisable to carefully evaluate the expected performance using CASA simulations that employ
the notional configurations, target declination, and expected uv-coverage of the proposed observations. In thiscase it is also advisable to include realistic noise and to CLEAN 4 the images carefully in order to realisticallyassess the results that can be expected. Special care should be given to assessing the range of acceptable θres ,taking into account the range of possible achieved θres for a given request, including the applicable QA2 beam
criteria and the in-practice deviations discussed in Section 7.2 (typically a ∼4% enlargement due to the presenceof additional antennas, although C-8 and C-9 are special cases).

7.5

Snapshots

The sampling function S of the visibility distribution is defined as:S(u, v) =NX

δ(u − uk , v − vk )

(7.5)

k=1
4 Most interferometric imaging in CASA is now done using TCLEAN, which is an improved implementation of the CLEAN
algorithm. The CLEAN task in CASA has been deprecated; in a near-future release, CLEAN and TCLEAN will be renamed andeventually the “old” CLEAN will be removed from the code.

7.5. SNAPSHOTS

93

Figure 7.8: uv plane coverage for notional configuration C43-1 with a 1-hour observation of a transiting source
at a declination of either −70◦ (left) or −23◦ (right). For the source with a declination of −70◦ , 25.7% ofvisibilities are expected to be flagged due to shadowing.

Figure 7.9: Cycle 8 angular resolutions as a function of source declination. Each stripe shows, for a particular
notional configuration, the range of the major and minor axes of the synthesized beams expected from a 2-hourobservation at 100 GHz and at transit, imaged with robust = 0.5. The notional 12-m Array configurations arearranged with C43-1 at the top and C43-10 at the bottom.

94

CHAPTER 7. IMAGING WITH ALMA

Figure 7.10: Geometrical mean of the major and minor axes of the synthesized beams as a function of source
declination. These correspond to a 2-hour observation at 100 GHz and at transit, imaged with robust = 0.5.
The notional 12-m Array configurations are arranged with C43-1 at the top and C43-10 at the bottom. The
7-m Array is also shown.
If S were a continuous function, e.g., a Gaussian, the synthesized beam would also be a Gaussian i.e., a central
peak with a smoothly decreasing response away from the center. Given the finite number of baselines, however,the sampling function is an ensemble of Dirac delta functions and its Fourier transform is a central peaksurrounded by a complex pattern of sidelobes. This “dirty beam” response is a consequence of the gaps in theuv plane, the sidelobes becoming increasingly prominent as the gaps increase (following the Gibbs phenomenon).
Conversely, as there are fewer gaps in the uv plane— i.e. better the uv-coverage— the PSF sidelobes becomeless prominent.
Because the baseline lengths and orientations as seen from the source change as a function of time due to the
Earth’s rotation, the uv-coverage increases and the PSF sidelobes are commensurately reduced in proportion to
the duration of the observation. Therefore, long integrations on a target can give better image quality. Short
integrations can still be valuable if the science target has a relatively compact, simple structure and is not
too faint. Such observations are sometimes called snapshots, and they produce obvious sidelobes which can be
mitigated by applying a uv taper, i.e. down-weighting of the visibilities on longer baselines, during the imaging
process. The uv taper is represented as the set of taper weights Tk in Equation 7.2.
Configuration
naturalbriggs (R = 0.5)
uniform

7-m
44.0%
42.2%
39.0%

C43-1
5.5%
7.8%
7.7%

C43-2
5.0%
6.6%
16.7%

C43-3
6.2%
6.7%
12.4%

C43-4
10.4%
7.3%
11.0%

Configuration
naturalbriggs (R = 0.5)
uniform

C43-6
4.6%
6.2%
11.3%

C43-7
9.6%
5.6%
11.2%

C43-8
7.8%
9.7%
10.1%

C43-9
11.1%
9.6%
8.5%

C43-10
13.0%
11.3%
12.0%

C43-5
6.3%
8.0%
13.1%

Table 7.3: Sidelobe levels for a 1-hour observation of an unresolved source at a declination of −23◦ with thedifferent notional array configurations. The levels are indicated with three different weighting schemes used for
imaging.
Table 7.3 gives the level of sidelobes for each notional configuration, for a 1-hour observation of a source at

7.6. LARGE SPATIAL SCALE RESPONSE

95

Figure 7.11: uv plane sampling distributions of a model ALMA observation with 1-minute integration (left) and1-hour integration (right), using the notional C43-1 configuration to observe a source at a declination of −23◦ .
Dec=−23◦ . Figures 7.11 and 7.12 show examples of a uv plane sampling distribution and cleaned image fora snapshot of 1-minute duration and a longer integration of 1-hour duration using the notional configuration
C43-1. As shown in Figure 7.11, the uv-coverage in 1 minute is quite uniformly sampled, but much less dense
than that of the 1-hour integration. In addition, the cleaned images of the snapshot and the longer integration(see Figure 7.12) are similar in terms of angular resolution and the apparent differences are quite small. The
main difference between the two (besides sensitivity) is in the dirty beam: the sidelobe level for the snapshot
will be much higher than for the 1-hour integration. The snapshot image will then require more careful cleaning
in order to avoid introducing spurious sources from the strong sidelobes. Condon et al. (1998) gave a very
comprehensive description of how this issue impacted the 20-cm NRAO VLA Sky Survey (NVSS).
A useful practice to disentangle sidelobe effects from real point sources, especially in imaging cases withhigh dynamic range, is to perform CASA simulations using a component list of the strongest sources together
with the notional array configuration. This test allows one to estimate the sidelobe fingerprint left by thestrong point sources after deconvolution (cleaning), although the residuals will likely be higher in practice due
to imperfect calibration. It is worthwhile to use the interactive mode during the deconvolution so that residuals
can be monitored. Finally, careful “masking”— or identification of spatial regions with reliably real emission—
can improve the dynamic range. Best results are obtained by carefully editing the mask at each (major) cycleof clean. Recent CASA versions include an automated clean masking heuristic which can improve image quality
over what is achieved with a broad or static clean mask (Kepley et al., 2020).

7.6

Large Spatial Scale Response

As described in Chapter 3, an interferometer measures the Fourier components of the sky brightness distribution
in an area of the uv plane defined by the array configuration used to observe the target. There is, in particular,some shortest baseline that a given array and configuration measures, ultimately limited by the physical size ofthe antennas. This shortest baseline corresponds to some largest spatial scale which can be usefully imaged by
the interferometer.
This spatial filtering is a serious issue that must be considered carefully for each science case. To illustrate
the concept, the annularly averaged amplitudes of the Fourier transforms of three uniform disks with sizes of
500 , 1000 and 2000 are shown in Figure 7.13 for an observation at 100 GHz. The smallest uniform disk is closest
to a point source and so it has power up to a baseline of 180 m. Meanwhile, the most extended disk has power
only up to ∼40 m. Therefore, an array with only baselines larger than 40 m will not be particularly sensitive
to emission on spatial scales larger than ∼2000 , and will filter out most of the emission from such an extended
disk.
An important consequence of such filtering is that an interferometer only detects a fraction of the total flux

96

CHAPTER 7. IMAGING WITH ALMA

Figure 7.12: Images obtained from a model ALMA observation with 1-minute integration (left) and 1-hour
integration (right), using the notional C43-1 configuration to observe a source at declination of −23◦ . Black
contours at 100, 200, 300, 500, 700 and 900 mJy beam−1 are overlaid.
density for sources with emission on size scales larger than its shortest baseline. Indeed, if the source only has
structures on size scales larger than the shortest observed baselines, one can “resolve out” the source entirely.
In order to ameliorate the effects of spatial filtering on extended sources, the 7-m and TP Arrays are available
to supplement the 12-m Array configurations if needed.
To quantify these effects, the maximum recoverable scale (θM RS ) is defined as the largest spatial scale towhich a given array is sensitive. It is in principle determined by the length Lmin of the shortest baseline in thearray, which measures spatial scales (i.e. Fourier modes with a period) of λ/Lmin . In practice, the uneven uv
coverage at the shortest baseline means that the sensitivity of this measurement to such large structures is notvery good, and a smaller value of θM RS is typically adopted. The exact filtering depends on the details of thelarge-scale structure as well as the short-baseline uv-coverage, and it is best determined by simulations. ALMA
has adopted a criterion of measuring 10% of the total flux density of a uniform disk, which for well-constructed
array configurations yields:
θM RS ≈

0.6 λ[radians]
Lmin

(7.6)

where λ is the observing wavelength in meters, and Lmin is the shortest baseline in meters. For reasons similar
to those explained in Section 7.4, ALMA uses the 5th percentile shortest baseline L5 instead of the very shortest
baseline Lmin to calculate θM RS ; using simulations of configurations the following equation was empiricallydetermined:θM RS ≈

0.983 λ[radians]
L5

(7.7)

where λ is the observing wavelength in meters, and L5 is the 5th percentile of uv distance in meters. This is theequation used to assess MRS in the OT for purposes of choosing configurations during proposal preparation.
Table 7.1 lists the θM RS for the different array configurations. If the scientifically required θres and θLAS cannot
be achieved by a single array or configuration, multiple 12-m configurations and/or the 7-m and TP arrays,
will be called for, as described in Section 7.8. Note that these expressions assume good uv-coverage. This is
typically the case for ALMA 12-m Array observations, but may not be for very short 7-m Array observations
due to the relatively small number of antennas.

977.7. MOSAICING

5 arcsec
10 arcsec
20 arcsec
0.8

V

0.6

0.4

0.2

0.0

0.20

50

100
UV radius (meter)

150

200

Figure 7.13: Annularly averaged amplitudes of the expected visibilities of three model uniform disks (annularaverages) at 100 GHz as a function of uv distance.
To emphasize the dependence of these effects on source structure, Figure 7.14 shows the annularly averaged
visibility amplitudes versus uv distance of an example astronomical source, M51. This example is taken froman H-α image, but it is used as a model to indicate the spatial structure expected at 100 GHz. The amplitudesof the visibilities can be approximated as a power law of uv distance with a negative index. This distribution
indicates that most of the power is located in larger scale structures and that power decreases rapidly at smallerscales. In this example, the visibility amplitude detected by the 7-m Array (at kuv ≈ 5kλ) would be ∼23 Jy,
whereas that detected by the notional configuration C43-6 (kuv ≈ 200kλ) would only be ∼0.9 Jy. As each source
will be different, ALMA users should ideally use simulations to estimate the power distribution and subsequent
flux recovery for targets they wish to observe.

7.7

Mosaicing

The field of view of a single interferometer pointing is determined by the antenna primary beam. A uniformly
λilluminated, circular aperture will have a beam width at half maximum (F W HM ) of 1.02 D. It will also havevery high side lobes due to the abrupt truncation of the antenna illumination pattern; indeed, these side lobes
would be particularly problematic for single-dish observations. Most radio and millimeter receivers illuminate
their antennas with approximately Gaussian illumination patterns that smoothly go down to -10 dB to -15 dB
response at the edges of the dish. The ALMA feedhorns were designed to illuminate the dish with a -12 dB edge
taper to provide a nearly Gaussian primary beam with low sidelobes while preserving as much of the resolution
and sensitivity as possible. This trade-off is a fundamental aspect of radio telescope design. The resulting
λF W HM of the ALMA 12-m antennas is measured to be F W HM = 1.13 D= 5800 at 100 GHz, and it varies
inversely with frequency. For example, Figure 7.15 shows a Gaussian profile that approximates the shape of the
primary beam at 112 GHz with F W HM = 5200 . As described in Chapter 3, the primary beam attenuation canbe corrected as the last step of imaging. In addition to correcting the sky distribution of the signal to its correct
value, however, this correction also increases the noise with angular distance from the primary beam center.
For example, at the radius of the FWHM, the noise will be increased by a factor of two compared to that at the
primary beam center. Moreover, if a map size larger than approximately the F W HM of the primary beam isrequired, then it is necessary to observe several adjacent pointings, i.e., a mosaic, to recover the sky emission.
The default mosaic pointing pattern used by ALMA is a fully sampled hexagonal grid with equilateraltriangles whose vertices are separated by θhex = Dλ√3 = 0.511 × F W HM . With this spacing, the mosaic will

98

CHAPTER 7. IMAGING WITH ALMA

Figure 7.14: Image of Hα emission from M51 used as a model of emission at 100 GHz (left) and the expectedvisibility amplitudes (logarithmic scale) plotted versus uv distance (right). Note that M51 cannot be observed
from ALMA.
sample the emission at the Nyquist
spatial frequency. Note that a hexagonal mosaic has spacing θhex along a√3
row (e.g., in right ascension) and 2 θhex between rows (e.g., in declination). Figure 7.16 gives an example ofsuch a mosaic. To estimate the number of pointings (Np ) necessary to cover an area of LX × LY using thishexagonal pattern, the following expressions
can be used:
LX
NX = (int) 0.511F
+
1.
W HM

NY

=

2×LY √+ 1.
0.511F W HM 3
(2NX − 1.) × N2.Y

(int)

Np ≈
For an observation at 100 GHz with LX = LY = 4 arcmin, 85 pointings are defined, similar to that obtainedby the above formulae. In the case of an odd number of rows, Np may differ slightly from the value returnedby the OT. Note that mosaicing with the 7-m Array is more efficient because with the smaller diameter of its
λantennas, the FWHMs are commensurately larger (F W HM = 1.13 Dalso holds for the 7-m antennas).
Like a single pointing, a mosaic has an analogous “mosaic primary beam response pattern” that is the
combination of the individual primary beams of the different pointings. Near the mosaic center, a Nyquist
sampled hexagonal mosaic pattern has a sensitivity about 1.58 times that of a single pointing, with the sensitivity
decreasing with the fall off of the mosaic√primary beam response pattern. Another frequently used mosaic pattern
has pointings separated by F W HM/ 2 (see for example the NVSS survey); this pattern covers an area more
efficiently but with little gain in sensitivity over a single pointing. Generally, the Nyquist sampled hexagonal
pattern (the default for ALMA) is a good choice for smaller mosaics and the sparser hexagonal pattern ismost often used for larger mosaics. The ALMA Observing Tool (OT) can be used easily to set up a mosaic ofadjacent pointings with a user-defined√spacing, though it is not recommended to exceed spacings greater thanthe constant noise pattern (F W HM/ 2) if a well-sampled mosaic image is desired.

7.8

Multi-array and Multi-configuration Observations

As shown in Table 7.1, different 12-m Array configurations provide different angular resolutions, θres , which
are a function of the longest baselines of the configuration. Similarly, the maximum recoverable scales, θM RS ,of each configuration depend on the shortest baselines present. To achieve the requirements entered by the PI
in the OT, θres and θLAS , multiple configurations may be needed. Note that θLAS is a property of the sciencetarget, while θM RS is a property of an array configuration. In particular, the most compact configuration for a
project must ensure that θM RS is larger than or equal to the θLAS of the science target.
Based on the user-entered values of θres and θLAS for a given Science Goal, the OT will automatically attempt

7.8. MULTI-ARRAY AND MULTI-CONFIGURATION OBSERVATIONS

99

Figure 7.15: Approximation of the primary beam profile of an ALMA 12-m antenna at 112 GHz with FWHM
= 5200 .

Figure 7.16: An example of mosaicing with a field of 2 arcmin extent at 100 GHz using a hexagonal patternwith Nyquist sampling (white crosses).

100

CHAPTER 7. IMAGING WITH ALMA

to choose configurations that will produce a final image with the requested scientific goals5 . In order to provide
good image quality, there are some restrictions on which arrays and configurations can be combined (based
mostly on the uv-coverage each provides). For example, at most two 12-m Array configurations are allowed andthe most extended configurations (C-10) cannot be combined with any more compact configurations. If such
restrictions result in the requested θLAS not being achievable, the OT will return a validation error and θLAS
must be modified. These allowable configuration pairings in the OT represent a set of designed, validated, andsupported pairings for imaging, but a PI may also request any set of array configurations as separate Science
Goals (for example to provide complementary shorter spacings for C-10 observations). With such an ad hoc
setup, simulations of the observations are highly recommended to determine how imaging would be affected.
Since the middle of Cycle 4, a “stand-alone ACA” option has been offered for observations that use the 7-m
Array, with the TP Array added if required, but without 12-m Array observations. It is currently not possible
to request observations that only require the TP Array except as complements to existing 7-m Array data thatsuggest that it is scientifically needed.
In detail, the array configuration combinations are selected as follows:
1. An interferometric array configuration (12-m or 7-m) is selected that comes closest to achieving the enteredvalue of θres .
2. If the θM RS of this array configuration is less than the requested θLAS , the largest structures in the source
will not be well imaged. A more compact 12-m Array configuration will be added, if allowed by the set ofcombinations listed in Table 7.4.
3. If the θM RS of the most compact configuration included thus far is still less than the requested θLAS , a
7-m Array component will be added.
4. If θM RS is still < θLAS , a TP Array component will be added if possible. Single dish continuum, Band9, and Band 10 observations are not currently supported so there is a fundamental limit to how large asource can be reliably imaged in these cases.
This procedure is carried out automatically by the OT and is entirely dependent on the values of θres and θLAS
that are entered by the user. A detailed list of the allowed combinations is given in Table 7.4. Figure 28 of the
Cycle 8 2021 ALMA Primer gives visual representation of required array combinations as a function of θres andθLAS .
Note: if the PI specifies a range of θres there may be multiple 12-m array combinations which could achieve
the Science Goal. For instance, C-5 or C-4 could serve for the extended 12-m configuration. This would imply
C-2 or C-1, respectively, for the compact 12-m configurations; but C-5 plus C-1 is not an allowed combination.
In this situation, the initial observations will narrow down the range of possibilities such that subsequent data
will be taken in the most “compatible” array combinations. In this example, if C-5 data are collected first, thenevery effort will be made to collect all of the extended array data in C-5, and subsequent, compact configuration
observations will be taken in a C-2-like configuration. For purposes of total time calculations in Phase 1, themost expensive combination will be assumed.
Table 7.4 also shows the relative integration times that will be used by each array/configuration. While
the overall integration time is set by the specific requirements of the Science Goal a PI defines, the relative
integration times between its component configurations/arrays are determined by general considerations as
discussed in Mason & Brogan (2013). The relative integration times do not depend on the details of the Science
Goal beyond the fact that the Science Goal definition determines which combination of configurations or arraysis needed. Broadly speaking, because of their smaller collecting areas, the TP and 7-m Arrays require more
on-source integration time than the 12-m Array. Furthermore, it is evident that the higher surface brightness
sensitivity of the more compact 12-m Array configurations requires longer 7-m Array integrations. These time
ratios were calculated by simulating matched image sensitivities when the more extended of two arrays or
configurations is uv tapered to give the same angular resolution as the more compact configuration. Thisapproach, used since Cycle 6, is an incremental improvement to the approach used in previous Cycles and which
was described in Mason & Brogan (2013). The actual time ratios adopted for ALMA observations, while guided
by these calculations, are subject to further operational constraints. In particular, the ideal time ratios are
5 The entire suite of potential multi-array/configuration observations that satisfies the Science Goal requirements is the GroupObs Unit Set or GOUS. The indvidual array, individual configuration components it comprises are the Member Obs Unit Sets or
MOUSes.

101

7.8. MULTI-ARRAY AND MULTI-CONFIGURATION OBSERVATIONS

θres (arcsec)
0.042
0.042
0.057
0.057
0.057
0.096
0.096
0.096
0.211
0.211
0.211
0.306
0.306
0.306
0.306
0.545
0.545
0.545
0.545
0.918
0.918
0.918
0.918
1.42
1.42
1.42
2.3
2.3
2.3
3.38
3.38
3.38
12.5
12.5

θLAS (arcsec)< 0.496> 0.496< 0.8140.814-4.11> 4.11< 1.42
1.42-6.7> 6.7< 2.58
2.58-11.2> 11.2< 4.11
4.11-16.2
16.2-66.7> 66.7< 6.7
6.7-22.6
22.6-66.7> 66.7< 11.2
11.2-28.5
28.5-66.7> 66.7< 16.2
16.2-66.7> 66.7< 22.6
22.6-66.7> 66.7< 28.528.5-66.7> 66.7< 66.7> 66.7

Array combination
C-10
C-9
C-9 + C-6
C-8
C-8 + C-5
C-7
C-7 + C-4
C-6
C-6 + C-3
C-6 + C-3 + 7-m
C-6 + C-3 + 7-m + TP
C-5
C-5 + C-2
C-5 + C-2 + 7-m
C-5 + C-2 + 7-m + TP
C-4
C-4 + C-1
C-4 + C-1 + 7-m
C-4 + C-1 + 7-m + TP
C-3C-3 + 7-m
C-3 + 7-m + TP
C-2
C-2 + 7-m
C-2 + 7-m + TP
C-1
C-1 + 7-m
C-1 + 7-m + TP
7-m
7-m + TPTime ratios
1
1
1 : 0.21
1
1 : 0.22
1
1 : 0.23
1
1 : 0.25
1 : 0.25 : 0.6
1 : 0.25 :0.6 : 1.0
1
1 : 0.26
1 : 0.26 : 1.21
1 : 0.26 : 1.21 : 2.1
1
1 : 0.34
1 : 0.34 : 2.4
1 : 0.34 : 2.4 : 4.0
1
1 : 2.4
1 : 2.4 : 4.1
1
1 : 4.7
1 : 4.7 : 7.9
1
1: 7
1 : 7 : 11.9
1
1 : 1.7

Total Time
1.0 × ∆extended
1.0 × ∆extended
1.21 × ∆extended
1.0 × ∆extended
1.22 × ∆extended
1.0 × ∆extended
1.23 × ∆extended
1.0 × ∆extended
1.25 × ∆extended
1.8 × ∆extended
2.3 × ∆extended
1.0 × ∆extended
1.26 × ∆extended
2.5 × ∆extended
3.3 × ∆extended
1.0 × ∆extended
1.3 × ∆extended
3.7 × ∆extended
5.3 × ∆extended
1.0 × ∆extended
3.4 × ∆extended
5.1 × ∆extended
1.0 × ∆extended
5.7 × ∆extended
8.9 × ∆extended
1.0 × ∆extended
8.0 × ∆extended
12.9 × ∆extended
1.0 × ∆extended
2.7 × ∆extended

Table 7.4: Array/Configuration combinations with the corresponding {θres , θLAS } conditions for an observation
at 100 GHz. All time ratios are with respect to the time spent in the most extended configuration. Thus,
1:2:3 means 1h in the most extended array; 2h in the intermediate array; and 3h in the most compact array.
Similarly the most extended configuration determines the angular resolution. The actual resolution obtainedwith combined configurations can be 50% lower due to different weighting (see text). Note that for the fullarray combination, the total time is not equal to the sum of the individual times because TP and 7-m Arrayobservations are run in parallel.

often impractically large for the 7-m and TP Arrays being used with C-1 or C-2. In previous Cycles, the time
ratio was “capped” at a maximum value— typically 5 for adjacent arrays or configurations in a given imaging
combination (with imaging combinations defined by Table 7.4). Starting in Cycle 6, a less restrictive cap of 7
for adjacent arrays or configurations was adopted, but in practice this choice only affects the 7-m Array time
ratio with respect to C-1 and C-2. Furthermore, all 7-m:12-m Array time ratios are rescaled by the factor bywhich the 7-m:C-1 time ratio was reduced from its ideal value. This approach has the effect of more uniformly
applying the operational constraint across different arrays and configurations with a modest and consistentimpact on image characteristics.
Several additional considerations can impact the relative observing times which the OT sets up for different

102

CHAPTER 7. IMAGING WITH ALMA

arrays in practice. First, the OT enforces a minimum on-source integration time in order to ensure that thetelescope is used efficiently. The minimum allowed on-source time is taken to be the greater of 5 minutes
and half of the integration time spent on the bandpass calibrator. Second, the 7-m Array needs integrationsof at least 1 hour to provide sufficient uv-coverage for good image quality6 . Snapshot observations with the
7-m Array are therefore strongly discouraged (see also Section 7.5). Third, for total power observations it isnecessary to observe a slightly larger area than the region of interest specified in the Science Goal in orderto obtain sufficiently high-quality information over the entire region. Finally, when a custom (12-m Array)mosaic is specified by the PI, the OT attempts to identify the appropriate corresponding 7-m and total power
map coverages which are needed. The actual implementation of this heuristic will, however, give rise to somevariation in the relative observing times, depending on the geometry of the PI-specified custom mosaic. In
addition, when selecting "time simultaneous" mosaic observations in the OT for the 12-m and 7-m Arrays, theOT will not select the same number of pointings for both arrays but select the optimal number of pointings thein 7-m array that cover the specified 12-m array area.

7.9

Multi-array and Multi-configuration Imaging

If data have been collected in multiple arrays or configurations as described in Section 7.8, the data from eachwill be processed separately and delivered if they pass Quality Assurance (see Section 11). At present, PI’s
are responsible for combining these products together, although they are encouraged to contact their ARC for
assistance if desired. PI’s may also refer to the ALMA M100 Science Verification CASA Guide7 for detailed
guidance on data combination. It is important to note that when combining data from multiple arrays or
configurations, the resultant non-Gaussianity of the dirty beam may cause a bias in flux measurement. Thiseffect is discussed by Jorsater & van Moorsel (1995), who present an analytic correction and also note that it
can be mitigated by deeper cleaning.
The recommended combination procedure comprises either one or two steps, depending on whether or not
total power data are collected. First, the interferometric data will be imaged together in a single, “joint”
deconvolution. This step can be done in CASA by passing all interferometric measurement sets— 7-m and one
or more 12-m Array configurations— directly to the TCLEAN task. All 7-m and 12-m data delivered during
Cycle 8 can be directly combined by the PI8 .
If total power data are part of a project, then there is a second step to the combination procedure, where
the deconvolved interferometric (7-m+12-m) image cube is combined with the total power image cube. The
recommended procedure is to do this by “feathering” them together. Feathering is a commonly used techniquein radio imaging for combining two images together by forming a weighted sum of their Fourier transforms. The
procedure is as follows:
1. The total power and interferometer images are Fourier transformed.
2. The beam from the total power image is Fourier transformed (F T SDB(u, v)), to be used as a weighting function. Alternatively, one can specify some smaller portion of the total power antenna aperture,corresponding to a wider (single-dish) beam.
3. The Fourier transform of the interferometer image is multiplied by (1 – F T SDB(u, v)). This step downweights the large spatial scale components of the interferometer map which are poorly measured, if measured at all.
4. The Fourier transform of the total power image is multiplied by the ratio of the volumes of the interferometer restoring beam to the single-dish beam, thereby putting the maps in the same units.
6 For a mosaic, this needed minimum integration time is applicable to each pointing in the mosaic plus its immediately adjacentpointings. Since the OT enforces a time-on-source minimum at the science target (not per mosaic pointing) level, simulations areadvised if large, high dynamic range 7-m Array mosaics are sought.
7 https://casaguides.nrao.edu/index.php/M100_Band3
8 Manually calibrated data deliveries from early ALMA Cycles that were calibrated using CASA versions earlier
than 4.3 require a special procedure to put the 7-m and 12-m Array data weights on an equal basis before thedata can be combined.
The required steps are described in the “Data Weights and Combination” CASA guide
https://casaguides.nrao.edu/index.php/DataWeightsAndCombination. All ALMA data calibrated by the ALMA Pipeline havecorrect weights, irrespective of Cycle number or CASA version.

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5. The results from 3 and 4 are added and Fourier transformed back to the image plane.

Figure 7.17: Expected uv-coverage for a notional C43-1 (1 hour) and 7-m observations (5 hours)

Figure 7.18: Radial density of uv-coverage with uv-distance using notional C43-1 (1 hour) and 7-m observations(5 hours)
The resulting cube provides high angular resolution due to the interferometric data, but will have moreaccurate large-scale features and total flux densities because the single dish data are present as well. A thorough

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explanation of feathering is given by Cotton (2017), and a comparison to other techniques for combining single
dish and interferometer data is found in Stanimirovic (2002).
An alternative method of combining interferometric and TP data is possible using a tool called tp2vis, which
was developed as a NA ALMA Development Study9 . This method, which can be run in CASA, converts a total
power image into appropriate uv data (pseudo-visibilities) which are then concatenated together with the muchhigher resolution interferometric data. This entire uv data set can then be cleaned to obtain an image that
contains all angular scales.
As an example, the uv-coverage and uv plane sampling distributions for a 1-hour observation with the notional C43-1 configuration and 5-hour observation with the 7-m Array are shown in Figure 7.17 and Figure 7.18,
respectively. The Cycle 8 7-m Array configuration with ten 7-m antennas provides uv measurements in the range
8-32 m and overlaps the 12-m Array configurations in the range Ruv < 15 m.

Figure 7.19: Simulated images obtained using notional C43-3 (top left; 1 hour), notional C43-3 + C43-6 (topright; 1 + 3.3 hours) and notional C43-3 + C43-6 + 7-m (bottom left; 1 + 3.3 + 1.3 hours) Array combinations,and the image model itself (bottom right).
Using the Hα emission of M51 as a hypothetical model (see Figure 7.14), Figure 7.19 shows the simu9 https://github.com/tp2vis/distribute

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105

lated images resulting from observing with a notional C43-compact configuration (C43-3) only; a compact plus
extended 12-m configuration (C43-3 + C43-6); and finally of also adding the 7-m Array. Natural weighting
was used and deconvolution was performed using the CLEAN algorithm (TCLEAN now recommended). The
recovery of larger scales is quite noticeable with the inclusion of the 7-m Array data. Using only the C43-6
configuration at 100 GHz provides an angular resolution of 0.2700 . Combined with the C43-3 configuration, theangular resolution is lowered to 0.3100 . Finally, the angular resolution with the full combination (C43-3 + C43-6+ 7-m) is 0.3200 , very similar to that of only the two 12-m Array configuration data but 17% larger than the
angular resolution obtained with the extended 12-m Array data alone. That difference is due to the respective
uv-coverage and weight of the array configurations in the combined dataset.
These simulations illustrate two general features of multi-configuration/array observations. First, they are
effective in retrieving a wider range of spatial scales than are accessible to a single configuration or Array.
Second, the addition of more compact configurations or arrays does tend to broaden the synthesized beam(PSF) slightly. This broadening can be mitigated by changing the uv weighting, e.g., via the robust parameter,
potentially at the expense of sensitivity and θRM S . These effects can be explored via the use of simulations
with the notional configurations.
References[1] Andrews, S. et al. 2018, Ap.J. 869, L41[2] Briggs, D. S. 1995, High Fidelity Deconvolution of Moderately Resolved Sources Ph.D. thesis, New Mexico
Institute of Mining and Technology[3] Briggs, D. S., Schwab, F.R., Sramek, R. A. 1999, Synthesis Imaging in Radio Astronomy II, ASP Conference
Series, 180, 127[4] Condon, J. J., R, W. D., Greisen, E. W., Yin, Q. F., Perley, R. A., Taylor, G. B., Broderick, J. J. 1998, AJ,
115, 1693[5] Cotton, W. D. 2017, PASP, 129, 094501[6] Jorsater, S. & van Moorsel, G. 1995, AJ 110, 2037
[7] Mason, B. & Brogan, C., 2013, Relative Integration Times for the ALMA Cycle 1 12-m, 7-m, and Total
Power Arrays, ALMA memo 598[8] Moriarty-Schieven, G. ed., 2021, Observing with ALMA: A Primer (Cycle 8 2021), ALMA Doc. 8.1, ver. 2[9] Stanimirovic, S. 2002, in Single-Dish Radio Astronomy: Techniques and Applications, edited by S. Stanimirovic, D. Altschuler, P. Goldsmith, & C. Salter, vol. 278 of Astronomical Society of the Pacific Conference
Series, 375. astro-ph/0205329[10] Keply, A. et al. 2020, Publications of the Astronomical Society of the Pacific, Volume 132, Issue 1008, pp.
024505

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Chapter 8

Observing Modes
The ALMA Observing Modes are the set of capabilities that ALMA offers each cycle to its user community.
Before offering a particular mode to the community, it is implemented in the ALMA online software package andverified using the required hardware. Here, the software implementation is described along with a descriptionof particular observing modes.
An observing proposal submitted to the ALMA archive will have an associated structure called the Observing Project that will accompany it along the whole length of its lifecycle. This structure is defined in the
ALMA Project Data Model (APDM), which specifies all the relevant components and their contents needed forsuccessful completion of a project. A summary view of the constituents of an Observing Project is shown in
Figure 8.1.

8.1

Observing Project Structure

The organization of each science project is subdivided into a well-defined structure with clear hierarchicallevels. At the bottom of this structure are the Scheduling Blocks (hereafter, SBs). An SB is the minimum set of
instructions describing an ALMA observation that can be fully calibrated. Projects are broken down into a setof these fundamental units for flexibility, given the properties of the ALMA site and the continuously-varying
status of the Observatory as a whole (including the weather), and to encapsulate the scientific objectives of the
proposal into individual entities. After a proposal has been accepted for observation, the SBs to be executedduring the observations are produced automatically by the ALMA Observing Tool (hereafter OT) during thePhase 21 . The SB may be edited, using the OT, in Phase 2 after the proposal has been accepted for observation
and also during the project execution if necessary2 .
An SB contains a large amount of information about what should be observed including, but not limited to,the positions and velocities of the science targets, details of the correlator setup and the integration and cycle
times of the different calibrations. However, the SB itself does not control the observations as it is just a single
set of XML instructions. Instead, the ALMA online software reads the SB and executes the observing script
appropriate to the type of observation required (e.g., single-dish, single field interferometry, etc.). The SB has
relatively little influence over the order in which the various sources are observed and does not describe all of thecalibrations that should be performed (a prime example being the measurements of the system temperatures).
Each SB typically consists of set-ups, calibrations, and target observations that can be observed within 1.5
hours. The end of an SB execution may be specified in terms of a maximum amount of time or when certain
well-defined science goals have been reached as specified in the Science Parameters section of the SB. An SB
cannot be stopped and re-started. Therefore, an SB either runs to completion, fails, or is terminated by the
Astronomer on Duty (hereafter AoD). Given the limited duration of the SBs, it is often necessary to observe
them several times to achieve the sensitivity required by the PI. The current maximum execution time fora particular SB has been chosen based on statistical measurements of the stability of the system. A system
failure may prevent the online software from storing the data in the archive, resulting in the loss of the observed
1 For a description of Phase 1 and Phase 2 see the Cycle 8 2021 Proposer’s Guide stage of the project lifecycle and associateddocuments
2 SBs can also be created in an ad-hoc manner for commissioning purposes

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Figure 8.1: Block diagram of an Observing Project from the point of view of the observation preparation (top)and internal hierarchical structure of the Scheduling Block in actual executions (bottom). All projects have thesame ObsUnitSet (OUS) levels, the Science Goal OUS level, the Group OUS level and the Member OUS level.
Scheduling blocks are attached to the Member OUS. Each time a Scheduling Block is executed, Control createsa new Execution Block structure (see text).

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project data. Thus, executing SBs for more than two hours becomes unsafe from the operational perspective.
To optimize this scheme, the concept of a session was implemented, which is the continuous execution of asingle SB until a certain goal has been reached (see detailed description later on). Sessions have the added
benefit that some of the calibrations can be shared among the different executions, which increases the overall
observing efficiency. For Cycle 8, sessions are primarily used for polarization and VLBI observations.
While the SB is the smallest entity used for observing, the Observing Unit Set (hereafter OUS) is the smallest
unit for data processing3 . The SB/Member OUS/Group OUS (hereafter MOUS and GOUS, respectively) are
the smallest structures that hold science observations that need to be observed/processed/combined together.
These data hierarchies therefore maximize observing flexibility and ensure that data gets processed as early andas fast as possible. In the OT, observations are divided into different Science Goals (see the ALMA Proposer’s
Guide). In order to follow this structure, each GOUS is attached to a Science Goal OUS.
Each execution of an SB can be calibrated separately (except for sessions, where Calibrations can be shared).
All executions of the same SB can then be merged at the imaging stage to produce calibrated science products(e.g. images or data cubes). Usually, there will be one SB in each MOUS, but the latter may hold multiple
executions of this SB. For polarization observations, all the SBs that belong to the same session should begrouped together for data processing. Unfortunately, this is not explicitly described in the SB.
If the calibrated science observations of a MOUS have to be combined with science observations of another
MOUS, then these are grouped together into one GOUS. Otherwise, they will be placed into different GOUSs.
A typical example of MOUSs that belong to the same GOUS are observations of the 12-m Array, the 7-m Array
and the TP array. According to the method above, these observations would be in three separate MOUSs, but
in the same GOUS.
Pipeline processing happens at the MOUS level, as soon as all observations of a MOUS are complete. It
is expected that in future Cycles, processing will also happen at the GOUS level, in the case that the GOUS
contains several MOUSs which have already been processed. The only other event that triggers data reductionis the end of an observing Cycle, when all the MOUSs and, potentially, GOUSs are reduced, irrespective of
their degree of completion. As polarization and other selected modes of observations do not currently fit thisscheme, the data reduction may be done manually by the ALMA staff.

8.2

Execution Structure

Once a given SB has been selected for execution (by the Scheduler subsystem or by the AoD), it is read into theonline Control software, and specifically by the Science Software Requirements subsystem (hereafter SSR). The
SSR subsystem commands the lower level Control software to create an Execution Block (EB) structure that is
attached to the SB. As an SB will be executed as many times as needed to fulfil the requirements, several EBs
may exist for a given SB. Each EB contains a record of the parameters and conditions under which the SB was
executed along with references to the acquired data. The internal hierarchical structure of the EB is also shownin Figure 8.1. The SSR subsystem constructs a sequential series of scans that Control executes for each of therequired calibrations. Each scan execution is in fact carried out by breaking it down into a series of subscans,each of which is itself broken into a series of integrations4 (the correlator software only admits sequences ofsubscans). Although commands are issued at the scan/subscan level, the correlator output corresponds to aparticular integration. In general, each calibration observation consists of a scan containing several subscans(e.g. the 5 data points of a pointing calibration constitutes a scan with five subscans (see Chapter 10). Similarly,
the integration time on a single science source between phase calibrations consists of one scan comprised of anumber of subscans. To optimize the execution, scans may be organized in scan sequences which are passed toControl for execution. Scans and scan sequences can be of arbitrary length, depending on the characteristics of a
3 There are three types of OUSs, the Science Goal OUS (no processing happens at this level), the Member OUS and the Group
OUS. Processing occurs usually at the Member OUS level, but the possibility to also process at the Group OUS level may beenabled in the future. A Member OUS is a collection of data (currently all data collected out of executions of a single SB) neededto achieve (part of) a Science Goal, and is usually associated with a specific array configuration. A Group OUS contains all Member
OUSs needed to achieve the science goals of a complete science proposal, and can include Member OUSs corresponding to different
ALMA configurations and/or arrays.
4 A scan is a period of data acquisition that achieves a particular OBSERVER INTENT (e.g., TSYS measurement, pointing
determination, science target observations, etc). A subscan is a distinct period of data acquisition collected in support of a scan(e.g., one pointing offset measurement in a pointing scan; one mosaic pointing of a mosaic scan, etc). Finally, an integration is theshortest period of data recorded in the data sets.

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given observation but subscans are recommended to be 30 seconds or less in most cases. Integrations tend to beon the order of 1 to 10 seconds where the final value has to be an integer multiple of the correlator dump time.
These values can be specified during the generation of SBs in Phase 2 with the OT; specifically, the subscan
duration is specified in the SB target parameters section and the length of the correlator integration time anddump time is specified in the SB Spectral Setup. Calibration results from the Telescope Calibration subsystem(TelCal) and QuickLook (QL) pipeline are usually attached to a scan. (e.g. antenna pointing results). The SSR
and the Control subsystem are responsible for the creation of all the metadata needed for data processing.

8.3

The Observing Process

For each of the SBs in a given project, a set of targets is specified (for more details, see the Cycle 8 2021 OT
User Manual). These targets can correspond to either calibration or science executions. Targets are organized inobserving groups where the first group (Group 1) is always the initial calibration group, with subsequent groups
detailing the science observations5 . All Science targets and relevant calibrators within a group are observed
before the next group is started. An SB can have multiple groups.
All groups other than Group 1 are considered complete when all Science targets in the group have been
observed for the requested time or have set below the elevation limit. After all groups are completed or the SB
execution time limit is reached, the primary Phase calibrator for the group, which triggered the SB execution
time limit as well as any deferred calibrators from Group 1, is observed.
Most observing modes, including single field interferometry, grouped source executions, pointed mosaics,
and polarization use the same ALMA observing script, called the standard interferometry script. The set ofnecessary calibration measurements (e.g. flux, bandpass, etc) usually specified in Group 1 are performed at the
beginning of the observing sequence. Unless previously specified by the user or ALMA staff, the sources are
selected at run-time by the SSR query algorithm using the parameters defined in the SB as input. If sources ofsufficient quality for calibration are found, the SB will execute.
Pointing, Atmospheric, and Sideband-Ratio calibrations are associated to the main (Bandpass, Amplitude,
Polarization, and Phase) calibrations on an as-needed basis which is determined by the SSR at run-time. For
example, a pointing calibration is usually done before the amplitude and bandpass calibrators are observed,
and again before the main observations of the science target and phase calibrator cycle. Within a group, the
Science targets are each observed in turn until observation of the primary phase calibrator (the calibrator withshortest cycle time in the group) is required. A typical cycle time for the phase calibrator may be 7–10 minutes
for standard observations, and 1–2 minutes for long-baseline observations (see Chapter 10). This process isrepeated until the observing requirements are met, or the SB reaches its maximum execution time limit. Any
additional (secondary) phase calibrators are observed as specified in the SB. For a description of what eachcalibration entails, see Chapter 10.
The user has several options to select optimal calibrators:- System-defined Calibration in the OT: let the OT set up default queries to the ALMA Calibrator Source
Catalogue which will be used to select appropriate calibrators at run-time. This is the recommended mode
for regular projects.
- System-defined Calibration (force separate amplitude calibration) in the OT: similar to the above System
Defined Calibration except SSR will enforce a solar system object as the primary flux calibrator and nota grid source. This can provide additional accuracy for some projects.
- User-defined Calibration in the OT: manually enter specific calibration sources or set up the queries using
alternative values for the parameters, but this carries some risk (for example, calibrators will not be
observed during the execution of a group if they are not visible at the time of the observation), and thus
must be fully justified in the Technical Justification of the proposal.

8.3.1

The Source Selection Algorithm

The ALMA system calibration for a given SB is typically done using astronomical sources selected at run-time.
Exceptions to this process are long baseline or high frequency observations or SBs with user defined calibrations
5 In some cases (e.g. polarization), additional calibrations may be added into subsequent groups and they will be interleaved
according to their cycle times.

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111

where calibrators are pre-selected and hard-coded into the SBs. To optimally select appropriate calibration
sources, selection criteria are implemented in the SSR using the following steps:• A list of sources is retrieved from the ALMA Calibrator Source Catalogue based on the query center
coordinates and the search radius defined in the SB.
• For each source in the list, a search for flux measurements at the SB representative frequency is performed.
If no flux measurements are found, the flux is extrapolated from other measurements using a spectral index
of -0.7 to the SB representative frequency.
• The flux values are weighted based on the proximity to the representative frequency, science target andtime since the last measurement present in the source catalog.
• An expected SNR is calculated from the flux and SB observing setup.
• The returned list of sources that passed the signal to noise criteria are ranked based on SNR and separation
with respect to the query center and flux error.
• The final list is sorted based on ranking.
Using these rules, the criteria for all the ALMA calibrations were implemented adding specific requirements
based on the nature of the target, such as:• Bandpass calibrator: The bandpass calibrator integration time defined in the SB (typically 5-15 minutes,
depending on e.g. band and spectral setup) and a number of dynamically determined parameters (e.g.
the number of antennas in the array and the estimated system temperature) are used to determine aflux density threshold for the catalog search that would correspond to a minimum SNR per antenna of
50. If no suitable sources are found, the SNR limit is lowered. Other factors that are taken into accountare elevation and shadowing. The search radius is typically 45 degrees from the query center, but if nosuitable calibrator is found the search radius is increased.
• Phase calibrator: An SNR of 15 is used in the flux estimation. The required integration time on the phasecalibrator is derived either using the widest spectral window (spw) bandwidth (usually 2 GHz), or theaggregate bandwidth when only narrower spectral set-ups are specified. Unless a value is set up in theSB, a search radius of 15 degrees from the query center is used as default (smaller cycle times and radii
are used for the long baseline and high frequency observations, as described in Chapter 10).
• Flux calibrator: A solar system object is searched in the first instance for flux calibration purposes if
this option was selected in the OT. Otherwise, a search is performed among grid sources and the firstobservable grid source is picked up. The solar system objects and grid sources used for flux calibration
are discussed in Chapter 10.
To help checking the consistency of calibration results, the SSR has a logic to select at least two different
sources for the sets of calibrators listed above.

8.4

Single Field Interferometry

Single field interferometry is the most basic form of observation that ALMA supports. It consists of standard
calibration scans6 associated with the constituent calibration targets, and science observations of a single field(primary beam, see Chapter 3 for details). A typical observation will start with a bandpass calibration. The
bandpass observation is executed to measure the spectral response of the system, and thus should be done on abright source with simple spectral properties, such as a bright quasar with no emission or absorption lines anda reasonably flat spectrum. The flux scale calibration will be performed next, which is intended to obtain theobserved flux of a well known source, such as a solar system object. The observed flux will be used to comparewith the established flux model of this object to obtain the scaling factor to be applied to all other sources in
the SB. Ideally, the flux scale calibrator sources should be small in angular size with respect to the synthesized
6 The reader should refer to Chapter 10 for further details on all the different system calibrations.

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beam so as not to resolve the source structure and add uncertainties in the flux calibration. In practice, manysolar system objects may be moderately resolved. In such cases, only a subset of the baselines may be used toestimate the flux based on accurate models of the objects available in the analysis software. From this result, a
scaling factor is derived which can then be applied to the data at the data reduction stage. If no solar systemobject is observable, the SSR will pick the first available grid source.
The phase information of the sources must be preserved and discerned from phase variations at the individual
antenna elements. This is achieved with the phase calibration during the course of an observation. Since thephase is expected to change much more rapidly in time than the amplitude, phase calibrators will be observed
more frequently than other calibrators. Because the phase varies on small scales on the sky, the calibrator must
be as close as possible to the science target. The phase calibration observations are taken right before and after
each observation of the science target, and the phase correction will be interpolated in time when applied to thescience target. As the atmosphere fluctuates rapidly (especially at higher frequencies), radiometric observationsof atmospheric water lines are also done to correct for these additional phase variations. These corrections canbe applied online and offline (see Section 10.4.3 for further details).
Multi-source observations are observations of astronomical objects within a region of about 5◦ . They canbe observed with one EB since the same phase calibrator and check source (see Chapter 10 for the descriptionof a check source) can be used for all targets. Other aspects of the observations (flux calibration, bandpass
calibration, phase-calibration, check source use) remain the same as for one target only that there are several
targets to image in the final data product.

8.5

Pointed Mosaic Observations

Pointed mosaic observations enable a single SG to cover a field of view larger than the primary beam by making
observations of multiple single fields that overlap in spatial coverage by an amount specified in the SB. Up to150 pointings are possible in a single SB. This limitation is set by the maximum execution time for a single
SB and the necessity to finish all fields at least once within an execution. In pointed mosaic observations,each of the fields will be assigned a different field ID in the data, but the same source ID. Thus, all fields will
share bandpass, amplitude and phase calibrations which are done as single fields. For larger fields that cannot
be covered by 150 pointings, multiple SGs may need to be defined. The mosaic is arranged as a single scancomposed by a number of subscans corresponding to the individual rows in the mosaic (see Section 3.5). Boththe science target’s specific last mosaic pointing position and index within the science target list are handled
by the SSR to ensure the next scan begins on the proper science target and proper offset position. The mosaic
observations can be set up by specifying 1 Rectangular Field in the OT.

8.6

Total Power (Single Dish) Observations

The purpose of adding data from single-dish observations using auto-correlations is to recover large scale emission
from the science target that may have been spatially filtered-out by even the shortest baselines of the 7-m Array.
For this reason, these observations are referred to as zero spacing, however, for convenience, these observations
are also sometimes referred to as total power (hereafter TP), although in practice they are taken in autocorrelation mode rather than using a total power (square law) detector. Four 12-m antennas connected to the
ACA Correlator are available for this purpose. For Cycle 8, only spectral-line observations are offered in thismode.
As with the standard interferometry script, (see Section 8.3), the standard single dish script uses the SSR
capabilities to perform some of the calibration observations (e.g. pointing) interferometrically. The SB of a TP
observation consists of a group of calibrations followed by an On-The-Fly (OTF) observation of a rectangulararea on the science target for line mapping with periodic offsets to a certain reference position observed forcalibration purposes. For the OTF and reference position integrations, only the auto-correlation data are written
to the ASDM in order to minimize data rate and size, whereas the rest of calibrations use cross-correlation
information for analysis.
Most of the calibration scans are executed in Group 2. The execution of Group 2 starts up with a pointing
calibration scan. Then, the OTF mapping of science targets are made with periodic executions of atmosphericcalibration scans inserted. The atmospheric calibration is made at the reference position of the science target.

113

8.7. POLARIZATIONThe OTF map is observed as a series of raster rows, scanning in the coordinate system specified in the SB.
In Cycle 8, scans are taken either in longitudinal or latitudinal directions as specified in the OT7 . In future
Cycles, scans may be taken in the two perpendicular directions in turn, to minimize scanning artifacts. The
reference positions, assumed to be positions which are free of spectral-line emission, are specified either inabsolute coordinates or as offsets from the map center. The recommendation for extragalactic objects thatare above a few degrees in Galactic latitude, is to use horizon coordinates. However, in cases where highcontamination is expected, e.g. Galactic CO, fixed offsets are recommended. A catalog of emission-free off
positions is currently under development. By default, the OTF map will cover an area half a beamwidth
larger than the interferometric observations on all sides of the map. This will ensure that undersampling at
the map edges does not affect the data combination process with the interferometric data. A raster row inthese observations is defined as a subscan, with a maximum length per scan (consisting of some number ofsubscans) of 600 seconds. The reference position is observed as specified by its cycle time during the sciencetarget scans. Pointing is calibrated on a bright calibrator near the Science target with a frequency indicatedin the SB, and atmospheric calibrations are taken every 10 minutes at the reference position to measure thesystem temperature.
The calibrated TP map of the science target will be in units of Kelvin, on the antenna temperature (T∗a )scale. Since all TP observations are expected to be combined with 12-m and 7-m Array data which comein calibrated units of Jy/beam, the TP data must also be converted into these units. This conversion from
Kelvin to Jy/beam requires knowledge of the main beam efficiency ηmb and the beam size θ. These values areautomatically derived and monitored by the observatory, using fits to the aperture efficiency of each antenna
as a function of time including, but not limited to, elevation, outside temperature and surface accuracy. TP
observations obtained prior to Cycle 6 instead had “amplitude calibration” maps measured separately for eachproject by obtaining a continuum map of a bright quasar or a planet with known flux.

8.7

Polarization

The ALMA antennas have receivers with linearly polarized feeds followed by a waveguide and a polarization
splitter.8 In this way, the incoming radiation is separated into two orthogonal components (X and Y) which are
down-converted and digitized independently. For each baseline, the digital signals are cross-correlated at thecorrelator where the outputs are the four cross-correlations visibilities XX, YY, XY, and YX (or Vxx , Vyy , Vxy ,and Vyx ). The relation between these four cross-correlations and the Stokes parameters, are ideally given by
Vxx = I + Q
Vxy = U + iV
Vyx = U − iV
Vyy = I − Q
where I, Q, U , and V are the Stokes parameters. In an ideal world, one would be able to combine the observed
cross correlated visibilities and recover the Stokes parameters as,
Vxx + Vyy
2
Vxx − Vyy
Q=
2
Vxy + Vyx
U=2
Vxy − Vyx
V =
2i
I=

7 The minimum time per row in a map is 3 sec, and maximum speed at which data can be taken is usually limited by thecorrelator.
8 For the ALMA receiver bands offered in polarization mode for Cycle 8, Bands 3, 4, 5 and 6 the polarization splitter is an
Ortho-Mode-Transducer (OMT), and for Band 7 it is a polarized grid. See Chapter 4 for details.

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From here, it is easy to see that the total intensity, given by Stokes I, is only a function of the parallel hands
XX and YY, the linear polarization is given by Stokes Q and U while circular polarization is given by Stokes V .
However, there are a number of additional quantities, which have to be considered and calibrated, that prevent
us from directly using the measured cross-correlation in this simple way. We briefly enumerate some of thesequantities here.
1. The splitting of the incoming radiation into the two orthogonal components is not perfect and small
projections of one component into the other are produced. This is called the instrumental polarization or
D-terms. The instrumental polarization is an antenna based quantity which also depends on the frequency
and the band (cartridge design and external optics). Additionally, this quantity is measured in the frameof the antenna which is parameterized by the elevation and azimuth axes (Alt/Az) and thus, it rotateswith respect to the frame of the sky. This rotation introduces an angular dependence into the visibilities
which is given by the parallactic angle (ψ). By design, the instrumental polarization is small (a few
percent), but not negligible.
2. The analog signal path followed by each of the individual X and Y polarizations is slightly different, which
introduces a small delay in the signal that needs to be accounted for.
3. The offline calibration procedure arbitrarily sets the phase of an antenna to zero (the reference antenna).
This results in the inverse of its X-Y offset being imprinted on the cross-hand phases of the other antennas.
This phase offset between the cross-hands also needs to be determined.
4. Other effects, such as the position within the primary beam (off-axis polarization), are still under commissioning. Thus, only on-axis polarization is offered for Cycle 8 (see below for a detailed explanation.)

Figure 8.2: The D-term plots of antennae DA42 (top), DV03 (middle), and PM01 (bottom) for an observationin Band 3. The vertical axis is the fraction of the input signal voltage in one polarization that leaks into the
output of the other polarization in voltage units and the horizontal axis is the frequency in MHz. The blue andred symbols represent DX (the fraction of Y polarization signal that leaks into the X polarization) and DY (thefraction of X polarization signal that leaks into the Y polarization), respectively.
By taking into consideration the instrumental polarization and the parallactic angle dependence, the linearized equations 8.1–8.4 for the visibilities can be re-written as
VXX = (I + Qψ ) + (Uψ + iV )d∗Xj + dXi (Uψ − iV ) + dXi (I − Qψ )d∗Xj
VXY = (I + Qψ )d∗Yj + (Uψ + iV ) + dXi (Uψ − iV )d∗Yj + dXi (I − Qψ )VY X = dYi (I + Qψ ) + dYi (Uψ + iV )d∗Xj + (Uψ − iV ) + (I − Qψ )d∗Xj
VY Y = dYi (I + Qψ )d∗Yj + dYi (Uψ + iV ) + (Uψ − iV )d∗Yj + (I − Qψ )

115

8.7. POLARIZATION

100
80

parallactic angle [deg]

60
40
20
0
-20
-40
DEC=30 deg
DEC=10 deg
DEC=-10 deg
DEC=-30 deg
DEC=-50 deg

-60
-80
-100
-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

source hour angle [hr]Figure 8.3: Parallactic angle (ψ) plot as a function of hour angle for the declination of 30, 10, -10, -30, and -50
degrees.
where dXj are the D-terms as a function of polarization and antenna, the asterisk denotes complex conjugates,
and Uψ and Qψ are the Stokes parameters as a function of the parallactic angle. Figure 8.2 shows an exampleof the D-term spectra in Band 3 for selected antennas. The D-term level is typically a few percent at Bands 3,
4, 5, 6, and 7 on axis with some variations over frequency9 . Without any D-term calibration, an unpolarized
source may appear to be polarized at the 1% level. The most straightforward way to calibrate the D-terms
is to observe an unpolarized source, where the cross-hands output will be purely D-terms since Stokes Q, U,
and V will have no signal. However, bright and unpolarized aastronomical sources are rarely found. Therefore,
ALMA uses an unresolved quasar as a polarization calibration source. These sources are monitored to ensure
they are bright enough (> 2%), and the exact polarization is determined during data reduction provided thatthe source is observed over a wide enough range (> 60◦ ) of parallactic angles to separate the effects of the source
polarization, the D-terms and the cross-hands phase spectra and delay. Figure 8.3 shows that the rate of changeof parallactic angle is fastest near transit and slowest for low elevation sources. Thus, care should be exercisedwhen choosing a polarization calibrator in order to maximize parallactic angle rotation. The ALMA observatory
will select appropriate calibrators for each project, but the users must take into account these limitations whenplanning the observation.
With the current calibration scheme, the expected minimum detectable degree of linear polarization, definedas three times the systematic calibration uncertainty, is 0.1% for compact sources (i.e., within the inner 1/3 ofthe primary beam FWHM) for both TDM and FDM observations. The minimum detectable degree of circularpolarization is 1.8% of the peak flux for both TDM and FDM observations. This level of accuracy for circularpolarization is currently on-axis, and thus the circular polarization imaging must be restricted within 1/10 of
the primary beam FWHM to avoid beam squint effects. Note that the systematic calibration uncertainty candegrade by a factor of ≈2 depending on, for example, the choice of calibrator or parallactic angle coverage.
The accuracy of absolute polarization position angle in a single-pointing image is 1◦ within the inner 1/3 ofthe FWHM of the primary beam, increasing to as much as 5◦ near the FWHM. These levels of accuracy will
only be reached if there is sufficient signal-to-noise in the polarized emission.
A D-term component also arises from the off-axis geometry of feed horn, antenna illumination, and thealignment of optics. This D-term component will vary across the primary beam pattern (see Chapter 4).
Generally, the D-term level becomes larger when increasing the offset from the beam center. This is theso-called off-axis instrumental polarization, which, for Cycle 8, will not be calibrated.
Spectral line polarimetry is also offered in Bands 3, 4, 5, 6, and 7 at arbitrary frequency setups. Figure 8.4
shows the D-term solutions of a representative antenna (DV22) as obtained during commissioning. Figure 8.5
shows a zoomed-in view in frequency of the D-term solutions shown in Figure 8.4. These figures show that the
spectral shape of the D-term solutions is smooth and no spur-like structure is seen even in highest frequency
9 A resonance has been documented for Band 6 between the feed and the OMT. This resonance introduces a small ripple in the
D-term solution which increases the leakage amplitude by a small amount, but still only a few percent.

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CHAPTER 8. OBSERVING MODES

Figure 8.4: A frequency vs real part of the D-terms plot for an antenna (DV22) obtained towards J0522-364.
Blue circles and red crosses are showing the D-term obtained using a setup of FDM with 2 GHz bandwidth andusing a setup with higher spectral resolutions (FDM 500 and 62.5 MHz bandwidth respectively). Four panels
show the D-terms obtained from the spw 0, 1, 3, 2 (from top left, clockwise).
resolution mode (30.5 kHz per channel at the right bottom panel of Figure 8.5). Figures 8.4 and 8.5 clearly
demonstrate that the instrumental polarization is mostly spectral resolution independent for these datasets.
For Cycle 8, ALMA will offer linear polarization continuum mosaicking in Bands 3, 4, 5, 6, and 7. For thisnew mode, the spectral range will be fixed to the current default continuum frequency setups (see Table 8.1.
Therefore, the P.I will not be able to freely choose the frequency tuning of a given spectral window. However,the PI will be able to choose between the TDM and FDM modes through the ALMA-OT interface using a
restricted frequency resolution when FDM mode is chosen. This scheme has been implemented to allow for
better continuum identification when mapping some sources of interest (e.g. high mass star forming regions).
The limits in the spectral resolution that can be selected, for FDM polarization mosaicking, do not consider
spectral averaging and are shown in Table 8.1. The maximum spectral resolution listed in the Table applies only
to continuum mosacking during cycle 8. Regular, on-axis, ALMA polarization observations are not subjectedto this restriction. The allowed area to be mapped is subject to the same 150-point restriction that applies tototal intensity (Stokes I) mosaics. The mosaic pattern can be arbitrary, but ALMA recommends a hexagonal
grid. While Nyquist sampling (half a beam overlap) is sufficient, a sampling of less than Nyquist (i.e., a more“loosely packed” mosaic) must be justified. A proposal requesting a mosaic sampling rate of less than Nyquist
might be rejected on technical grounds. The average error estimates for linear polarization mosaics are 1 degree
in polarization position angle, and 0.1% in polarization fraction in the regions of the mosaic that correspond to
the inner 13 FWHM of a given pointing. Near the FWHM of a given pointing, the estimated upper limits for theerrors increase to 5 degrees and 0.5%. These errors were determined from a grid of offset pointing observations
toward highly linearly polarized point sources (e.g., 3C 279) that spanned the region of the primary beam out tothe FWHM. Although increased sampling is allowed with the required justification, we did not find significant
improvements in the errors.10
Also for Cycle 8, ACA stand-alone polarization observations will be offered. Single-field interferometricpolarization observations with the ACA are available in Bands 3 to 7 with arbitrary frequency setups. The
measurements are accurate for the central one third of the FWHM beam for linear polarization. However,circular polarization with the 7 meter antennas has not been explored. It should be important to note, that
effects such as beam squint can produce spurious circular polarization as we move across the antenna beam (the1/10 FWHM in band 3 for a 7 meter antenna is ∼ 1000 for an array resolution of 1200 at 100 GHz). Multiple
10 See Hull et al. 2020, PASP, submitted.

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8.7. POLARIZATION

Figure 8.5: A close-up view in frequency space of the real part of D-term shown in Figure 8.4. Blue circles andred crosses are showing the D-terms obtained from setup #1 (FDM, 2 GHz bandwidth) and setup #2 (FDM,
500 and 62.5 MHz bandwidth respectively).
pointings are permitted, however mosaics are not supported at this time. The same calibration scheme employed
for the main array will be used for the ACA as well as current imaging techniques. However, data combinationin full Stokes between the ALMA main array and the ACA is not supported in CASA at this time. Because
the ACA is always in a compact configuration, a restriction of 40◦ in elevation for the polarization calibrator is
implemented in the dynamical scheduling system to avoid shadowing.
Band

spw 1
(GHz)

spw 2
(GHz)

LO 1
(GHz)

spw 3
(GHz)

spw 4
(GHz)

Maximum Spectral Resolution(MHz)

Velocity Resolution(km/s)

3
4
5
6
7

90.5
138.0
196.0
224.0
336.0

92.5
140.0
198.0
226.0
338.5

97.5
145.0
203.0
233.0
343.5

102.5
150.0
208.0
240.0
348.5

104.5
152.0
210.0
242.0
250.5

1.953
1.953
1.953
1.953
1.953

5.6
3.9
2.8
2.4
1.7

Table 8.1:
Default frequency setup for polarization continuum observations including maximum spectral
resolutions allowed for mosaicking.

8.7.1

Sessions

Although not directly related to polarization itself, sessions are the observing scheme designed to executepolarization projects with ALMA. In order to allow for the observation of large projects and to avoid theexecution of long SBs (more than 2 hours), the concept of a session was implemented in the the online ALMA
software. A session is defined as the continuous execution of the same SB until the scientific criteria are met.
The session preserves the integrity of the observation by keeping the information from the previous SB execution
in the run-time memory. Thus, the session will manage the calibrator’s cycle time in order to avoid unnecessary
observations giving an additional level of optimization for ALMA. By default, calibrations such as the bandpass
will be done every hour, thus saving observing time while the default cycle time for the polarization calibrationis set to 35 minutes. The phase calibration-science target loop will be interrupted when an additional calibrationis needed based on its cycle time (e.g. polarization)11 . This is done in such a way that the phase-science bracket
is preserved. The session will remember the last time the polarization calibrator was observed and interleave
the calibration when needed.
In general, the required parallactic angle coverage can be achieved with two to three executions of the SB,
which results in about 3 to 4 hours of observation. The actual number of EBs is set by the ALMA dynamicscheduling system in order to cover the required parallactic angle coverage. Other cases in which the session
scheme might be useful are large mosaics, surveys (multi-target), and large single dish raster maps, but those
11 The cycle time parameters are user controlled and can be explicitly specified in the OT target parameters section.

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CHAPTER 8. OBSERVING MODES

cases are not yet offered in session mode for Cycle 8.

8.8

Multiple Region Modes

In the frequency division modes (FDM) of the correlator (see Section 5.1.2), the final spectrum is synthesizedusing individual filters 62.5 MHz wide. When the total bandwidth is between 125 MHz and 1 GHz, it is possible
to move these individual filter positions to create spws covering a number of disjointed spectral regions. This iscalled the Multiple Region Modes. The constraints are:
• The spw width must be a multiple of 62.5 MHz.
• The aggregate width of these spws must be equal to that of the original bandwidth selected.
• The spws must all fit within the 2 GHz baseband used.
• The other parameters (resolution, polarization and sensitivity options) must be the same for all spws.
This mode is useful when a number of line features which require high spectral resolution are spread acrossthe IF bandwidth. Since the filters have a unit width of 62.5 MHz, if the user chooses a mode with 250 MHz
total bandwidth, it is possible to place four separate windows, each with 62.5 MHz width, anywhere within the
2 GHz baseband. In Cycle 8, a maximum of four spws per baseband will be offered.

8.9

Observation of Ephemeris Objects

Observation of solar system objects (with the exception of the Sun) is supported as in previous Cycles. Several
well known solar system objects including planets, satellites and asteroids can be selected from a pulldown
menu in the Observing Tool. For other sources, including non-sidereal objects, an external ephemeris file canbe supplied as an input. The JAO is not responsible for observing ephemeris objects using old or outdated
ephemerides. It is the responsibility of the PI and the observing team of observations of ephemeris targets toprovide a valid target ephemeris file during the Phase 2 process and any update during the Cycle if necessary.
The ephemeris file must be in JPL Horizons format. A typical ephemeris file may consist of the date (time),
Right Ascension, Declination, range and range rate, for example:*******************************************************************************
Date__(UT)__HR:MN
R.A._(ICRF/J2000.0)_DECdelta
deldot***************************************************************************
2012-Jun-26 13:00
06 22 57.33 +23 16 11.23 1.01653182506561 -0.2593303
2012-Jun-26 13:01
06 22 57.49 +23 16 11.14 1.01653170585632 -0.2583150
2012-Jun-26 13:02
06 22 57.66 +23 16 11.05 1.01653158664703 -0.2572937
2012-Jun-26 13:03
06 22 57.82 +23 16 10.96 1.01653146743774 -0.2562665
2012-Jun-26 13:04
06 22 57.98 +23 16 10.84 1.01653134822845 -0.2552333
2012-Jun-26 13:05
06 22 58.14 +23 16 10.74 1.01653122901917 -0.2541942
2012-Jun-26 13:06
06 22 58.30 +23 16 10.66 1.01653122901917 -0.2531491
More information on the format and precision needed is available in the ALMA Observing Tool documentation.

8.10

Solar Observations

Continuum mode solar observing was first made available for ALMA Cycle 4. It will continue to be supported,albeit with limitations, in Cycle 8. In particular, the following conditions apply to solar observing in Cycle 8.
• Only Band 3, Band 5, Band 6, and Band 7 continuum observations using the following default frequencies(GHz) are offered:8.10. SOLAR OBSERVATIONS

119*******************************************************************************
LSB
USB
Band
LO Freq.
BB1
BB2
BB3
BB4
*******************************************************************************
3
100
92-94
94-96
104-106
106-1085
198
190-192
192-194
202-204204-2056
239
229-231231-233245-247247-2497
346.6
338.6-340.6
340.6-342.6
350.6-352.6
352.6-354.6• Interferometric observations must be done using the TDM mode (see section 5.1.1); frequencies are fixed to
2 GHz-wide spws centered on the frequencies shown in the table above. The spectral-line FDM observing
mode is not offered for solar observations (Section 5.1.2).
• Simultaneous observations in different frequency bands is not offered. Each execution block can only
include one band.
• Observations will be available in each band and configuration as follows:***************************************************
ConfigBand 3
Band 5
Band 6
Band 7***************************************************
C-1
X
X
X
X
C-2
X
X
X
X
C-3
X
X
X
C-4
X
• Because the WVR receivers are saturated when the dishes point at the Sun, online WVR phase correction
will not be applied and offline WVR correction for on-source (solar) data is not possible (see Section
8.10.2).
• Interferometric observations will use a combined array comprising both 12-m and 7-m antennas and will
be processed with the 64-element correlator (Section 5.1).
• To minimize shadowing of 7-m antennas, observations will be carried out when the Sun is above an
elevation of 40◦ .
• Mosaicing of larger FOVs can be carried out with up to 150 different pointing offsets relative to the phasecenter specified in the ephemeris.
• As for the rest of ALMA observations, a single observation (an Execution Block) cannot exceed 2 hours,
which will include the time overheads for bandpass and flux calibration. These calibration overheads
amount to about 25 mins.
• The minimum integration time of interferometric observations is fixed to 1 second.
• Observations may be performed using dual linear polarization (XX, YY) or single polarization (XX)correlations; full polarization measurements are not currently offered for solar observations.
• Total-Power full-Sun fast-scanning single-dish observations are offered as context and to recover the largest
angular scales for interferometric observations; proposals requesting only Total-Power single-dish observations will not be accepted in Cycle 8.
• Single-dish Total-Power mapping will be “monomode” (double-circle scan pattern) with a 2400 arcsecdiameter circular FOV centered on the solar disk (see below).
• Single-dish full-Sun will not be executed when the Sun is at elevations above 70o because the required
fast-scan azimuth slew speeds are too high.
• The time cadence of full-sun images obtained from total power observations is fixed to about 10 minutes
for Band 3, 12 minutes in Band 5, 14 minutes for Band 6, and 25 min for Band 7.

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CHAPTER 8. OBSERVING MODES

8.10.1

Solar Observing Modes

Solar observations with ALMA are possible because the surface of the antennas is designed to scatter the opticaland IR radiation to an extent that the subreflector and other elements in the optical path are not damaged ordegraded. However, additional steps must be taken to allow useful observations of the Sun to be made. ALMA
receivers are designed for a maximum RF signal corresponding to an effective brightness of about 800 K at thereceiver input. Since the quiet Sun has a temperature of ∼5000-7000 K at ALMA frequencies, the solar signal
must be attenuated or the receiver gain must be reduced to ensure that receivers remain linear, or nearly so.
The initial solution adopted by ALMA was the use of a “solar filter” (SF) that is mounted on the Amplitude
Calibration Device (ACD) of each antenna (Section A.5). When placed in the optical path, the solar filter isrequired to attenuate the signal by 4+2λmm dB with a return loss of -25 dB (-20 dB for ν > 400 GHz) and across polarization induced by the filter of -15 dB, or less. While the use of solar filters has been demonstrated towork, their use introduces several disadvantages, not the least of which are cumbersome calibration procedures.
Yagoubov (2013b, 2014) pointed out that the ALMA SIS mixers could be de-biased to reduce the mixer gainand effectively increase the saturation level to a degree that allows solar observations without the use of thesolar filters, at least for non-flaring conditions on the Sun. These produce lower conversion gain and since thedynamic range scales roughly inversely with gain, these settings can handle larger signal levels before saturating.
In addition to the SIS bias voltage, the local oscillator (LO) power can be altered in order to further modify
the receiver performance. However, LO power settings have not yet been fully optimized for solar observing.
Two so-called “Mixer De-Tuned” or “Mixer De-Biased” settings have been adopted for solar observations inBand 3, Band 5 and Band 6. These are referred to as solar observing modes MD1 and MD2.
• Band 3: MD1 mode uses a bias voltage that sets the SIS mixer to the 2nd photonic step below thevoltage gap whereas MD2 mode employs a bias voltage corresponding to the 2nd photonic step above thegap. For MD1 mode, the Band 3 receiver temperature suffers a modest increase, to ∼50 K, and receivercompression is limited to ∼10%. For MD2 mode, however, the Band 3 receiver temperature increases
significantly, to 800 K, but receiver performance is believed to be essentially linear.
• Band 5: MD1 mode settings are nominal for ALMA; i.e., the bias voltage is that used under normal
observing conditions. MD2 mode employs a bias voltage corresponding to the 1st photonic step above thevoltage gap. The receiver temperatures are higher, in the 500-600 K range, but the receiver is essentiallylinear.
• Band 6: MD1 mode settings are nominal for ALMA; i.e., the bias voltage is that used under normal
observing conditions. Receiver compression is again on the order of ∼10%. MD2 mode employs a bias
voltage corresponding to the 1st photonic step above the voltage gap. Again, the receiver temperature issignificantly higher, 800 K, but the receiver is essentially linear.
• Band 7: MD1 mode settings are nominal for ALMA. Here, too, the bias voltage is that used undernormal observing conditions. Receiver compression is somewhat higher than it is for Band 3 and Band 6,of order 15%. No stable MD setting has been established for an MD2 mode.
The MD1 mode is considered to be a “quiet Sun” mode (coronal holes, the solar limb, quiescentfilaments, prominences, quiet areas outside of active regions) whereas the MD2 mode is recommended for the “active Sun” (active regions, active filaments, science objectives that require
accurate photometry).

8.10.2

Array Observations

The Sun is an extremely large source compared with the Primary Beam of either the 7-m or 12-m antennas(see Chapter 2). The Primary Beam is filled with complex emission when pointing at the Sun, as are the beamsidelobes. The ALMA array ultimately measures the brightness temperature contrast relative to the background
Sun, which is resolved out by the array. As noted earlier, in order to recover the absolute brightness temperatureof solar targets, it is necessary to include not only interferometric observations (by the 7-m and 12-m antennas),
but also Total Power measurements made with a single dish. Single dish fast-scan mapping of the Sun in Total
Power mode is addressed in the next subsection.

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8.10. SOLAR OBSERVATIONS

An advantage to using MD mode observing is that the water vapor radiometers (WVRs), which are used tocorrect differential phase errors introduced by precipitable water vapor over the array, are not blocked by the
ACD. They can therefore be used, in principle, to make such corrections to solar data. Unfortunately, unlessthe optical depth of the sky is ∼2.5 or more, which would represent highly non-optimum observing conditions,
the WVRs saturate on the Sun. Until the WVRs are modified or replaced to increase their dynamic range
to accommodate the Sun, phase corrections based on WVR measurements will not generally be possible whenpointed at the Sun. For this reason, solar observations are currently restricted to compact array configurations
to minimize such phase errors.
Another consideration, again regardless of whether SFs or the MD modes are used (see Section 8.10.1),
is the system IF attenuator settings. The input power changes significantly as the antennas move from the(solar) source to a calibrator and back. The IF chain has two variable attenuators (in steps of 0.5 dB) toensure that signal levels remain within nominal limits: one in the IF Switch and one in the IF Processor. A
concern is whether the variable attenuators themselves introduce unacceptable (differential) phase variation
between source and calibrator settings, thereby corrupting phase calibration referenced against suitable sidereal
calibrators; and whether there are differences between the spw bandpass response between source and calibrator
scans as a result of attenuator settings. Careful testing has shown that this should not be a significant concern.
Bandpass calibration is carried out in the usual manner using MD modes: i.e., a strong calibrator is observedin an MD mode and the bandpass solution is obtained. Bandpass shape and stability were checked for MD
modes and attenuator states in Bands 3 and 6. It was found that perturbations to bandpass amplitudes andphases were small. For the IF Switch and IF Processor settings adopted for MD mode observing it was foundthat the RMS difference between bandpass phases for an MD attenuator state and the nominal attenuator state
was generally a fraction of a degree for both Band 3 and Band 6, the maximum being 1.2 deg. Similarly, thenormalized amplitude difference was typically a fraction of 1%. No explicit correction for differential bandpass
is needed.
In the non-solar case, the antenna temperature (Tant ) is small compared to the system temperature, andTant can therefore be neglected for amplitude calibration (see Chapter 10). In contrast, unlike most cosmic
sources, the antenna temperature of the Sun is large (∼7000 K at 100 GHz). It is therefore necessary to measureboth the system temperature and the antenna temperature when pointing at the Sun in order to compute the
System Equivalent Flux Density (SEFD) to correctly scale visibility amplitudes.
To estimate the antenna temperature Ta∗ on the Sun, “single-dish” measurements must be performed using
all antennas of the array. Specifically, the standard observing sequence for solar interferometric observations
will include the following measurements:• a “sky” observation Psky , offset from (by typically 2o ) and at the same elevation as, the target (Sun)• a “cold” load observation Pcold (also known as the “ambient” load), in which an absorber at the temperatureof the thermally-controlled receiver cabin (nominally 20 o C) fills the beam path
• a “hot” load observation Phot , in which an absorber heated to ∼70 o C fills the beam path
• a “zero” level measurement Pzero , which reports the levels in the detectors when no power is being supplied
Then the telescope moves to the target (Sun) where the IF attenuation levels are set appropriate to the input
power. After the target scan, the telescope again moves to the “sky” position and takes another measurement,
called the “off” measurement Pof f , without changing the IF attenuation.
The antenna temperature of the science target is then given by:Ta∗ = (Psun − Pof f )(Psky − Pzero )(Thot − Tcold )(Pof f − Pzero )(Phot − Pcold )The auto-correlation data output from the baseline correlator cannot be used for this measurement because
it has insufficient dynamic range to measure Pzero . Instead, the necessary measurements rely on Total Powerdata obtained by the baseband detectors.

8.10.3Single-Dish Mapping

Fast scanning observations are ideal for recovering the flux or brightness distribution on angular scales ranging
from the ALMA primary beam width to the scale of the target in question (typically a few arcminutes), or up

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CHAPTER 8. OBSERVING MODES

to the full disk of the Sun. Briefly, fast-scan mapping entails making Total Power (and more recently, autocorrelation measurements) as the telescope pointing is driven continuously and smoothly through a sampling
pattern on the target that avoids sudden acceleration or deceleration of the antenna drive motors. A majoradvantage of fast scanning is that it minimizes the impact of atmospheric variation, and the full solar disk can
be mapped in as short as 7 minutes.

Figure 8.6: Left: Schematic illustration of a double-circle scan pattern used to map the full disk of the Sun.
Actual patterns sample the source more densely to ensure that it is no less dilute than Nyquist sampling.
Right: Example of a fast-scan map of the Sun obtained in Band 6.
While various types of scan patterns have been developed and tested for ALMA dishes, Cycle 8 supports
the use of a “double circle” pattern, which maps a circular region on the sky. The double-circle pattern isparticularly well suited for full-disk mapping because its coverage matches the shape of the solar disk and it
repeatedly revisits the region of the center of the disk, allowing atmospheric opacity variations to be corrected
for (see Figure 8.6). Standard observing procedures include focus and pointing checks on suitable sources prior
to the fast-scan mapping.

8.10.4

ALMA Solar Ephemeris Generator Tool

The tool (URL http://celestialscenes.com/alma/coords/CoordTool.html) was developed by the Czech
ARC Node to be used together with the OT in preparing solar observations and was tested during the December
2015 solar campaign. It is a javascript based application which runs in any modern browser and on many different
operating systems.
User interface consists of several panels. In the input panel, it is possible to select the latest SDO/AIA
image in several bands or to upload the users’ own FITS files. Currently, only uncompressed FITS with definedsolar WCS keywords using CROTA2 formalism are supported. Visualization and display panels enable the user
to pan and zoom in/out the region of interest or to show/hide coordinate grids and tweak the image display byfalse coloring and level scaling functions typical of other astronomical software packages and the OT.
The actual pointing is done by clicking the desired feature with a green cross marking the position. The
coordinates of the pointing are displayed in several coordinate systems inside the pointing panel, where it isalso possible to manually define the pointing.
Finally, in the observation panel, the user defines start and end times of the observation and differential
rotation profile which will be used for generation of an OT-compatible ephemeris file. There are several rotation
profiles to choose from or the user can define his/her own. Clicking Generate ephemeris file for OT will display
the generated file which can be downloaded by following the Download data below link and then imported into
the OT.

123

8.11. VLBI OBSERVING MODE

The ephemeris file is generated from the JPL Horizons file which the tool queries directly from Horizons
website. However, during Cycle 4 regular observing sessions there was a period when JPL Horizons site went
offline and hence the Ephemeris Tool was unable to function properly. Work is currently underway to enableprecise ephemeris calculations in the Ephemeris Tool even when JPL site goes down.
The ALMA Solar Ephemeris Generator Tool comes with a user manual and it is served on several sites forbackup purposes. Currently, there are no plans to include the tool functionality into the OT.

8.11

VLBI Observing Mode

The Very Long Baseline Interferometry (VLBI) Observing Mode (VOM) is a variant of the standard interferometry mode with some additional capabilities to allow ALMA to participate in global VLBI networks operating
at millimeter wavelengths. Since Cycle 4, ALMA VLBI mode observing has been offered in Band 3 in conjunction with the Global Millimeter VLBI Array (GMVA)12 and in Band 6 in conjunction with the Event Horizon
Telescope (EHT) network13 . For details about proposing for these opportunities, see the current ALMA Callfor Proposals (http://almascience.org/proposing/call-for-proposals/).
For all VOM observations in Cycle 8, ALMA will be operated as a phased array of up to 41 12-m antennas,
depending on the configuration and weather conditions. The typical expectation is for ∼37 12-m antennas,
making phased ALMA equivalent to a parabolic antenna of diameter deq ∼73 m, neglecting efficiency losses.
From Table 9.3, the aperture efficiencies in Band 3 and Band 6 are 0.71 and 0.68, and Tsys is 70 K and 100 K,
respectively. Defining Gain ≡ Aeff /(2kB ) where kB is the Boltzmann constant and SEFD ≡ Tsys /Gain, thecorresponding estimates for these quantities are:
Gain
SEFD
Gain
SEFD

= 0.71π(0.5deq )2 /(2kB ) × 10−26 = 1.05 K/Jy
= 67 Jy= 0.68π(0.5deq )2 /(2kB ) × 10−26 = 1.0 K/Jy
= 100 Jy(Band 3)
(Band 6)Note that the VOM is not compatible with the use of subarrays.
When ALMA is operated as a VLBI station, all standard interferometry data products are also output by the
ALMA correlator. Therefore, during any VOM execution an observer simultaneously obtains data equivalent
to a standard ALMA interferometric observation of the science target, in addition to the VLBI data products.
The latter are recorded independently on Mark 6 VLBI recording systems and are shipped to common sites forcorrelation with the other VLBI site data before delivery to the PI (see below). Some important details of the
VOM are elaborated in the next subsections.

8.11.1

General VLBI Considerations

The supporting VLBI networks (i.e., the GMVA for Band 3 and the EHT for Band 6), together with ALMA,
place certain restrictions on the observing process for VLBI experiments involving ALMA. These are largely
driven by the complexity of orchestrating the simultaneous, reliable execution of a common VLBI schedule, as
well as the calibration requirements of the individual telescopes that comprise the global array. In practice,planning an ALMA VLBI observation is similar for Band 3 and Band 6, aside from details such as differing
bandwidths and frequencies.
Successful VLBI proposals will be passed to a network Scheduler who builds the common VLBI schedules(encoded in a so-called VLBI EXperiment, or VEX file built with SCHED14 ) for a particular observing campaign.
In these schedules, some number of contiguous hours will be devoted to each set of science targets and necessary
VLBI calibrators.
The schedule will be worked out between the Scheduler and the PI well in advance of the observation.
Most sites participating in the VLBI network also have a “friend” of VLBI who assists the Scheduler in working out details specific to that site. Sample VLBI schedules from previous campaigns are available from theaforementioned GMVA website.
12 See http://www3.mpifr-bonn.mpg.de/div/vlbi/globalmm/
13 See http://www.eventhorizontelescope.org/
14 http://www.aoc.nrao.edu/software/sched

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In general, the required time on the VLBI science target(s) and VLBI calibrators will be broken into a
number of VLBI scans of several minutes duration, separated by gaps of the order of several minutes to allow
time for local calibrations (pointing, system temperature measurements, etc.) and antenna slew time sufficient
to meet the needs of each observatory. VLBI observations that include ALMA will require that the gaps
between VLBI scans are of sufficient length to allow for the performance of the calibrations normally required
for standard interferometric observing, including flux, gain, bandpass, and polarimetric calibrators (see below).
In Cycle 8, targets that are sufficiently bright to permit phase self-calibration (≥500 mJy) shall be observed ina so-called “active” phasing mode as has been used in previous cycles. Cycle 8 will also introduce a new VLBI
observing mode that allows weaker sources to be observed via “passive” phasing as described in Section 8.11.3.
The amplitude calibration is anchored to a Solar System Object when possible, and the flux solutions arebootstrapped to a strong source (≥500 mJy) included in the VLBI schedule.
Most VLBI stations currently record circular polarization (either left, right, or dual), in contrast to ALMA
which records dual linear polarizations. Consequently, every VLBI observation with ALMA must be treated as apolarization observation in order that a transformation from linear to circular polarization can be made correctly
during post-correlation processing. A special software tool, PolConvert, is available for this purpose. Robust
execution of PolConvert requires a minimum session duration of 3 hours (session length, not time on sciencetarget) to achieve adequate parallactic angle coverage on the polarization calibrator sources for the computationof polarimetric “leakage” or D terms (see Section 8.7).
Other VLBI observatories have receiver capabilities that differ from ALMA. One complication is that the
sample rate used at ALMA is non-traditional for VLBI, so care must be taken in the experiment set-up to
ensure that the VLBI data can be correlated with the other stations. The VOM spectral set-ups chosen foreach band have been selected to address these constraints and therefore are fixed. For Band 3 (at 3mm)
there are four 1.875 GHz wide-bands centered at 86.268, 88.268, 98.328 and 100.268 GHz, respectively. In
Band 6 (at 1.3 mm) the bands are centered at 213.1, 215.1, 227.1 and 229.1 GHz, respectively. A second
complication is that not all millimeter VLBI sites are capable of matching ALMA’s full recording bandwidth.
The EHT currently matches ALMA’s maximum recording rate at all sites (64 Gbps); the GMVA records
what its sites can provide, up to the maximum of ALMA’s 2-GHz, dual-pol recordings, but in all cases atleast 4 Gbps (512 MHz per polarization), centered in ALMA’s first baseband at 86.268 GHz. (See https://www3.mpifr-bonn.mpg.de/div/vlbi/globalmm for current GMVA capabilities.)
Calibration of VLBI data generally requires observations of VLBI calibration targets interleaved with themain science target. At ALMA, these VLBI calibration measurements are carried out in a manner analogous tothe observations of the science targets (i.e., using the VOM and active phasing of the ALMA array). The VLBI
calibrators are generally chosen for their utility across the entire global array to meet a particular calibrationneed (e.g., fringe-finding, bandpass calibration, polarization calibration) and need not be the same calibrators
as observed for calibration of the (ALMA-only) standard interferometric data.
During VLBI observations, the observatories are usually not interconnected by a fast network, so the VLBI
recordings (onto disk modules) of the antenna baseband signals are physically transferred to common correlation
facilities managed by the appropriate network (MPIfR Bonn and MIT Haystack Observatory for the Band 3
and Band 6 data, respectively). These sites are responsible for the correlation of the VLBI data and deliveryof the correlated VLBI data products to the observer, as discussed in Section 8.11.2. Correlation is performed
using the DiFX correlation software.15

8.11.2

ALMA Considerations for VLBIAs mentioned in the previous section, all VOM observations should be viewed as polarimetric observations. The
reader is referred to Section 8.7 for guidance on this.
In order to participate in a VLBI observation, there are two special requirements at ALMA. The first isthat the ALMA control system must tune receivers appropriately and point to the targets specified in the VEX
schedule at the appropriate times. The second is that the signals from the ALMA antennas must be coherently
summed up, decimated, and recorded on media suitable for delivery to the common VLBI correlator. In orderto form this coherent sum, the (arbitrary) phases of the signals at the antennas need to be adjusted during theobservation so that they can be coherently added. The necessary signal processing for this takes place within
special cards and circuitry in the ALMA correlator, and using special software within the ALMA control system.
15 http://www.atnf.csiro.au/vlbi/dokuwiki/doku.php/difx/start8.11. VLBI OBSERVING MODE

125

These components were developed by the ALMA Phasing Project (APP).16 Further information on the APP
and the ALMA Phasing System (hereafter APS) is described in Matthews et al. (2018).17 Key aspects of the
APS are also presented in the following sections, with particular emphasis on those aspects which are essential
for the VLBI proposer or data analyst. The discussion begins with a description of the VOM Scheduling Blockin the next section. The subsections immediately below discuss, respectively, the scan sequences used by the
VOM, some important details about how the APS works, and finally, a few comments about the analysis of
VLBI data (a full discussion is outside the scope of this document).
VLBI Observing Mode Schedule Block and Execution
As with other observing modes, VOM observations are executed with a Scheduling Block which provides
observation-specific details to an SSR observing script. In the case of the VOM, the script is referred toas StandardVLBI.py.
The Scheduling Block is created from the observing project and the VEX file using a special tool called
VEX2VOM. This tool reconciles the Phase 2 Scheduling Block with the schedule and targets specified in the VEX
file and thus provides the detailed operating instructions for the SSR observing script. The preparation of the
final Scheduling Block with VEX2VOM is done by the Friend of VLBI or the AoD prior to execution, once all thenecessary details of the observing array are known.
Like the StandardInterferometry.py script, the StandardVLBI.py script ensures that the necessary calibrations as specified by the OT are performed with the desired cadence. Unlike the StandardInterferometry.py
script, it must give precedence to the scheduled VLBI scans which need to occur at the appointed times. As
mentioned above in Section 8.11.1, the VEX file will include gaps of various durations which are created toallow the observing script to make ALMA-specific calibration observations. Thus the script organizes its workby first noting when the next VLBI scan will occur and then noting which calibrations can be executed within
the time remaining until the VLBI scan, and finally executing those calibrations that fit. The VLBI scans in
the VEX file include a start time specified in so-called VEX time format, YYYYyDOYdHHhMMmSSs, so the
execution of the StandardVLBI.py script by the SSR will look similar to the following:
perform initial ALMA calibrations
VLBI Scan 2016y089d07h00m00s on Target-X for 300s
perform some ALMA calibration
VLBI Scan 2016y089d07h10m00s on Target-X for 300s
perform some ALMA calibration
VLBI Scan 2016y089d07h20m00s on Target-X for 300s
perform some ALMA calibration
VLBI Scan 2016y089d07h30m00s on Target-X for 300s
perform some ALMA longer calibrations
VLBI Scan 2016y089d07h50m00s on Target-X for 300s
perform some ALMA calibration
VLBI Scan 2016y089d08h00m00s on Target-X for 300s
. . .
perform final ALMA calibrations
VLBI Scan Sequence
The VEX file specifies the observations in terms of VLBI scans which begin and end at appointed times. The
VOM translates these requests into a sequence of (ALMA) correlator scans which typically start prior to thespecified time in order to allow the phasing system to converge on a good solution. Each of these correlatorscans appears in the ALMA meta-data, and is processed by the telescope calibration system (TelCal) according
to the specified intents. The relevant ones for this discussion are intents for ‘phasing’ and for ‘WVR correction’.
The phasing intents direct TelCal to calculate the phases of the signals (i.e., the signals of each polarizationin each band for each antenna) relative to those of a designated “reference” antenna. These phases are calculated
16 The APP (S. Doeleman, Principal Investigator) was funded by a Major Research Instrumentation award from the National
Science Foundation and an ALMA North America Development Project award.
17 Matthews, L. D., Crew, G. B., Doeleman, S. S., et al., PASP, 130, 5002.

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from “channel-averaged” data products produced within the correlator. Presently there are eight channel averages per baseband calculated during one of these correlator subscans (see Fig 8.7). With those phases known,
commands are issued to the tunable filter banks (TFBs) within the station cards in the correlator to adjust theantenna phases by exactly the computed values so as to bring all signals into phase with those of the reference
antenna. Once these adjustments have been made, a “residual” phase correction typically needs to be made on
the following correlator scan, and indeed, such corrections continue to be made every scan until the end of therecording. The phasing loop is closed in the sense that small errors in the phase adjustments may be correctedon subsequent scans. This is the so-called “slow” loop which is illustrated schematically in Figure 8.7.
VLBI Scan

Record On...

Correlator Scan Sequence...
TelCal Solving...
TFB Commands...
WVR Data...
Unphased∆

Phased∆Phased∆PhasedTime

Figure 8.7: VLBI Scans in the Phasing System. Each VLBI scan is partitioned into “subscans” for correlation
and “slow” timescale processing (of order seconds) in TelCal. WVR adjustments are made in the CDP on a“fast” timescale (every second). See text for full discussion and explanation.
While the correlator scans are shown as time-contiguous in Figure 8.7 (green bar), there are in fact small
gaps to allow for potential reprogramming of the correlator processing. Even so, the solutions from TelCal(purple) do not arrive at the TFBs (red) until after the correlator scan has started—the time of application
is noted and the early part of the scan is excluded from the subsequent phase calculation. Usually one phaseapplication is needed to get an acceptable solution, so the recording should start no sooner than the start of
the third correlator subscan. These parameters are all programmable, and judicious choices for them are madewhen the Scheduling Block is created. For Cycle 8, the subscans are 16 s long with 1 s (channel average)
integrations; there are then about 30s of observations prior to the start of the recording. Note that signals fromthe antennas flow continuously to the summation logic and are recorded independently of the correlator subscan
timing, so there are no comparable gaps in the VLBI data. In addition to the “slow” loop, there is also a “fast”
loop that optionally may be enabled and which uses the WVR data from each antenna to correct the antennaphases in real time in response to the wet component of the atmosphere. These corrections are performed at afrequency of ∼1 Hz (blue in Figure 8.7). This loop is open (corrections are continuously made, but feedback isonly achieved through the “slow” loop). It may be used if conditions warrant. There is no limit to the durationon the operation of these loops other than general ALMA limitations with regard to total data collected.
VLBI Phasing System
Moving beyond the timing of the phasing system, there are several other aspects of the system that an ALMAVLBI observer should be familiar with. All ALMA observations operate with an array of antennas (i.e., thoseavailable to a scheduled observation). Of these, a portion of the antennas are controlled by the phasing system
to form the coherent sum signal which is used for the VLBI recordings. The previously mentioned reference
antenna is merely a designated member of this “phased array”. At least two antennas from the active array(designated “comparison antennas”) are held outside the phased array. These comparison antennas are thus

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available for diagnosing the performance and efficiency of the phased array system. Finally, after construction,
the summed signal is decimated to two bits per sample (as is the case with all of the ALMA signals in theVOM), so it is possible to have the ALMA correlator correlate the sum signal during online processing. This isdone by co-opting the Correlator Antenna Input (CAI) of some antenna that is not used by the VOM (usuallyCM10) and inputting the sum signal into the correlator as if it had come from this “sum antenna”. The sum
signal therefore appears as antenna on pad “APP001” in any ASDM file containing ALMA data acquired with
the VOM. There are a few things to note about the data and metadata for this antenna:• there are no useful metadata, as this is not a physical antenna• there are no WVR data, for the same reason• the data are highly correlated with other antennas in the phased array since the same receiver noise ispresent in both.
• this antenna should generally be flagged during analysis of the (ALMA-only) interferometric array data
The selections of antennas for the phased array and the comparison array are made when the Scheduling
Block is created, although these may be adjusted if necessary shortly prior to or during the observation. Normally, the antennas to be phased are chosen to lie within a certain radius from the array center (up to several
hundred meters, depending on the band and the observing conditions). The efficiency of the phasing systemdecreases on longer baselines, so in practice, maximum baseline lengths in the phased array will typically be<∼1 km. The reference antenna is in general selected to be centrally located, and typically at least one of
the comparison antennas is chosen to be within the radius of the phased array. Because of the decimation to
two-bits, the number of phased antennas must always be odd.
A final important note concerns delays between antennas. The ALMA control system estimates the total
delays between all antennas and adjusts the signals through a variety of techniques (in hardware and software)so that the visibilities found in the dataset have essentially zero delay on each baseline, (i.e. there is no slope
in a plot of visibility phase as a function of frequency on any baseline.) However, a (significant) component of
the delay is removed with a frequency dependent phase rotation in the online correlation processing, not in the
hardware, so there is some significant delay present in the signals at the TFBs where the APS phase corrections
are made and correspondingly in the logic which creates the “sum antenna” signal. Thus in order for the phasingsystem to work properly, it is necessary to turn off this component of software delay correction and to insteadcorrect it in the phasing calculations. To do this, the observing band is subdivided into several channel averages(at least 8) and the normal phase-solving procedure produces different, independent phases that can be applied
to the TFBs corresponding to each channel average. While this removes most of the delay, it does leave a small
residual phase-slope within each channel average. It also leads to the restriction that the source needs to bebright enough in each of the channel averages so that a usable phase solution can be found. A flux density limit
for actively phased VLBI targets of ≥500 mJy is therefore imposed (but see Section 8.11.3).
VLBI Observing Mode Analysis
As pointed out in Section 8.11, any VOM observation actually involves two concurrent interferometric observations: one on the ALMA scale that results in correlated data products between all participating ALMA
antennas and one on a global scale, where ALMA serves as a station in a global VLBI array. A description of
the reduction and analysis of ALMA VLBI data is beyond the scope of this document. This process is, however,informed by the analysis of the ALMA-scale observation with regard to observatory performance (SEFD, systemtemperature, etc.), which for the most part may be obtained in the usual way. However, since the VLBI signalthat is recorded is that of a “sum” antenna whose properties in turn depend on the phasing performance, a few
details should be pointed out.
One of the most significant is that the correlated amplitude of the signal measured by an ideal phased arrayshould scale as the square root of the number of phased antennas, assuming the antennas are identical (atALMA, only 12-m dishes are typically used in the phased sum and they have similar effective areas; if the 7-m
dishes were included, the relation would become more complicated). In practice, a number of effects conspire tolower performance from this ideal relation18 to ∼80% of what would be expected in a perfect system. Part of18 ALMA-05.11.63.03-0001-A-REP.pdf

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this efficiency loss stems from the fact that the sum antenna signal is decimated to two bits from the individual
antenna signals (about 7%) in addition to the original decimation of to two bits (about 12%) for a total reductionof about 0.8 (this is based on analyses subsequent to those reported in Matthews et al. 2018, PASP, 130, 5002).
To this must be added phasing efficiency losses caused by decorrelation, which are weather-dependent. This loss
is typically ∼10% and its effect on the visibility amplitudes is calibrated during QA2. For a specific observation,
the net effective area of the ALMA “sum” dish may be estimated directly from the ASDM data on a per-scanbasis.
The performance of the phasing system is captured in the metadata of CalAppPhase table of the ASDM file.
There is one table entry per scan per baseband. In each table, there are temporal bounds on validity (i.e., therange of time within the scan of stable phase) and entries to list the disposition of the antennas amongst thedifferent categories (phased antennas, reference antenna, and comparison antennas) and whether this representsa change from the previous scan. The table primarily reports a number of phase values, Nv , which is dependent
on the “packing mode”. There is one value per channel average per polarization per antenna. Additionally, theCalAppPhase table reports lower-level details of the phasing system, including online per-antenna assessmentsfrom TelCal of the antennas drawn from the quality of the phasing solution. This table may be used inconjunction with the ALMA data for a particular scan to calculate the phasing efficiency and thus to make anappropriate correction to the absolute VLBI correlation amplitudes.
As indicated in Section 8.11.1, the VLBI correlation products are delivered to the PI for analysis, separate
from the ALMA ASDM data. Traditionally for the GMVA the former has been in the form of FITS-IDI files.
A complication for work with ALMA data is that the polarization conversion is performed with a software tool
(PolConvert) that requires input from a CASA analysis of the ALMA data set (see Goddi et al. 2019, PASP,
131, 5003). This conversion can be performed on the FITS-IDI file or at the correlator using the raw correlator
output if the CASA analysis is available. Arrangements for doing this will be worked out between the PI of eachproject and the supporting observatory collaborations (GMVA and EHT) following the observation. During the(PolConvert) process, a detailed calculation is performed from the calibration tables to provide a traditional
ANTAB format file for amplitude calibration of the visibilities on baselines that include ALMA.

8.11.3Observing Targets Fainter than 500 mJy with Passive Phasing

To insure adequate SNR for the calculations necessary to phase up the ALMA array, (“active”) phasing iscurrently restricted to sources that are point-like and have correlated flux densities ≥500 mJy on short (< 1 km)
intra-ALMA baselines. However, beginning in Cycle 8, VLBI science targets weaker than 500 mJy may beobserved using a “passive phasing” technique. In this mode, a phase calibrator close in angular distance to thescience target (termed a “phasor”) is used by the APS to phase the antennas immediately prior to a slew tothe science target. The phasor must be point-like and brighter than 500 mJy on intra-ALMA baselines andideally should be within ∼6 or 3 degrees of the science target for Bands 3 or 6, respectively (see section B.6.1
in the Cycle 8 2021 Proposer’s Guide). When selecting a phasor, closer is better than brighter. If there are nosuitable phasor candidates within the suggested limits, the proposer should justify in the proposal the need touse a more widely separated calibrator (see section B.6.1 in the Cycle 8 2021 Proposer’s Guide). In addition tohigher overheads for slewing, losses in correlated amplitude as a result of phase decorrelation are likely to occur
on the science target when using a phasor more than a few degrees from the target, particularly in Band 6.
In practice, there is no lower limit to the flux density of science targets that can be observed with passive
phasing, aside from SNR considerations on the VLBI baselines. However, while the 500 mJy flux density
threshold is removed from the science target in the passive phasing mode, the phasor source itself is actively
phased and must adhere the same requirements for flux density and source structure as any standard, actively
phased VLBI target.
With passive phasing the need to periodically observe the phasor will result in some reduction of observing
efficiency compared with the case when it is possible to actively phase the array directly on the science target.
There are also trade-offs to consider when choosing the phasor/science target duty cycle. Typical passive phasing
observing sequences will consist of a short (∼1–3 min) VLBI scan on the phasor, immediately followed by alonger scan on the science target itself (up to ∼5 min). For accurate absolute flux calibration, care must be
taken not to exceed the expected atmospheric coherence time during the science target scans, since correlated
amplitude will diminish with time as phase coherence is lost. In general, shorter scan sequences will havehigher overhead but will be more robust against atmospheric variability, which cannot be predicted precisely in8.11. VLBI OBSERVING MODE

129

advance. The proposer should indicate (for the scheduler’s benefit) their preferences regarding this trade-off.

8.11.4Phased-Array Observing

A special case of the passive phasing technique (hereafter the Phased-array Mode or PM) is now available
for general use in Cycle 8. This mode has been tested successfully in Band 3 via observations of the Velapulsar.19 The PM utilizes phased ALMA as a standalone array. Although this is not a VLBI observation in the
traditional sense, ALMA is operated as a phased array and VLBI technology is used to record the baseband
data for subsequent use in pulsar analyses or searches.
In Cycle 8, the PM is offered only in Band 3 for pulsar science projects. Extension of the PM to other bands infuture cycles is expected to be straightforward, but it will require additional testing and commissioning. As with
the VOM, the PM requires ALMA to be operated as a phased array using the APS. Thus, a schedule of recordings
is required, which is analogous to the situation with VLBI observations. The PM will be supported by the GMVA
collaboration, headquartered at the Max Planck Institut für Radioastronomie (MPIfR) in Bonn, Germany.
Therefore for successful proposals, the schedule will be generated by the GMVA Scheduler in consultation withthe principal investigator (PI) well in advance of the observation. In preparation, the PI will be required to
specify various observing considerations using the OT. The total potential recording bandwidth available forBand 3 will be 4×2 GHz (for both polarizations) and each baseband/polarization will contain 32×62.5 MHz
frequency channels.
Phase-up of the array for the PM will broadly follow the same mechanism used by the standard VLBI passive
phasing mode as described in Section 8.11.3. In practice, the total required integration time will be broken
into a number of scans, each of up to several minutes in duration, separated by ∼1–3-minute actively phased
exposures on a phasor target selected from the ALMA Calibrator Source Catalogue. Provided the weather isstable, the phase coherence on a pulsar target may be maintained for as long as several minutes in Band 3.
Requirements for the properties of the phasor are the same as for non-pulsar passive phasing experiments (seeSection 8.11.3), although the separation to the phasor may be relaxed with justification in the proposal (seesection B.6.1 in the Cycle 8 2021 Proposer’s Guide).
After the observation, the recordings will be sent to MPIfR for subsequent processing. This post-processing
involves the generation of FITS-format data of a special type used by the pulsar community (known as PSRFITS20 ). These data are suitable for pulsar and transient searching, pulsar timing, or any other relevant scientificobjectives (see the next section).
Pulsar Mode Post-processing and Data Products
Every PM project will generate two types of data products: pulsar data in the form of a high time-resolution
time series (in PSRFITS format) and the ALMA standard interferometric data (in ASDM format). A sketchsummarizing the overall data flow is shown in Figure 8.8. To generate the pulsar data product, the baseband
data are first read off the disk modules into a collection of VLBI Data Interchange Format (VDIF) data files(one per scan per sub-band per polarization).
Next, a software routine21 is used to convert the VDIF files into the search-mode PSRFITS format. To
obtain one time sample for a single frequency channel, the routine extracts the time series in both polarizations(with identical time stamps) from one “packet" in the VDIF file (also referred to as a frame), performs a
Discrete Fourier Transform, makes conversions from voltage to intensity in the frequency domain, and collapses
the power over the whole Fourier spectrum. There are 125,000 frames per second for each recorded data stream(one polarization from one baseband). Detections can then be outputted in the form of total intensity only,
intensity of dual polarizations, coherence products, or full Stokes products.
The time samples (in 32-bit floating point) are then packed together following the structure of the PSRFITS
specification, retaining the original frequency resolution. The time resolution of the output file may be as highas 8 microseconds, but multiples of that (smaller files) can be produced upon request. The final data productwill be on a per scan and per subband basis and will be suitable for direct processing by standard pulsar software
19 Liu, K., Young, A., Wharton, R., et al. 2019, ApJ Letters, 885, L10.
20 https://www.atnf.csiro.au/research/pulsar/psrfits_definition/Psrfits.html
21 Available at: https://github.com/xuanyuanstar/vdif2psrfits

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Mark VI
VLBI
RecorderChannelized
PSRFITS

VDIF

Packet Buffer
Metadata

Data
Transport

Full
Resolution

Pol 1

Mark VI
VLBI
Playback

VDIF

Pol 2

ALMA
Correlator

PSR
Archive
Time-avg
PSRFITS

vdif2psrfits tools

Figure 8.8: Diagram showing the data flow during a pulsar mode (PM) observation. Baseband data recordedat ALMA will be sent to MPIfR (Bonn, Germany) for playback and PRSFITS generation. Reproduced from
Figure 2 of Liu et al. (2019).

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131

such as presto22 , psrfits_util23 , and dspsr24 to perform pulsar and transient searching, pulsar timing, or
any other desired scientific investigations. The data rate (per second) for each spectral window is given by 4
bytes × number of polarizations × 32 channels × 125,000; for example, for 8-µs resolution and 4 polarizations,
it is 4 × 4 × 32 × 125, 000 = 64 MB/s.
For PM observations of a known pulsar, the post-processing will not include construction of the integrated
pulse profile (which requires the ephemeris of the pulsar). However, this can be done later by the PI.
Technical Justifications for Phased-Array Observations
Upon the submission of a proposal requesting PM observations in Cycle 8, the PI will be required to provide
the following information via the OT. Note that there will be one science target per goal (per SB), but multiple
goals per project are allowed, if justified.
• Name and position (RA and DEC) of the science target.
• Total observing time requested. In PM projects, approximately one third of the total requested time
will be spent on the science target and the rest of the time on the VLBI calibrators (including thephasing calibrator and other calibration targets in the schedule). Additional calibrations for the ALMA
interferometric data are performed during schedule gaps.
• Phase calibrator (phasor). This should generally be chosen from the ALMA Calibrator Source Catalogue.
However, a phasor may be chosen from outside of this Catalogue, if justified.
• Selection of the spectral window. In Cycle 8, Band 3, there are four 2-GHz spectral windows, centered at
86.268 GHz, 88.268 GHz, 98.328 GHz, 100.268 GHz, respectively. The PI can choose between one and fourof these by declaring it in the justification box.
• Time resolution of the PSRFITS data product. This needs to be an integer multiple of 8 µs.
• Polarization of the PSRFITS data product. The PI can choose any one from the following: (1) Total
intensity; (2) dual polarizations (XX & YY); (3) coherence product; (4) All four cross correlations (XX,XY, YX, & YY).
• Any additional request, if applicable.

8.12High Frequency Observing

High-Frequency Observations (specifically Bands 8, 9, and 10) require some special observing techniques, mostly
because of the combined ill effects of lower atmospheric transmission and fainter and more widely spaced
calibrators at these frequencies. These techniques, which are just addenda to regular observing modes, arebeing progressively implemented in the ALMA observations since Cycles 6, after some extensive testing iscarried out. It is expected that all of them will improve not only the quality of the final data products, butalso the overall observing efficiency at the ALMA highest frequencies. For reference, a brief description of thenomenclature that could be used by Contact Scientists and the ALMA Observatory in general when mattersregarding high-frequency projects are discussed, reported or communicated to PIs is given below:• High-Frequency Cone-Searches and Calibrator Surveys: Observations in the high-frequency ALMA
bands require that the availability of calibrators near the target source is assessed near the time of theplanned observations. Searches for phase calibrators and check sources (see Chapter 10 for details) within
10 degrees of the science targets (i.e., the so-called “Cone-Searches”) in each SB are carried out by ALMA
staff and Allegro, the EU ARC Node in the Netherlands, within 90 days of the high-frequency observations. The results of those measurements are subsequently ingested into the ALMA Calibrator Catalogue,
so that they are available for queries at the time the actual observations take place.
22 https://www.cv.nrao.edu/~sransom/presto/
23 https://github.com/demorest/psrfits_utils
24 http://dspsr.sourceforge.net/

132

CHAPTER 8. OBSERVING MODES• Bandwidth Switching (BWSW): For high-frequency observations (Bands 8, 9, 10) with spectral setups including only narrow-band spws, the PI will be asked to add an additional wide-band spw. Thisapproach increases the accuracy of the gain calibration, allowing a solution across the combined spws
and/or transferring of the wide-window solutions to the narrow spws.When adding extra spws is notpossible (i.e., projects that have occupied all the spws with narrow-band set-ups), it is possible to use
bandwidth switching, in which the phase calibrator is observed with wider spws for increased signalto-noise. The wide-to-narrow spw complex-gain offsets are measured from observations of the bandpass
calibrator, allowing the phase cal solutions to be transferred to the target field. For more details, see
Chapter 10.
• Sideband separation by 90-degree Walsh phase-switching (Bands 9 and 10): The Band 9 and
10 receivers are of DSB design, i.e. do not separate or suppress either sideband, and signals from bothsidebands are superposed on a single IF output per polarization (see Chapter 4). Prior to Cycle 6, the only
option available for interferometric observing in these bands has been to use orthogonal LO frequencyswitching sequences to suppress the contributions of one sideband to the visibilities. Since Cycle 6 ameans of sideband separation is also offered, resulting in twice the output bandwidth and number ofchannels. The separation uses orthogonal sequences of 90-degree phase shifts applied at the first LO ineach antenna, combined with synchronised accumulation over the sequence duration of the three phasecombination states of the cross-correlations of each baseline by the correlators. The result is subsequently
combined to produce the two sideband spectra in the correlator data processing software. There are 128
patterns in a switching sequence, each pattern switching on 16 ms intervals, and therefore total length of2048 ms. This mode therefore adds a constraint: the dump and integration durations of the correlator
must be a multiple of 2048 ms. Due to an unrelated requirement that subscans must start and end on
48 ms Timing Event (TE) boundaries, and 2048 ms not being a multiple of 48 ms, the allowed values ofsubscan durations are somewhat limited, as will be seen when adjusting times in the OT. In Cycle 8, onlya single pair of spws (LSB+USB) in each baseband is offered, and either the TDM (2 GHz, 256/Npolchannels) or widest bandwidth FDM (1.875 GHz, 7680/Npol channels) modes must be used (additionallyfor FDM, the spw should not be moved from the center of the baseband). The modes in the four basebands
remain independent, e.g. one baseband can use FDM to observe a spectral line, while the other basebands
can use TDM to detect continuum.

Chapter 9

ALMA Sensitivity Calculator
The main tool for calculating the sensitivity of ALMA is the ALMA Sensitivity Calculator (ASC). This is
an application contained within the ALMA Observing Tool (OT) that is used to perform various conversions
between sensitivity (in either flux or temperature units) and time. Its main use is to take the user-requested
sensitivity and calculate the necessary observing time for each source in a Science Goal using parameters such as
the representative frequency, source declination, number of antennas and the expected precipitable water vapour(PWV). Many of the inputs cannot be changed by the user and, for example, the OT will always assume a fixed
number of antennas for the particular cycle and will always use the standard PWV octile that is appropriate
to the frequency of observation.
In addition, a separate version of the ASC is available in the OT which allows a user (via a GUI) to experimentwith various sensitivity options such as the number of antennas and PWV octile. An almost identical version is
also available as a web application that can be found in the ALMA Science Portal1 . This differs from the GUI
version incorporated in the OT in that it is possible to enter some parameters that are outside the ranges thatare applicable to the current observing cycle.

9.1

Calculating the System Temperature

When determining the time required to achieve a particular sensitivity, the system temperature, Tsys , is afundamental parameter as it takes into account various sources of noise that make it difficult to detect the very
weak astronomical signals that ALMA is trying to detect. The most prominent sources of noise are from thereceivers and from the atmosphere. The latter is highly variable, both in time and frequency, and thus dynamicscheduling and careful placement of spectral windows (spws) are crucial.

9.1.1

Sky Temperature

The OT’s estimate of both the atmospheric zenith opacity, τ0 , and the sky temperature, Tsky , are calculatedusing the Atmospheric Transmission at Microwaves (ATM) code2 . This provides values of the opacity and theatmospheric “output radiance”, in steps of 100 MHz, for the seven different octiles of PWV. The sky temperature
is converted from the radiance using the Planck function and includes the contribution due to the CMB.
The ATM code only provides measurements of the sky temperature at the zenith, Tsky (z = 0), and therefore
the OT must account for the greater atmospheric emission at lower elevations. It does this by assuming thatthe emission from the atmosphere can be approximated asTsky = Tatm (1 − e−τ0 sec z ).

(9.1)

Inserting the ATM values of Tsky (z = 0) and τ0 into Equation 9.1 allows the mean physical temperature of the
1 http://almascience.org/
2 See Pardo, J. R., Cernicharo, J., Serabyn, E., 2001, ITAP, 49, 1683. This calculates the sky temperature by integrating theatmospheric temperature profile, this having been formed from the average of 28 radiosonde measurements taken at the ALMA
site during November 1999.

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CHAPTER 9. ALMA SENSITIVITY CALCULATOR

Octile
1
2
3
4
5
6
7

PWV (mm)
0.472
0.658
0.913
1.262
1.796
2.748
5.186

Table 9.1: Octiles of PWV measured at the ALMA site from years of monitoring data and used in the ASC.
The first octile corresponds to the best weather conditions and shows that 12.5% of the time, PWV values atleast as good as 0.472 mm can be expected. Subsequent octiles give the corresponding value for 25%, 37.5%.
etc.
atmosphere, Tatm , to be measured i.e.
Tatm =

Tsky (z = 0).
(1 − e−τ0 )(9.2)

This can be reinserted into Equation 9.1 to calculate the sky temperature at any zenith angle asTsky (z) = Tsky (z = 0)

(1 − e−τ0 sec z )(1 − e−τ0 )(9.3)

Tsky (z) is then corrected for the fact that the required noise temperatures (Tn ) are defined assuming Pν = kT
and thus a correction for the Planck law is required, i.e.


hν/kT
Tn = T ×(9.4)
ehν/kT − 1
The octiles characterize the amount of PWV that can be expected at the ALMA site, i.e. a value of PWVat least as good as the first octile value can be expected 12.5 per cent of the time, a value at least as good as
the second octile 25 per cent of the time, and so on. The octiles corresponding to the ALMA site (determinedfrom many years of monitoring) are shown in Table 9.1.
When estimating the time for a project, the OT will always select a PWV octile that is appropriate to thefrequency being observed. It does this by calculating the time required for each octile and then choosing (andreporting) the highest (worst) octile for which the increase in time relative to the first is less than 100 per cent. A
consequence of this definition is that the octile also depends on source declination, i.e. sources at low elevations
will require better weather conditions. The resulting curve of octile versus frequency is shown in Figure 9.1, fora source declination of zero degrees. A user can override this choice in the GUI or web application versions, but
submitted projects will always use an automatic choice.

9.1.2

CMB Temperature

The temperature of the Cosmic Microwave Background is included in Tsky and thus does not feature further inthis document.

9.1.3

Receiver Temperatures

The receiver temperatures of the various receivers have been updated in Cycle 7. For Bands 3 to 8, these are
now based on actual measurements at the telescope and are generally conservative i.e. refer to the worst value
seen at any part of the band. The values used in the ASC are given in Table 9.1.3. Note that single sideband
noise temperatures are reported for Bands 1-8 and double sideband temperatures for Bands 9 and 10.
At the moment, no attempt is made to incorporate the frequency dependence of the receiver temperature,i.e. only a single value is used per band. Ultimately, it is the intention to use the actual measured values for all
receivers and to incorporate the frequency response across the band.

9.1. CALCULATING THE SYSTEM TEMPERATURE

135

Figure 9.1: Plot of PWV octile assumed by the ASC as a function of frequency, for a source declination of zero
degrees. The vertical lines separate different bands, the numbers of which are shown at the top of the plot. The
water line at 183 GHz (Band 5) is particularly prominent. In general, higher frequencies require drier observing
conditions.

Note that the ASC doesn’t concern itself with the so-called “zero-point fluctuations” as the requisite half
photon of noise (hν/2k) has already been included in the noise measurements provided by the various receivergroups (A. Kerr, private communication).
The receiver temperatures are already expressed in terms of the Planck expression and thus do not require
the correction given in Equation 9.4.

9.1.4

Ambient Temperature

Ambient temperature is essentially spillover from the sidelobes of the antenna beam corresponding to emission
from the ground and the telescope itself. This is held constant at 270 K (median value as measured from many
years of monitoring data at the ALMA site). However, the value used by the ASC is converted to a noise
temperature according to Equation 9.4 and thus its total contribution is frequency dependent and can vary
between the different sidebands.

9.1.5

DSB Receivers

Due to the way that the astronomical signals are down-converted to an intermediate frequency, every heterodyne
radio receiver simultaneously detects radiation from two sidebands. This means that, if nothing were done toprevent it, a spw processed by the correlator would contain two sets of astronomical signals mixed in with one
another, one from the “signal” sideband and an undesirable one from the “image” sideband. In the case of 2SB

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CHAPTER 9. ALMA SENSITIVITY CALCULATOR

ALMA Band
1
2
3
4
5
6
7
8
9
10

Receiver Type
SSB
SSB
2SB
2SB
2SB
2SB
2SB
2SB
DSB
DSB

Trx,ASC (K)
25
30
40
42
50
50
72
135
105
230

Table 9.2: Receiver temperatures assumed in the ASC as a function of ALMA band. For Bands 3–8, these are
all based on actual measurements made at the telescope and correspond to the worst value seen within eachband. For many bands, these are considerably better than the original specifications in Table 4.1.
receivers, the contribution from the image sideband (emission from the source and noise) is suppressed to a very
high degree. However, for DSB receivers (Bands 9 and 10) it is only possible to remove the source contribution(either by LO offsetting or 90-degree Walsh switching) and so the noise cannot be neglected.
One important consequence of this is that, if a spw has its image counterpart in an area of very poor
atmospheric transmission, it can greatly increase the system temperature and lead to very long on-source times.
Therefore, it is important to avoid areas of bad atmospheric opacity in the image spws and the OT therefore
shows the location of these in the spectral visual editor (Figure 9.2).
One subtlety is that the tuning software will always place spws in the upper sideband if possible. Therefore,
to take a simple case, a single spw centered at 637 GHz will find its image equivalent in the middle of the zerotransmission feature at ∼621 GHz. Where possible, this situation can be avoided by defining dummy spws suchthat the line of interest is forced into the other sideband (Figure 9.2).

9.1.6

System Temperature

The OT version uses two distinct formulas depending on whether a double sideband receiver is being used, ornot. The DSB equation is the following:
Tsys,dsb =1
ηeff e−τ0 sec z



2 × Trx + ηeff (Tsky,s + Tsky,i ) + (1 − ηeff ) × (Tamb,s + Tamb,i )



(9.5)

where
• Trx – receiver temperature• Tsky,s – sky temperature at the requested frequency in the signal sideband• Tsky,i – sky temperature in the image sideband• Tamb,s – ambient temperature in the signal sideband• Tamb,i – ambient temperature in the image sideband• ηeff – the coupling factor, or forward efficiency. This is equal to the fraction of the antenna power patternthat is contained within the main beam and is currently fixed at 0.95
• e−τ0 sec z – the fractional transmission of the atmosphere, where τ0 is equal to the zenith atmosphericopacity and sec z is the airmass at transit (the ASC always assumes that the source is being observed attransit).

9.2. THE SENSITIVITY CALCULATION

137

Figure 9.2: A Band 9 spectral setup as displayed in the spectral visual editor in the OT. The top figure shows
an example of how the image equivalent of a single spw can fall into an area of poor atmospheric transmission,leading to much higher Tsys than necessary. Placing a dummy spw at a higher frequency can remedy thesituation (bottom).

The terms ηeff and e−τ0 sec z both attenuate the source signal and thus we must divide through by them in orderto obtain a measure of the system noise that is relative to the unattenuated source. Note that this is always
done at the signal frequency.
For SSB and 2SB receivers, the equation is the following:


1
T
+
η
T
+
(1
−
η
)
×
T
(9.6)
Tsys,ndsb =
rx
eff
sky,s
eff
amb,s
ηeff e−τ0 sec z
where the terms are all the same as in Equation 9.5.

9.1.7

System Temperature (web application and OT GUI)The equations to calculate the system temperature used by the web application and the OT’s GUI are similar
to the above, however, both are unaware of the details of the tuning setup and so do not know the location of
the image sideband and cannot perform a rigorous calculation of its contribution to the system temperature.
In this case, the same equation is used for all receiver types and the DSB noise contribution is simply double
the single sideband case. This is controlled via the sideband gain ratio, g:
1+gTsys =
T
+
η
T
+
(1
−
η
)
×
T
.
(9.7)
rx
eff
sky,s
eff
amb,s
ηeff e−τ0 sec z
For Bands 1 and 2 (Single Sideband; SSB) and 3-8 (Sideband Separating; 2SB), g = 0. For DSB receivers,g = 1.

9.2

The Sensitivity Calculation

Once Tsys has been determined it is possible to calculate the point-source sensitivity given a requested amountof on-source observing time or vice versa. At no point is any account made for the expected level of loss insensitivity due to problems with the telescopes such as residual pointing and focus error.
Under certain circumstances it will not be possible to achieve the theoretical sensitivity, particularly if thesource being observed is very bright and/or the u, v coverage relatively sparse. In these situations the image

138

CHAPTER 9. ALMA SENSITIVITY CALCULATOR

can be dynamic-range limited due to residual source flux scattered across the map as a result of calibration
errors and imperfect source deconvolution.

9.2.1

12-m and 7-m Arrays

When dealing with the 12-m and 7-m Arrays, the point-source sensitivity, σS , is given by the standard equation:
σS =wr 2 k Tsysp.
ηq ηc Aeff (1 − fs ) N (N − 1) np ∆ν tint

(9.8)

The various parameters are:• wr – robust weighting factor. ALMA Pipeline imaging and subsequent QA2 assessment is performed
assuming that the visibilities are weighted using robust weighting, specifically a Briggs robustness factorof 0.5. Simulations have shown that this factor is equal to 1.1.
• Aeff – effective area. This is equal to the geometrical area of the antenna multiplied by the aperture
efficiency ηap = R0 exp (−16 π 2 σ 2 /λ2 ) where σ is the rms surface accuracy of the antenna. The latter is
set to the design goal of 25 µm and 20 µm for the 12-m and 7-m antennas respectively3 . Ro is the productof a number of different efficiencies and is equal to 0.72. See Table 9.3 for values of antenna efficiencies invarious ALMA bands.
• fs – shadowing fraction. For the more compact 12-m configurations and the ACA 7-m Array, antennas
can block the field-of-view of other antennas in the array and thus reduce the total collecting area. The
shadowing fraction is a function of source declination as shown in Fig. 7.5.
• ηq – quantization efficiency. A fundamental limit on the achievable sensitivity is set by the initial 3-bit
digitization of the baseband signals. This is equal to 0.96.
• ηc – correlator efficiency. This depends on the correlator (64-input or ACA) and correlator mode, although
the efficiency of all 64-input Correlator modes is equal to 0.88. The ACA efficiencies do depend on themode, but this is only taken into account in the OT, not by the web application or OT GUI, which
therefore assume a value of 0.88.
• N – number of antennas. This defaults to 43 for the 12-m Array and 10 for the 7-m Array.
• np – number of polarizations. np = 1 for single polarization and np = 2 for dual and full polarization
observations.
• ∆ν – resolution element width. As already mentioned, this should be equal to 7.5 GHz for continuum
observations. This is due to the maximum usable bandwidth of a spw being limited to 1.875 GHz by theanti-aliasing filter through which the baseband signal passes. np ∆ν is often referred to as the effective
bandwidth.
• tint – total on-source integration time.
The associated surface brightness sensitivity (K) is related to the point-source sensitivity (Jy) by
σT =

σS λ2
2k Ω

(9.9)

where Ω is the beam solid angle. This is related to the user-entered spatial resolution, θ, by
Ω=

πθ2
.
4 ln 2(9.10)

This assumes that the telescope beam is a circular Gaussian with a half power beamwidth of θ.
3 Note that not all antennas might achieve this specification. The performance of a given antenna will also vary with the thermal
conditions and the length of time between surface realignments.

139

9.3. USER INTERFACE

Band
3
4
5
6
7
8
9
10

Frequency (GHz)
100
145
183
230
345
405
690
870

ηap,12 m (%)
71
70
69
68
63
60
43
31

ηap,7 m (%)
71
71
70
69
66
64
52
42

Table 9.3: Aperture efficiencies at typical continuum frequencies for both the 12- and 7-m antennas. The
effective area, Aeff , is equal to ηap multiplied by the physical area of the dish i.e. 113.1 m2 and 38.5 m2 for the
12-m and 7-m antennas respectively.

9.2.2

Total Power Array

In the case of the TP Array, a different equation is usedσTP =2 k Tsysp.
ηq ηc Aeff N np ∆ν tint

(9.11)√
This is similar to Equation 9.8, but there is only a factor of N in the denominator and there is no need totake shadowing into account.
Particularly for continuum observations, the above equation is likely to be too optimistic due to rapid
fluctuations of the receiver gain and atmospheric opacity. These require extremely demanding calibration
strategies and, as these have not yet been commissioned, only spectral line total power projects are currently
possible.

9.3

User Interface

The main way that a user interacts with the Calculator is through a GUI in the OT or via the web applicationin the ALMA Science Portal – both are essentially identical. By entering various parameters, the time required
to achieve a particular sensitivity (in either Jy or K) can be calculated, or vice versa. The inputs that affectthe sensitivity or time are given below; a screenshot of the OT’s GUI version is shown in Figure 9.3.
• Source declination – this is used to calculate the maximum elevation of the observation and thus theminimum airmass i.e. the ASC assumes that the source is transiting. It is also used to calculate theamount of shadowing that is likely to affect the ACA 7-m and the smaller 12-m configurations.
• Observing frequency – this sets the receiver temperature, antenna efficiency and the PWV octile.
• Bandwidth per polarization – this otherwise straightforward parameter should be set to 7.5 GHz forcontinuum observations (see Section 9.2.1). For spectral line observations, it is usually set to the frequency/velocity resolution that one requires in one’s spectrum.
• Water column density (Precipitable Water Vapor; PWV). The user is able to enter one of the seven octile
values, or the calculator will set this automatically depending on the frequency entered.
• Number of antennas – the ASC currently assumes 43 from the 12-m Array, 10 from the 7-m Array andthree from the TP Array.
• Angular resolution – this affects the time estimates when sensitivities are specified in temperature units.
The calculator will not perform any calculations when Kelvins have been specified, unless a non-zero value
for angular resolution has been entered. The calculator will also issue a warning if the angular resolution
falls outside of the range corresponding to 125-m and 1-km baselines.

140

CHAPTER 9. ALMA SENSITIVITY CALCULATOR

Figure 9.3: Screenshot of the GUI version of the ALMA Sensitivity Calculator as implemented in the ALMA
Observing Tool. The white area at the bottom is for displaying error messages i.e. parameters out of bounds.
The example here shows the achievable sensitivity for all three arrays for an on-source time of 10 minutes.

The calculator reports the values of Trx , τ0 , Tsky (including the correction for the source elevation) and Tsys
that correspond to the entered frequency and PWV.

9.4

Total Time Estimates

Note that the time calculated by the ALMA Sensitivity Calculator does not account for telescope overheads(calibration, software and hardware latencies, etc.) and is only used to calculate the expected on-source time.
However, the time estimates calculated by the OT do include these various sources of overhead and Chapter 5of the OT User Manual should be consulted for details on how the total time required to observe and calibrate
an ALMA project is calculated. The web application and OT GUI will only provide on-source times.

Chapter 10

Calibration and Calibration Strategies
This chapter describes the methods and philosophy used by ALMA in order to calibrate the correlated visibility
function data. Since calibration provides a central and important part of ALMA’s production of images,
this chapter contains many references to other chapters that describe other aspects of the ALMA systems. In
particular, the reader of this chapter will want to be familiar with the Principles and Concepts of Interferometry
described in Chapter 3 and the ALMA Observing Modes described in Chapter 8.
Most PI observations are calibrated and imaged using the ALMA Pipeline (packaged with CASA), while asmall number modes are still “manually” processed in CASA using a Python generated script (see Chapter 11).
In either case, an understanding of the current calibration process is needed by the PI in order to evaluate thereceived data package.

10.1

Fundamental Synthesis RelationshipThe relationships between the visibility function V(u, v) and the sky emission I(l, m), embodied in the vanCittert-Zernike theorem (see Chapters 3 and 7), are:
ZZ
V(u, v) =A(l, m)I(l, m)e2πi(ul+vm) dldm = Aeiφ
(10.1)
ZZ
A(l, m)I(l, m) =V(u, v)e−2πi(ul+vm) dudv

(10.2)The visibility function, V, is thus the summation of the emission distribution of the source I(l, m) (where (l, m)
are its direction cosines), convolved by the exponential term that is the delay difference of the signal from thesource to each antenna. The primary beam term, A(l, m), describes the relative sensitivity of the antennas
and is only a few arcminutes in size. The (u, v) spatial coordinates are not the physical separation of the twoantennas, but their separation perpendicular to the source direction, since it is this difference that contributes
to the phase offset between the two antenna signals at the correlator (see Figure 3.4). The visibility function(real and imaginary part) is often separated into the amplitude, A, and a phase, φ, since many calibrations
apply to amplitude and phase independently.

10.2

Calibration Fundamentals

10.2.1

Calibrated and Measured Visibility Data

The visibility function that is obtained at the output of the correlator for any baseline antenna pair (i, j) isaveraged and quantized over a short interval of time (tk ), with the output as an array of values associated withmany frequency channels (νf ). The use of the quantized form of Equation 10.2 to produce images using thediscrete Fourier Transform, after the calibration and editing described in the present chapter, is discussed in
Chapter 7.

142

10.2.2

CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIESCalibration Simplification

The complex multiplier correction required to change measured visibility function Vm to the true visibility
function V0 called the complex baseline gain , Gi,j (tk , νf ). It is a function of antenna pair (i, j), time (tk ), andfrequency, (νf ), and is defined by the equation:
i,jVoi,j (tk , νf ) = Vm
(tk , νf ) ∗ Gi,j (tk , νf ).

(10.3)

Only two total intensity polarizations (XX and YY) are considered here. See Section 8.7 for the additional
calibrations associated with all four (XX,XY,YX,YY) correlation products.
Although the baseline by baseline calibration approach is valid, the number of complex gain calibration
terms for any time is equal to the number of the baselines, which is about 1000 for a typical ALMA observation.
If every time-stamp and frequency channel required a calibration term, then the files containing the calibration
solutions would become as large as the visibility data. However, there are three factorizations of the complex
baseline calibration gain that are valid and generally used:
Antenna-based: Nearly all of the changes that corrupt the visibility function (e.g. atmosphere, system noise,amplitude changes, delay changes) can be decomposed into the two complex antenna-based gain factors
associated with any baseline. This reduces the number of gain correction terms for an N-element arrayfrom N (N − 1)/2 baselines to N antennas. Each antenna calibration has considerably more sensitivity
since it is determined from a type of averaging over large number of visibility baselines. This antennabased gain separation property is called closure1 . Some non-closing calibrations are associated with certain
correlator problems such as the effects of interference and large non-linear antenna-based corrections.
Amplitude and Phase-based: The corruption of the visibility function is often associated with effects thatindependently change the visibility amplitude or its phase. For example, the dry atmosphere can produce
a phase error caused by unmodeled delay above an antenna, and also absorb the signal that causes anamplitude error. However, these corrections will have different time-scales and frequency dependence, andcan be estimated and corrected independently. A counter example would be if some part of the systemproduced independent variations of the real-part or imaginary-part of the visibility function.
Dispersive and Non-Dispersive: Many antenna-based changes are associated with delay variations along
the antenna signal paths. These calibration errors produce antenna-based phase changes that vary linearlywith frequency, and are called non-dispersive. The linear phase-frequency relationship implies that thesedelay-type corrections need to be measured at only one frequency and then scaled to other frequencies.
Dispersive changes are any other phase changes, for example a phase jump at all frequencies at any timeor the propagation effects of the ionosphere.
The above calibration assumptions lead to the following calibration terms for baseline (i, j),
Gi,j (tk , νf ) =Ai (tk , ν0 ) ∗ Aj (tk , ν0 ) Temporal amplitude+Ai (t0 , νf ) ∗ Aj (t0 , νf ) Bandpass amplitude
φi (tk , ν0 ) − φj (tk , ν0 ) Temporal phase+φi (t0 , νf ) − φj (t0 , νf ) Bandpass phase+∆Gi,j (tk , νf ) Any additional correction
where
Ai (tk )(ν0 ) is the temporal amplitude variation of antenna i
Ai (t0 )(νf ) is the frequency amplitude variation of antenna i
φi (tk , ν0 ) is the temporal phase variation of antenna i
φi (t0 , νf ) is the frequency phase variation of antenna i
The last line represents any residual non-closing (dispersive) calibration errors.
1 See e.g. Taylor et al., 1999, Synthesis Imaging in Radio Astronomy, ASP Conference Series, Vol. 180, 1999

(10.4)

10.2. CALIBRATION FUNDAMENTALS143

It is assumed that the sum of all antenna signal changes produced by many different effects are linear in
their amplitude product or in their phase sum. For example, the antenna signal from an amplitude change ofan amplifier and that from an atmosphere absorption change will combine linearly.

10.2.3

Reference Antenna

The phase calibration for any baseline depends on the phase difference between the two relevant antennas. Thus,
the same increase in the antenna phase for all antennas will not change the baseline phase correction. To bringspecificity to the antenna-based phase corrections, the most common convention is to choose one antenna as thereference antenna, which is defined to have zero phase at all times over a specified set of frequency channels.2
This convention then determines unambiguous antenna-based phases with time and frequency. Care should
be used in the choice of reference antenna. Any anomalous phase changes with time or frequency that affectthe reference antenna will be reflected (negatively) in the phases of the other antennas. Particularly harmful isa phase jump in the reference antenna that will cause a phase jump of opposite sign in all of the other antennaphases. While not affecting the value of the corrected visibility phases, these antenna-based calibration phases
are often used for system monitoring and other more sophisticated calibration methods (see Section 10.5.3),
so an unstable antenna reference will make additional use of the antenna phase solutions difficult. For the
more extended configurations, this concern motivates the use of a reference antenna near the center of thearray where the atmospheric phase changes are likely to be some sort of average over the entire array. For asimilar reason, it is preferable, if possible, to keep the same reference antenna for polarization observations andfor other observations that span many hours across independent Execution Blocks (EBs), so that the antennaphases retain some continuity. However, this may not be possible in some cases.
Since the calibration amplitude corrections are multiplicative, a reference antenna amplitude, while possible,
is not needed and is usually counterproductive. Finally, for calibration types for which the amplitude and phasecorrections are coupled (e.g. determining cross-talk in polarization calibration), a reference antenna should not
be used. See Section 8.7.

10.2.4

Calibration Measurements Using Hardware Devices

Accurate calibration parameters can be obtained from many monitoring devices associated with aspects of the
ALMA system. Examples are the gain and noise measurements of the receivers and measured changes in thedata path lengths from the antennas to the correlator. Environmental effects such as the delay from the water
vapor above each antenna can be estimated from water vapor radiometers (see Section 10.4.3). The dry air
delay above each antenna is estimated by measuring or computing the pressure, temperature and humidity fromweather stations located throughout the array.

10.2.5

Calibration Measurements Using Astronomical Sources

This calibration technique is simple: a steady calibration signal from an unresolved calibrator radio sourceof known properties (point source, known flux density, frequency spectrum, and accurate celestial position) is
observed with one or all of the antennas. The difference between the measured visibility function and that
expected from the known properties of the calibrator source gives the calibration amplitude and phase as afunction of time and frequency. For some calibrations (e.g. antenna pointing check or bandpass determination;see Sections 10.4.4 and 10.4.6, respectively), the precise strength or exact position of the calibrator is not needed;
what is important is that it is a stable beacon.
One of the more serious calibration errors is produced by the fast and systematic delay changes in the
troposphere over the ALMA array. In order to remove these delay changes, an observation method known asphase referencing is used. This method simply alternates observations between the science target and a nearby
astronomical calibrator source (phase calibrator). The faster the switching and the closer the calibrator to thescience target, the more representative will be the interpolated calibration values derived from the calibrator tothat of the science target. More details are given in Section 10.4.9.
2 Most ALMA frequency set-ups contain four or more independent frequency channel groups, called spectral windows (spws).
The same reference antenna should be used for all of the spws in the dataset.

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Source Catalog

To aid in the selection of calibrators for any observation, an ALMA source catalog has been compiled andcontains parameters for over 3000 calibrator sources south of declination 40◦ . The approximate minimum flux
density of a source at 90 GHz included in the catalog is about 10 mJy. Most are unresolved at long ALMA
baselines, have little or no large-scale structure, and usually have a radio position more accurate than about
0.00300 . The source density is about one source per nine square degrees, so that one of the calibrators will be
on average about three degrees from any random science target position.
The location and strength of the calibrator source chosen for the calibration will depend on details of thecalibration purpose. For example, if a calibrator source is needed to determine the pointing or focus parametersof an antenna at any frequency and elevation, a series of calibrator observations at a range of elevations isneeded. Each short observation will measure the source visibility amplitude changes with pointing direction or
focus settings. In these cases, the calibrator is used simply as a constant beacon whose signal changes as theantenna is moved away from its nominal setting.
About 40 bright calibrators (called "grid sources") are observed with the 7-m Array every two weeks inorder to track their variability; this is typically ∼10% per month. While most calibrators are largely constantduring this time, occasional flaring does occur. The observations are currently made at 97.5 and 343.5 GHz,and occasionally at 233 GHz. Included is one scan of a solar system object with an accurate flux density model:
Uranus, Neptune, Mars (less accurate during storms), Callisto and Ganymede, Titan, Ceres, Pallas and Vesta.
The resultant absolute flux density accuracy for grid sources is about ∼5% to 10% between Band 3 and Band7, based on a relative calibration uncertainty from measurement statistics between observations of 3% to 6%(1 sigma), and a typical 5% uncertainty in the models. The polarization variation of these quasars are also
monitored and is discussed in Chapter 8.

10.2.7

Flagging Data Based on Calibrations

Some flagging of the data are made before calibrations are done, e.g. an antenna out of lock, large incorrect
pointing of an antenna, or shadowing of an antenna by another. However, a significant part of the data flagging
is inferred from calibration values that are anomalous in some way. This discrimination is made relatively simple
for ALMA data since most calibration values should be similar among more than 40 antennas that are used formany observations.
During most forms of calibration that use a relatively strong source, the consistency of the calibration values among similar antennas is expected. Some cases are obvious, such as the loss of correlation amplitude
associated with baselines that contain one particular antenna. The ALMA Pipeline task lowgainflag will flagantennas with gain < 0.5 or > 1.5 times the global median because such large deviations are can rarely becalibrated. Intermediate cases require assessing how well the calibrated data matches the model visibilities forthe calibrator (point source). This philosophy is implemented in the ALMA Pipeline tasks bandpassflag andgfluxscaleflag, which search for outliers in the scalar difference of the corrected amplitude and model amplitude on the bandpass calibrator and the flux and phase calibrators, respectively. Antenna-based, baseline-based
and time-based issues are searched for and flagged above a rigorously-developed set of thresholds. Antennas orbaselines that have been fully flagged on the phase calibrator are propagated to the science target via either
the caltable (for the case of antennas) or explicit flags (for the case of individual baselines). See the ALMA
Pipeline documentation, available off the ALMA Science Portal, for further details. Issues that affect only asmall subset of channels are not easily detectable by current ALMA Pipeline heuristics, and are usually due tohardware issues, such as errors in the correlator. One of the goals of ALMA Quality Assurance (AQUA) andQuality Assurance (QA) 0 (see Section 11.2) is to find these kinds of frequency-dependent issues earlier so that,
where necessary, their cause can be investigated and fixed.

10.3

Observatory Calibrations

This section summarizes the fundamental ALMA observatory calibrations that are carried out by the observatory
outside of PI science observations. Some of these calibrations are done infrequently and may only be redone if
an antenna has been through a period of a major change or overhaul, or if an antenna has been moved during
re-configuration of the array.

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10.3.1

Antenna Primary Beam Pattern

To first order, the relative response of the antenna sensitivity as a function of angular offset from the pointing
center varies with the antenna diameter and frequency. Assuming that the antenna surface and focus areaccurately determined, the field of view, θ (defined as the angular width between half-power sensitivity), inradians, is inversely proportional to the number of wavelengths λ in the antenna diameter D, such that:θ = 1.13λ/D(10.5)

More details on the shape and characteristics of the primary beam are given in Chapter 3 and in Baars (2003)3 .
The beam pattern shape is important for constructing accurate mosaic images.

10.3.2

Antenna Surface Efficiency

The large-scale and small-scale surface irregularities of each antenna surface were measured (mostly using
interferometric holographic techniques on a bright quasar) and improved to meet specifications4 . The antenna
efficiencies for each ALMA band are given in Table 9.3. For the 12-m antennas, the efficiency ranges from about
70% at Band 3 to about 30% at Band 10. For the 7-m antennas, the efficiency ranges from about 70% at Band
3 to about 40% at Band 10.

10.3.3

Antenna Pointing Accuracy

The antenna pointing correction is the difference between the true sky location of the peak sensitivity of
the antenna primary beam and the location shown on the azimuth and elevation encoders. Pointing offset
observations are made for about 40 bright quasars over the sky5 . Using an analysis system called TPOINT6 ,the all-sky pointing offsets are fit in elevation and azimuth to 19 parameters. The residual all-sky point error
is about 200 . There is also a fast switching mode in which the relative pointing difference between two sources
separated by less than two degrees is about 0.600 . The switching time, including settling of the antennas andelectronics is about 2 seconds.

10.3.4

Antenna Focus

The emission reflected from the main antenna surface is directed toward the feed for each band using a subreflector that can be tilted and moved. The appropriate focus curves (subreflector offsets and tilt) are generated
and stored for each antenna, and these remain fixed for weeks. Additional information is given in Appendix A.

10.3.5

Antenna Integration Calibrations

Scheduled array configuration changes are made approximately every 3 to 4 weeks, during which typically about
8 antennas are moved over a period of about 10 days. After a change in the configuration of the array, a setof antenna integration calibrations are carried out before a recently moved antenna is integrated back into anarray used for PI science.
Improved Antenna Pointing
Additional pointing observations are needed after an antenna has been moved to a new pad. Of the 19 total
fitted pointing parameters, five are expected to change: the azimuth and elevation offset, two antenna tilt terms
and one overall rotation term. This is part of the antenna integration process and uses a short all-sky-pointing
observation, described in Section 10.3.3. These short observations are needed to obtain the a nominal pointing
accuracy over the sky of about 200 .
3 http://legacy.nrao.edu/alma/memos/html-memos/alma456/memo456.pdf, (ALMA Memo 456)
4 Mangum et al, 2006, PASP, 118,1257
5 https://safe.nrao.edu/wiki/pub/ALMA/CalExamples/PointingCalStepByStep.pdf
6 http://www.tpointsw.uk/index.htm

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Antenna Offset Delay and Focus
The signal path length between an antenna (excluding the variable delay of the source signal to each antennaduring an observation) receiver to the correlator will change considerably after an antenna is moved. If these
offset path length differences are not removed, the correlated visibility between antennas will show a large phaseslope over the frequency band. For example, if the signal path length from an antenna to the correlator is offset
by 10 cm, this will produce a phase slope of 100◦ over a 2 GHz spw and produce significant decorrelation over
the the spw. The delay offset is measured by a short observation of a strong quasar using a reference antennathat has not been modified or recently moved. A more accurate removal of a delay offset and the frequency
characteristics are determined from the bandpass observation in most PI observations.
The focus parameters associated with an offset in the azimuth and elevation with a possible small rotation
are also checked during the antenna integration process.
Antenna Positions
In order to make high quality images using phase referencing techniques, the relative antenna locations must
be known to an accuracy of 0.3 mm. This limits the systematic phase errors between the calibrator and thetarget during phase reference observations. If uncorrected, the error produces distortions in the target image.
From Equation 10.1, the maximum phase difference, ∆φ in degrees, between a calibrator and a sciencetarget, that is produced by an error in the antenna position, ∆B (mm), is given by:
0.02 × ∆B × ν × Sep = ∆φ

(10.6)

where Sep (deg) is the calibrator-target angular separation and ν (GHz) is the observing frequency.
Occasionally, an initial antenna position error may be as large as 5 mm. In Band 7 (350 GHz), for example,
this would result in a phase offset of 50◦ between the calibrator and target even in the fortunate situation offinding a phase calibrator within 3◦ of the science target. This offset remains relatively constant over one hour,
so its effect on the image quality would be worse than that of short-term atmospheric variations of comparable
size.
The accurate antenna positions are determined from a sequence of many short observations of bright quasars
that are observed over the sky, called all-sky delay observations. Many strong quasar calibrators are observed,
each for 5 seconds, with about 40 seconds needed to move between each quasar, often more than 40◦ away inorder to sample the entire visible sky in about 20 minutes. The observations are made at Band 3, where mostquasars are strongest, and using four spws in TDM mode for a total bandwidth of 8 GHz. During the antenna
integration process at the beginning of a configuration or when an antenna is moved and is added back to thearray, the observations may be limited to a small number of antennas over about 30 minutes to obtain about 1
mm accuracy before PI observations are started.
However, near the end of an antenna move period when the array pattern has been set, a more accurate
all-sky delay observation is run, often using the entire 12-m Array to improve the SNR of the solutions. For atypical observing time of about 45 minutes, the accurate antenna-based delay for about 50 scans are obtained,
and the systematic delay for each antenna versus azimuth and elevation are fit to an improved antenna position,
often with an accuracy of < 0.1 mm. An analysis script in the TelCal system, called tc_antpos, is used todetermine the fit. An example of the fit for one antenna of the scan delays before and after the correction of
the fitted residual antenna offsets is shown in Figure 10.1.
After the all-sky delay run, the updated antenna positions are placed in the online Telescope Monitor andControl DataBase (TMCBD) that is used by the delay server. The updated antenna positions are also currently
placed in a file which can be accessed by the ALMA Pipeline and other offline reduction systems to correct theobservations that were made before the better antenna positions were updated in the system.
The antenna position uncertainties depend on the distance from the array center (the reference antenna isusually chosen near the array center), because the atmospheric phase variations, caused by large-scale turbulence,
generally increase with baseline length. The typical antenna position errors are about 0.05 mm per kilometerof baseline length. Hence, at the longest baselines, a typical antenna position uncertainty could be as large as
1 mm.

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147

Figure 10.1: Antenna Position Determination: The antenna position fit for antenna DA46, at 3.5 km fromthe reference antenna, from a 50-minute all-sky-delay observation on Dec 25, 2017. Each of the 45 points show
the delay solution from one scan, separated by about 1 minute. The observations were made at Band 3 where adelay change of 0.001 ns is equal to a phase change of 40◦ . The red points show the original delay measurements
and the scatter is caused by antenna position offsets as a function of quasar elevation and azimuth, The black
points show the delay after correction of the DA46 antenna position error by about 4 mm. After correction, thespread of phases between sources over the sky is about only 20◦ , so the expected phase difference from a residual
antenna position offset between a target and calibrator that are just a few degrees apart will be considerably
less.

10.4

Execution Block Calibrations

This section describes how an ALMA science Execution Block (EB) is calibrated. Each EB contains theminimum set of necessary calibration observations, which are automatically defined in the Scheduling Block(SB).
Several EB’s (each limited to about 1 hour integration on a target) may be needed to obtain sufficient SNRor (u, v) coverage to meet the science goals as defined by the PI. When there are multiple EBs, the calibrator
sources observed may differ between EBs if, as in most cases they are selected at run-time by the SSR queryalgorithm (see Section 8.3.1); only in a few cases will calibrator sources be fixed in the SB by ALMA staff.
The specific antennas in the array may also change between EBs. It is useful to keep the same reference
antennas when calibrating each EB even though the EBs are calibrated separately. The quality of the EBs may
differ, mostly because of the different phase stability conditions. The AQUA QA0 and QA0+ assessments (seeChapter 11) are carried out after each EB is observed in order to assess the quality of the data.

10.4.1

Making the Measurement Set

Data from ALMA are stored at the ALMA site, at the JAO in Santiago, Chile, and mirrored to each of the
ALMA Executives in North America, Europe and East Asia (See Chapter 13). These data are transformed into
an ASDM (ALMA Science Data Model) data structure using asdmExport (see Chapter 12). This format is thenconverted into a measurement set (ms) using the CASA task importasdm. These steps will not be executed bymost PIs, but could be useful for special tests and calibrations in certain cases.

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CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIES

Amplitude Calibration Procedure (System Temperature Measurement)

An important ALMA online calibration determines the antenna receiver sensitivity and the radiative sky temperature. These corrections are obtained from a 15-second scan where a hot load, ambient load, and sky
are alternately placed in front of the feed. Both 12-m and 7-m antennas are equipped with these Amplitude
Calibration Devices (ACDs). The design, use and accuracy of these ACDs are discussed in Section A.5.1.
At frequencies below about 400 GHz, where the system temperatures are are stable, an ACD scan is madeevery 10 to 20 minutes. However, at higher frequencies, and wherever the opacity is large and more variable, allscans will have an associated ACD measurement. The online measurements of Tsys and Trx are stored in the
CalAtmosphere table in the ASDM datasets, and are displayed in real-time at the telescope to detect problems
immediately for QA0 assessment (see Section 11.2).
An example of the Tsys measurements from a Band 9 observation is shown in Figure 10.2. The two antennas
show the typical range of the Tsys measurements at this high frequency. Notice that the Tsys in each spw contains
narrow lines that are associated with tropospheric emission. For example, the additional line emission of 20%
in the first spw near channel 60 is the emission from the ozone line at 673.914 GHz.

Figure 10.2: System Temperature at Band 9: The measured system temperatures at Band 9 for a target
source for two antennas with different properties. Top row is for DV05 for four spws, bottom row is for DV09
for four spws. The ordinate is the system temperature, the abcissa is the channel number in each spw. The
average frequency for each spw is 673.9, 675.9, 677.9, 679.9 GHz, and the channel separation is 1.56 MHz. The
two polarization Tsys differs significantly for DV05. The finite width of each Tsys curve is caused by the small
time variation over the 50-minute EB.

10.4.3

Water Vapor Measurements

Variations from water vapor (Precipitable Water Vapor; PWV) in the antenna line-of-sight cause significant
delay variations, up to 0.5 mm/second, corresponding to 50◦ of phase/second at 90 GHz. The changes are
driven by wind turbulence and cloud structure, and cover a large range of spatial scales from 5 meters to many
kilometers. All 12-m ALMA antennas are equipped with a Water Vapor Radiometer (Dicke-type) that measuresthe emission from atmospheric water vapor every 1.1 seconds at four frequencies near 183 GHz, in nearly thesame direction as the ALMA pointing. The phase correction method using the radiometers was developed by
B. Nikolic et al. (2013)7 , and information about their design and use is given in Section A.6.
7 Nikolic, B. et al., 2013, A&A, 552, 104

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149

These WVR corrections are made by the online calibration software system in TelCal8 . An offline script using
the CASA task wvrgcal also converts the water vapor emission to a predicted antenna delay. At present, only
the uncorrected visibility data are archived and the WVR correction is applied offline as part of the calibration
process. In addition to allowing a global solution (across the observation) for the brightness temperature todelay conversion coefficients, the offline application of the delay correction enables small edits or scaling of the
WVR emission to delay to be made if needed9 . The online corrected data, however, will be available for use of
the AQUA and QA0 (Chapter 11) analysis of each observation.
The WVR correction often reduces the water vapor-induced phase fluctuations on time scales of 2 seconds
to many minutes by 50% or more, enabling more observations to meet the rms and image quality success level.
An example of the antenna-based phases at Band 9 for an antenna before and after WVR correction is shownin Figure 10.3. The PWV was ∼0.45 mm for this example, and it is the typical improvement for relatively
low WVR content. The ALMA Pipeline task hifa_wvrgcalflag determines the WVR correction, generates
flags for WVR data that are out of range or noisy, and automatically interpolates from up to three neighboring
antennas (if near enough).

Figure 10.3: WVR correction: The improved temporal phase by using the WVR correction is shown in thefour panels for different antennas at Band 3 in the long baseline configuration over a period of three minutes
during a strong bandpass source observation. The red lines show the temporal phase before correction; thegreen lines after correction. The short-term variations are removed as is most of the longer term drifts. The
offsets from zero phase are arbitrary.

10.4.4

Antenna Pointing Improvement

Additional pointing observations are sometimes included in an EB (see Section 8.2). For observations > 350
GHz, the pointing between sources more than about 20◦ apart may differ by more than 200 from the nominal
pointing solution. For observations that demand the highest pointing accuracy, for example < 0.500 , a pointing
8 http://adsabs.harvard.edu/abs/2011ASPC..442..277B
9 L. Maud, https://arxiv.org/abs/1707.03506

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every 10 minutes on a source near the phase calibrator or science target can be done (known as pointing
referencing).

10.4.5

Antenna Position Improvement

The determination of the most accurate antenna positions (typically 0.2 mm accuracy), from a comprehensive
all-sky delay observation, usually occurs after all antennas have been moved during an array re-configuration.
The shorter observations made just after one or more antennas have been place on a new pad (see Section 10.3.5)
are accurate to about 1 mm. PI observations executed before the most accurate antenna positions have been
made are not processed by the ALMA Pipeline until the final position updates are placed in an offline file which
is used during calibration to apply the most accurate antenna position corrections. However, the AQUA andQA0 analysis of these observations are not impacted by any remaining ≈ 1mm antenna position offsets.

10.4.6

Bandpass/Frequency Calibration

The goal of the bandpass calibration is to determine the relative amplitude and phase of the frequency channels
across each spw. Because of the excellent temporal stability of the ALMA bandpass (Kameno 2015)10 , thebandpass calibrator is observed only once at the beginning of an EB. It is generally a bright quasar within about30◦ of the science target, and is chosen from the list of grid sources (see Section 10.2.6). The scan length is
between 2 minutes and 30 minutes and depends on the strength of the calibrator and the bandpass accuracy
needed.
The ALMA online software selects a bandpass calibrator based on the latest flux measurement, so that a
SNR of 50σ per antenna and 128 MHz bandwidth can be achieved. If a suitable calibrator cannot be found, theonline software may relax
threshold down to
pa SNR of ∼ 14. With these criteria,√ the p√ spectral dynamic range canbe calculated as SNR × 2 × N (N − 1)/2 × ∆ν/128 MHz, where a factor of 2 is arisen by two orthogonal
polarizations, N is the number of antennas, and ∆ν is the desired frequency resolution. For example, we geta spectral dynamic range of ∼ 830 with SNR of 50σ, 20 km s−1 velocity resolution at observation frequencyof 300 GHz, and 43 antennas. Please see Table 2 of the ALMA Cycle 8 2021 Science Primer (available off the
Science Portal) for the relation between velocity resolution and channel width.
There are two steps in obtaining the relative bandpass calibration. First, the temporal phase variations overthe bandpass scan, (see Equation 10.4) is determined by averaging the bandpass source over most of each spw,
for each time stamp tk . An example of these phase changes a scan is shown in Figure 10.4.
After temporal phase variations over the bandpass scan are removed, the second step determines the bandpass
amplitude and phase dependence for all channels in each spw/polarization. The bandpass solutions are usuallynormalized to average amplitude 1.0 and phase 0.0 for each spw. An example showing the bandpass solution
for four antennas at Band 9 is given in Figures 10.5 and 10.6. This typical bandpass shape is relatively flat toabout 3% and 8◦ over the 2 GHz width, often with a channel to channel rms of about 1% and 1◦ . Occasionally(however, not in the example shown), there may be a significant phase slope that was not removed during theantenna integration calibrations which will be removed with the bandpass calibration. The 200 MHz-width
ripples in the bandpass have several possible causes related to small signal path reflections in the antenna
structure and in the electronics. They are stable with time, however. Finally, at the edges of many spws,
significant amplitude departures occur and are generally flagged. In this example, the ALMA Pipeline task
hifa_bandpassflag flagged channels 0-9 and 123-127 for all antennas/spws.

10.4.7Flux Density Scale

The correlated visibility amplitude scale obtained from the correlator output is the ratio of the correlated
signal with the total system noise, and is usually much less than about 1%. Since each antenna receiver noiselevel plus the emission from the atmosphere above each antenna are accurately measured in units of theireffective temperature by the ALMA calibration devices, the percentage correlation is converted to Kelvin (K)by application of the system temperature (Section 9.1.6).
The most straightforward conversion of the visibility amplitude from units of K to units of Jansky (Jy) is
to include in the EB an observation of a source with a known flux density. Since most quasars calibrators arevariable (typically 10% per month, with the stronger ones more variable), the inclusion of a solar system object
10 https://almascience.nrao.edu/documents-and-tools/documents-and-tools/alma-technical-notes/ALMATechnicalNotes15_FINAL.pdf

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151

Figure 10.4: Bandpass Phase-up: The phase variation for a Band 9 bandpass calibrator. (Top) Xpol and
Ypol phase and their difference for 675 GHz spw, (Middle) Xpol and Ypol phase and their difference for 679
GHz spw, (Bottom) 679 GHz - 675 GHz spw for Xpol only and their difference. The WVR correlation has
been applied to all data. The phase variations over time are extremely well correlated between polarization andspws, and these phase offsets are virtually constant over an EB.

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Figure 10.5: Bandpass Amplitude: The bandpass amplitude at Band 9 for four antennas, Xpol are shown as
blue dots and Ypol as green dots. Xpol channels below 10 and Ypol channels above 120 should be be flagged.
Notice that the line emission near channel 60, seen in the Tsys solution (Figure 10.2), has been significantly
reduced after multiplication of the raw visibility amplitude by the Tsys factor.
(see Section 10.2.5) at the higher frequencies is recommended. The flux density models are determined between
30 and 2000 GHz11 , and are accurate to about 5% at the lower frequencies. This increases at frequencies above
Band 7, however, since the spectral extrapolation of the grid source flux densities is not accurate; in Bands 9
and 10, the conversion from K to Jy is accurate to about 20%. Thus, one scan of an object can determine the K
to Jy factor. Since the solar system objects all have significant angular sizes so the K to Jy factor determination
should be limited to the shorter baselines. With the success of the grid source monitoring observations every
10-14 days to follow their variable flux density, most PI observations now include one scan of a grid quasar touse as both the bandpass and and flux density calibrator.
Assuming that the conversion of the visibility amplitude from percentage correlation to Kelvin is accurately
made, the further conversion from K to Jy can be estimated solely from the antenna effective area at theobservation frequency. The effective area is equal to the antenna surface collecting area times the antenna
efficiency (see Table 9.3 and Section 10.3.2 for details of the efficiencies of the ALMA antennas).
For frequencies up to 400 GHz (12-m antenna efficiencies between about 60% and 70%; 7-m antenna efficiencies between about 65% and 70%) this leads to an SEFD (Source Equivalent Flux Density) = 35.0 K/Jy for the
12-m Array and an SEFD = 96 K/Jy for the 7-m Array. The SEFDs increase at the higher frequencies. However, these conversion values may be more accurate than those from quasars and solar system objects, especiallyat the higher frequencies (Section 9.2.1). This SEFD flux calibration method is currently being tested.

10.4.8

Amplitude Temporal Variations

The amplitude scale factor determination from K to Jy is obtained only at the time of the scan used to determine
this ratio. At low elevations and for frequencies above 350 GHz, there are small temporal variation of gain with
11 https://library.nrao.edu/public/memos/alma/memo594.pdf

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153

Figure 10.6: Bandpass Phases: The bandpass phase at Band 9 for four antennas, Xpol blue dots and Ypol
green dots.
time related to antenna efficiency changes with elevation or from the differential heating of the antenna surface
support legs or small systematic pointing changing. These changes can produce amplitude changes up to 10%,especially during daylight hours. If the phase calibrator used (see Section 10.4.9) is relatively strong, then its
flux density can be determined from comparison with the bandpass strength. Then, during the observation, theamplitude solution part of the phase-referencing solution can be used to estimate the temporal gain variations
over the observation.

10.4.9Phase Referencing Calibration

One of the most important calibrations needed for obtaining good quality images is phase referencing calibration.
It is usually the final calibration after the others, discussed above, have been made. The temporal amplitude
variations during most PI observations, discussed in Section 10.4.8, are rarely as critical as the phase calibration.
The EB structure consists of many cycles of visits to the phase calibrator, with visits every ∼80 seconds for themost extended configurations or up to every 600 seconds for the most compact configurations.
The first reduction step uses the CASA task gaincal to determine the antenna-based phase correction fromall phase calibrator scans. The phase solutions are usually made separately for each spw and polarization,
but they all have virtually the same temporal variation since the instrumental phases between the spws andpolarization are steady to a few degrees over an hour or more. For this reason, when the phase calibrator isrelatively weak (less than 30:1 SNR per antenna solution), the spw and polarization channels can be summed
after the phase offset is removed to obtain one temporal solution for all spws and polarizations.
The second step of phase referencing interpolates these antenna-based phases to the other scans in the EB.
Some interpolation options are discussed below. As discussed in Section 10.2.3, the choice of reference antenna
is important, and a non-flagged and stable antenna near the array center should be chosen, even if several
iterations of phase calibration are needed to determine this a satisfactory reference.
Some comments on efficient and accurate phase referencing are described below.

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Phase Transfer from Calibrator to Target(s): The simplest method is to linearly interpolate the calibrator
scan-averaged antenna-based phases between two consecutive phase calibrator scans to that of the sciencetarget or other sources. This is done with the CASA task applycal. More complicated interpolation
methods including the use of several phases over a scan, or several scans over a longer period of time, arepossible, but the simple linear interpolation is usually satisfactory.
Calibrator Cone Search and Detectability: An acceptable phase calibrator for a given science target isthe closest source that is above the necessary SNR limit and point-like. For most science targets, the best
calibrator choice from the ALMA catalog is clear. In some cases, often if one or several possible calibrators
have SNR<100 and have no flux density measurement in the last three months, calibrators are included
in a short flux-checking observation, called a cone-search, that is made about about two months before
the science observation is to take place. Checks for an extended structure or resolution of the calibrators
are also made. Cone-searches are also used to select the appropriate check source for an observation (seeSection 10.4.10).
Phase Calibration Sensitivity: The strength of the phase calibrator should be sufficient to produce a scansolution per antenna with a minimum antenna-based SNR of 15. This SNR leads to an antenna-based
solution of a 7% amplitude error and 4◦ phase error. With the typical number of antennas and scans used
for most PI observations, this noise-like calibration error will average over the science target scans andantennas, and limit the image accuracy to < 0.01% of its peak intensity if it is not otherwise noise limited.
Combining spws: Since the phase difference among the spws and polarizations are relatively constant over
one to two hours, the calibration sensitivity can be increased by a factor of 2.8 if visibility data from thefour spws and both polarizations are first combined. The phase differences among the channels can be
determined from the bandpass observation (Sec 10.4.6), and are stable to a few degrees.
An example of the phase calibration of two antennas from Band 9 observations for a 1-km configuration isshown in Figure 10.7. For nearly all ALMA calibration, the X- and Y-polarized phases follow each other to afew degrees since nearly all of the variations are caused by tropospheric delay changes over each antenna. A
good check on the signal-to-noise of the calibration scan and other problems is given by the X-Y phase difference
easily obtained from CASA task plotcal (poln=’/’). The difference should be relatively flat with variations
that are consistent with the expected rms noise. Hence, unstable periods of calibration from an antenna can beeasily recognized with the appropriate data flagging made.
In some cases, a close inspection of the phase referencing results may show suspected antennas or time
periods where additional flagging may be useful. Some considerations include:
Scan Decoherence: When the phase variations over a calibrator scan are large, there is considerable decoherence of the visibility data. Such decoherence can be verified for the stronger phase calibrators using
solution times less than the scan length to see the fast phase changes. This decoherence is larger at longer
baselines and effectively decreases the resolution of the observation. No corrective action is recommended.
It is better to acknowledge the decoherence, rather to make amplitude corrections that often depend on
the relative strength of the calibrators and the targets.
Calibrator Image: An image of the phase calibrator is provided as part of the calibration products. It
should be a high quality point source (after cleaning) with a peak intensity and integrated flux densitythat agrees with the flux density assumed in the calibrations. The residual sidelobes or rms noise should
be a small fraction of its peak intensity. If the phase calibrator image does not meet these expectations,then the calibration and editing process is suspect and should be re-investigated.

10.4.10Check Source Observation

For any observation with maximum baseline length greater than 5 km, and/or at frequencies greater than 400
GHz, check source scans are included in an SB. The criteria for choosing a check source from the ALMA catalog
are that the calibrator should be: (1) about the same distance from the phase calibrator as the phase calibrator
is from the science target and (2) strong enough to produce an image with SN R > 15 using all scans and spws.
This flux limit is about a factor of three less than that for the phase calibrator used for the observation. As withthe phase calibrator selection, most chosen check sources are unresolved even at the longest ALMA baselines,

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Figure 10.7: Calibrator Phases: The calibrator temporal phase at Band 9 for two antennas. (Left) 1.0 km
from the reference antenna. (Right) 0.3 km from the reference antenna. Over the 4000-second EB, 10 phasecalibrator scans were made, each of 60-second length with three 20-second points connected to show the internalscan phase variation. The X and Y polarizations show virtually the same temporal changes, as expected. Withineach scan, the phase change is about 20◦ . Between scans separated by 7 minutes, the difference is about 50◦ andis a little larger for the longer baseline. The X-Y phase difference (green (points/line) shows the approximate
SNR of each solution, and is much less than the atmospheric variations. The offset is arbitrary for clarity.
but exceptions do occur. The check source is typically observed two or three times per EB with a scan length
the same as the phase calibrator scan.
The check source is sufficiently strong and its image is routinely made in the QA0+ analysis procedure after
each execution. An image of the check source is also made by the ALMA Pipeline during data processing.
An analysis of the check source image quality from many long baseline observations in 2017 suggests that its
peak to total flux density ratio is a good indication of the observation quality (see Chapter 11). This ratio
varies with the rms phase difference between phase calibrator scans, and with its angular separation from thephase calibrator. These check source distortions (including a position offset from its known position) are a good
indication of the target image quality which is often too weak or too extended to be used on its own to estimate
the quality. Generally, the science target distortion and its position offset is similar to that of the check source,
but approximately scaled by their relative distances from the phase calibrator.

10.4.11

Estimate of Image Quality in QA0

An initial evaluation of an EB’s quality is made within hours of an observation, and is discussed in Section 11.2.
While many observing and data properties affect the image quality, it is significantly affected by the propertiesof the tropospheric phase variations over time and over the array, and these properties are readily obtained
from the phase calibration (Section 10.4.9). For that reason, a QA0 metric, based on phase variations inphase-referencing is described here.
The tropospheric phase variations, to first order, decrease the effective resolution of an observation because
the longer spacings have more phase variations than that of the shorter spacings. For all sources, this will
decrease the peak flux density by smearing out the structure, and is often called phase-referencing coherence.
Using phase-referencing observation tests over a range of tropospheric phase variations and calibrator-target
angular separations, the expected coherence, as a function of calibrator phase rms between scans and a functionof the calibrator-target angular separation, are illustrated in Figure 10.8. These results are relatively independentof the maximum baselines and observing frequency.
The explicit peak/integrated flux densities in the following roughly equate to the QA0 status described in
Chapter 11. If the peak/total flux density of the object is > 0.85, the observation is considered to be satisfactory,
i.e. QA0 Pass. For example, from the tests, a calibrator-target separation of < 2◦ with a scan-to-scan phasecalibrator rms of 45◦ should provide a good quality image. A calibrator-target separation of 5◦ needs a phase

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Figure 10.8: Phase Referencing Coherence: Simulation results to determine the relationship between image
quality and phase referencing parameters. (Top): The peak/integrated image quality versus the PhaseCalTarget separation. Curves for different PhaseCal scan phase rms’s are shown. (Bottom): the peak/integration
image quality versus PhaseCal scan phase rms. Curves for difference PhaseCal-Target angular separations areshown.

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calibrator rms of ∼ 25◦ in order to pass. For a Peak/Total < 0.6, the observation should probably fail and be
re-observed, (QA0 Fail). Thus, for a calibrator-target separation of 5◦ , the rms scan phase difference should beless than about 40◦ to pass. The intermediate quality images with peak/integrated between 0.6 and 0.8 generally
have a QA0 Semi-pass designation and QA2 processing is needed to determine if the EB is successful. Of course,
the image quality using the shorter baselines only will produce a more coherent image, but see Section 11.2 for
the QA0 rules for the number of antennas with sufficiently low phase rms that can be used for QA0 Pass.
When there are multiple EBs in an MOUS, the image quality metrics should be compared for the checksource (if available) and the science target for each EB. Sometimes, the image quality/phase stability will differ
significantly among the EBs, but the image weighting does not consider the phase coherence properties. Hence,
down-weighting or even removing a poorer quality EB could be investigated to determine which set of EBs
produces a better quality image.
In addition, the position registration among the EBs is best evaluated by comparing the check source position
peak among the EBs, or from a strong target compact feature if one exists. Offsets at the level of 0.2 times theresolution are reasonable and of no concern. Larger offsets between the peak emission may be seen if one ormore EBs has relatively poor phase conditions and if the target is somewhat complex. If some EBs have good
agreement in the check source position while others do not, an image made from the first EBs can be used as
the initial model image for self-calibration (see Section 10.5.1) of the other EBs.

10.4.12Calibration for Specific Observing Modes

The above sections apply to most ALMA interferometric observing modes (see Chapter 8) including, but notlimited to, single or multiple EBs, single pointings or mosaics, non-moving or moving (Ephemeris; 8.9) targets,
single or multiple configurations or single or multiple sources per EB. However, there are certain observing
modes where special calibration is needed at the time of observation. These are described below.
Polarization Calibration
For ALMA polarization observations, the current calibration scheme, systematic calibration uncertainty, andimaging of the four Stokes parameter data, I,Q,U ,(V ), are described in detail in Section 8.7. After the normal
XX and Y Y gain calibrations are made, three additional calibrations are needed: determination of the X andY relative delay in the receiver analog path, the determination of the cross hands phase (XY -phase), and thedetermination of the “D-terms”, or the lack of purity in the polarization decomposition into a linear base X andY . Most polarization observations require two or three EBs to cover a sufficient range of paralactic angle (≥60◦ ).
Total Power Calibration
Details of the Total Power observing mode, including the current calibration scheme, are described in Section 8.6.
Solar Calibration
Details of the Solar observing mode, including the current calibration scheme, are described in Section 8.10.

10.5

Additional Calibrations

This section contains suggestions for additional analyses and calibrations beyond those normally done for standard ALMA data reduction. Depending on the science goals, the observing conditions, and the complexityof the science target image, further processing by the PI may improve the image quality. Several common
techniques are described, but additional information and support can be obtained from the local ARC.

10.5.1

Self-Calibration

The phase referencing technique makes periodic observations of a known point source to measure the temporalantenna-based amplitude and phase calibrations during an observation. These calibrations are ’transferred’ tothe target from which an image is made. If the target is bright and sufficiently compact, further calibration

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CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIESof the target data can be obtained because of closure property of interferometric data (Sec 10.2.2). For the
12-m Array, any further calibration of the ≈ 1000 baseline visibility functions can be made by determining theapproximately 50 antenna-based corrections. This redundancy permits an iterative process that 1) improves
the visibility data calibration, and 2) improves target image accuracy.
A description of the philosophy, criteria and methods for self-calibration (hereafter, self-cal) is given in
Brogan, Hunter & Fomalont (2018)12 . Because of its iterative nature and the need to have sufficient SNRof the target over an reasonable solution period, self-cal methods vary depending on many properties of thedata. Based on current tests (QA0+ automatic attempts to self-cal ALMA observations; see Section 11.3), it isestimated that for about 25% of ALMA science targets, self-cal can improve the quality of the image, sometimes
by a factor of five or more as measured by the peak flux density to the rms noise in the image.
Suggested Self-Cal Steps with an Example
The first step towards successful self-cal is to determine if self-cal is possible for a given science target.
Is self-cal improvement likely? As a rule of thumb, the peak/rms of the initial phase-referenced image
should be at least 20. Whether the initial image is from the continuum data or a spectral line featuredoes not matter, but the image/data link must be maintained.
First try: For the initial attempt to determine if self-cal improvement is likely, try a phase-only self-cal on thenormally calibrated target data with the cleaned target model in the visibility model column13 A solution
time of one scan (one to five minutes) is a reasonable first step. A good indication of the self-cal successis to compare the X or Y phases versus scan for many antennas using plotcal with poln = ” and poln =’/’. An example is given in Figure 10.9.
The next steps are typical if the previous step is successful with good SNR (small X-Y phase difference).
Further phase-only self-cal: Repeat the phase-only self-calibration with a more optimum solint interval.
If the continuum is used, combine the spws using the bandpass source to align the phases to improve the
SNR if a solution is needed. Make sure that the improved image model is used for the next iteration. Afterapplication of this phase self-cal, clean the target relatively deeply, especially for a target that contains
both large-scale and small-scale emission. It is better to include as much flux in the clean components
as possible, even with some increased noise components. If in doubt, keep cleaning around the known
emission regions. Another phase-only self-cal iteration can be considered, perhaps with a shorter solution
interval.
Amplitude and phase self-cal: If the peak/rms ratio is more than about 100, additional self-cal iterations
that include an amplitude correction is recommended. Use a model from the previous phase-only self-cals
that have been cleaned deeply so that most of the flux density is in the model image. The usual timescaleof intrinsic amplitude changes are about 5 to 10 minutes so use this solution interval even if the phaseself-cal scale is much less. Use the option calmode=’ap’ rather than calmode=’a’. This will produce a
better solution in the amplitude stability even though the phase corrections should be minimal. The
amplitude self-cal solutions often show outlier points associated with brief antenna drop-outs that should
be flagged. For strong sources, a peak/rms > 1000 is often possible but requires several additional self-cal
iterations with careful editing of the data.
The self-cal example shown here was from a one-hour observation in November 2017 at 250 GHz using 43
antennas with a maximum baseline length of 11 km. For this example, the image improvement from the normal
phase-referenced image to that made after two phase self-cals with a solution interval of 18 seconds (1/3 of atarget scan) is shown in Figure 10.10. For additional details, see Brogan, Hunter & Fomalont (2018).
12 Brogan, Hunter & Fomalont, 2018, https://arxiv.org/abs/1805.05266
13 Make sure the model column exists and contains data corresponding to the image clean components, otherwise use the task
FT on the clean model to generate this model column data.

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Figure 10.9: Self-cal Phases: The self-cal phases for four antennas. The blue points are the X-pol self-cal
phases. The green points are the X-Y pols self-cal phases, offset by 100◦ for clarity. The scan length was 55
seconds and the frequency was 240 GHz. The X-Y difference is a function of the solution SNR and shows thatthe ’X’ or ’Y’ self-cal phases are not noise limited.

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Figure 10.10: Self-cal Image Improvement: (Left): The image derived from the normal calibration using
48 12-m antennas at 227 GHz, with a phase calibrator–science target separation of 3.8◦ and a cycle time of 70
seconds. (Right): The image after two self-cal phase iterations, with a solution time of 18 seconds (1/3 scan).
For the normal and self-cal images, respectively, the peaks are 48 and 80 mJy and the rms noise values are
0.35 and 0.22 mJy, respectively. This gives a peak/rms of 137 and 364, respectively, or about a factor of three
improvement. The theoretical noise level for the integration time and frequency is 0.20 mJy.

10.5.2Astrometric Observations/Calibrations

General Information
An astrometric-type project is one where measuring the accurate celestial position of the science target is one of
the main scientific goals. Examples are: identifying the radio emission associated with that of an optical target
with a positional accuracy better than the nominal one or measuring the positional change of a target over a
period of hours to years using appropriate multi-epoch experiments.
The choice of the observing Band, array configuration(s), and target integration time depends on the properties of the science target: angular size, flux density and spectrum, expected celestial motion and the precisionneeded. The choices may be influenced by the availability of configurations during the cycle. Although the more
extended configurations and higher frequencies might potentially provide more accurate astrometric precision,these astrometric gains are often outweighed by the limited time available at high frequencies, due to weather,and at configurations >3 km with good phase conditions.
Beginning with Cycle 8, an astrometry panel is present in the Calibration Setup editor of the ALMA
Observing Tool. As discussed in the Cycle 8 2021 Proposer’s Guide, Section A.9.5, if the astrometric goal canbe achieved using a standard imaging experiment, as mentioned below, then no action is required by the PI andthe default option should be selected. Otherwise, see "Enhanced Positional Accuracy" below.
Nominal positional accuracy: In standard experiments the positional accuracy is limited by the SNR of theimage and the configuration used. The relationship between the rms positional accuracy, the resolution,and the peak SNR of the target is, posacc = beamFWHP / SNR / 0.9 where posacc is the position rms
accuracy on the target, beamFWHP is the Full Width Half Power Resolution, SNR is the SNR of the image
target peak, and the 0.9 is a factor to account for a nominal 10% signal decorrelation.
In nominal ALMA observing conditions, the atmospheric phase fluctuations limit the (posacc / beamFWHP )ratio to 0.05 at best so that an image with SNR>20 will not improve the target positional accuracy, and asmaller SNR will degrade the accuracy. Hence, it is suggested that the spectral energy distribution (hence
observing frequency) and source structure (if any) of the target is considered, so the requested sensitivity
at the representative frequency allows for an SNR ratio of 20. If the synthesized beam is finer than 0.15",

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the positional accuracy is a factor of ∼2 poorer that the one given by the above equation. This is inducedby the phase stability degradation with increasing baseline length.
Enhanced Positional Accuracy: Enhanced positional accuracy is suggested for PI’s who, need a positional
accuracy better than nominal, have a problem with the distance to the default phase calibrator, or needmulti-epoch observations to determine target motion.
In case “Enhanced Positional Accuracy” is selected, a check-source will be added by default to the observations to be used for assessment of astrometric accuracy and phase transfer quality. Both the phasecalibrator and check-source will be automatically selected at the start of the observation. In case the PI
decides to identify and fix their own choice of calibrators, that is possible via the “user-defined calibration”
in the top panel of the “Calibration Setup” editor. Instructions to do so are described in the Cycle 8 2021
Proposer’s Guide.
Tests pursued thus far have shown that if the separation between target and phase-calibrator is more thanfour degrees, the astrometric accuracy may worsen beyond the nominal (see Maud et al. 2020, ApJS,
250, 18). The proposed enhancement method is to choose a second phase calibrator (via the “user-definedcalibration” option) that is not much further away from the target than the first calibrator and ideally inthe opposite direction (see instructions below). By combining the responses of both phase calibrators, theeffective target-phase-calibrator separation can be effectively reduced.
Types of Astrometry goals:
Absolute Positioning: Phase referencing between a target and a phase calibrator measures the angular separation
between the two objects generally to an accuracy of about 5% if the synthesized beam is larger than 0.15” (10%if smaller; see equation above). Previously, astrometric observations were most commonly done at Band 6 or
7 and in configurations C-4 to C-7 because these array configurations are regularly scheduled and good phasestability with them is relatively common. If the absolute position of the target is needed to an accuracy below
the nominal one, then the reference phase calibrator should have an J2000-ICRF VLBI absolute positional error< 2 mas, it should also be sufficiently bright and close to the target (< 4 deg). To check these, please check the
instructions below.
Target Temporal Motion: To measure the relative motion of a target over time, the same phase calibrator
should be used for all epochs (fixed in the "user-defined calibration"), even if its J2000-ICRF VLBI absolute
position error is above 2 mas. Both the absolute position and temporal motion accuracy is not improved withphase self-calibration iterations.
Relative Motion Between Two Close Targets: If two or more objects are in the same ALMA field of view
(nominally within the 40% primary beam power area), then the accuracy of their relative separation depends
on their SNR, not on the position accuracy of the phase calibrator. The use of self-calibration may also improve
the image quality (see Section 10.5.1) and thus the accuracy of the relative positions of different compact objects
in the field.
Calibrator availability
By accessing the ALMA Calibrator Source Catalogue, one can search for calibrators around the target position.
By filling in those fields, the PI should get in return a list of the closest calibrators and the observed fluxes atdifferent frequencies (the most frequently observed Bands are 3 and 7, with occasional measurements at Band6). The characteristics that should be checked are:
• Is the positional error smaller than 2 mas? Add “Measured RA Err.” and “Measured DEC Err.” inquadrature and multiply by 1000 since these columns are in units of arc-second.
• Is the calibrator bright enough at the frequency of interest? The value in the "Flux" column should
provide a minimum SNR of 15 within 30 seconds (Section 8.3.1 in Technical Handbook; use the Exposure
Time Calculator for this purpose or its web version). If the frequency of interest is not available, consider
interpolation between Band 3 and Band 6 or 7 values (consider using the task “getALMAFlux” within the
CASA extension Analysis Utils package). If only one measurement exists at a Band that is not the oneof interest, please select “Enhanced positional accuracy”.

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CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIES• Is the calibrator resolved at the requested spatial resolutions? In this case, you need to use the values in“UvMin” and “UvMax”. These should comply with UvMin<2.5E5/MRS and UvMax>2.5E5/beam, where
MRS and beam are the Maximum Recoverable Scale and the synthesized beam achieved by the selectedconfiguration.
Note that due to flux variability and lack of intra-month/year monitoring of fainter calibrators, if thecandidate calibrator barely complies with the flux criterion, the user is suggested to select “Enhanced positional
accuracy” ’. In this way, the observatory might check the calibrator flux prior to the observation during routine
observatory calibration observations.
J2000 ICRF quasar Frame and ICRS stellar frame and Ephemeris Motion
Because nearly all ALMA calibrators are distant quasars with J2000 epoch position on the FKN ICRF quasar
frame, the normal phase referencing to an experimental target will provide its J2000 ICRF position after
calibration and production of its image. However, most solar system and stellar objects (some of which havea moving phase center defined by an ephemeris track) are on the International Coordinate Reference System(ICRS) position grid with an origin at the barycenter of the solar system. This is the coordinate system used by
Hipparcos and for many objects in our Galaxy. The difference between the ICRF and ICRS coordinate systems
is about a 20 mas between the target positions. Hence, make sure that the coordinate system of the field sourceis specified correctly.

10.5.3Band-to-Band Phase Calibration

As noted in Section 10.4.9, the closer a phase reference calibrator is to the target, the more accurately thecalibrator scans will remove the tropospheric and instrumental antenna-based phase errors from the target
scans. For frequencies above 350 GHz, where the density of quasar calibrators in the sky is relatively low,
ALMA observations with 12-m Array configurations longer than 3 km and for 7-m Array observations that have
low sensitivity, a relatively close calibrator to the target at the experiment frequency is often not available.
The goal of band-to-band phase transfer is to calibrate a target observation at high frequency νh by observing
the phase calibrator at lower frequency νl where there is a greater chance of finding a detectable calibrator close
to the target. The accuracy of this calibration method requires that the measured antenna-based spw phase of
the low frequency calibrator scan φl (t) is converted accurately to what would have been measured at the target
frequency, φh (t). The conversion has two parts: a simple frequency scaling between the low and high frequency(so called non-dispersive, delay-like behavior); plus a nearly constant instrumental phase offset ψ among all of
the spws that must be measured for each 60 min experiment. This relationship is illustrated in the following
equation:φh (t) = φl (t) ∗ (νh /νl ) + ψ(10.7)The instrumental phase difference ψ is determined by quickly alternating observations of a bright quasar, called
the Differential Gain Calibrator (DGC), between the low and high frequencies with a cycle time of about 30
seconds. From a 5-minute set of DGC scans near the beginning and near the end of a 60-minute experiment, thevalue and stability of the instrumental phase, ψ, for each low-frequency to high-frequency spw pair is measured.
The DGC phase accuracy is about 5−10◦ , often limited by the short-term variable atmospheric phase variations,and it is generally constant over a 60-minute period. Occasionally, an antenna/spw DGC phase will have a small
phase slope over the experiment, or a discrete phase jump. These rare occurrences can be detected in the DGCscans and corrected, or the offending antenna/spw data removed.
In Cycle 8, it is anticipated that band-to-band calibration may be used for 7-m Array observations in Bands
8, 9 and 10 in cases where there is no suitable high-frequency phase calibrator. A detailed investigation of the
optimum scheduling of the DGC is underway using test data obtained in Bands 3 and 7 in the Cycle 7 long
baseline configurations.

10.5.4Band-Width-Switching

If all of the spws are narrow bandwidth (< 1 GHz total bandwidth), it is likely that a reasonably nearby phasecalibrator cannot be detected within a scan. In this case, the strategy for phase calibration is to observe the10.5. ADDITIONAL CALIBRATIONS

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phase calibrator with wide-band spws and the science target in the desired narrow bandwidth by switching thespectral setup between the relevant scans. In a method similar to band-to-band calibration, a strong DGC
calibrator is initially observed at both the wide and the narrow bandwidths in order to determine their phasedifference among the spws that should be constant with time. There will be a slight delay change among thedifferent spws, but they will be much closer in frequency than that for band-to-band observations. Tests are
now in progress to determine the stability of the wide-to-narrow bandwidth phase difference.

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CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIESChapter 11

Quality Assurance
The goal of ALMA Quality Assurance (QA) is to ensure that the data products delivered to the PIs meetthe expected quality standards. That is, the delivered products have reached the desired control parameters
outlined in the science goals (or is as close to them as possible), they are calibrated to the desired accuracy, andcalibration and imaging artifacts are mitigated as much as possible.
The QA analysis will be based on a calibration plan that specifies which observations must be acquired,and at which intervals, to monitor system performance and environmental factors as they evolve with time.
Furthermore, it will also be used in (a) assessing the merging of data within each science goal taken withdifferent configurations, (b) the inclusion of 7-m Array and TP Array data, and (c) the final image quality.
Errors introduced by user supplied parameters, such as incorrect source coordinates, inadequate frequency
setting (e.g. an incorrect redshift) or inadequate sensitivity limits (leading to an inadequate integration time orinadequate uv-plane coverage) are outside the scope of the ALMA QA, unless the error occurred due to faulty
information or tools provided by the Observatory.
To be more efficient in detecting problems, ALMA QA has been divided into several stages that mimic themain steps of the data flow. The broad classification of this multi-layered QA approach is:
QA0: The first check and monitoring of the calibration and overall performance during and just after anobservation, performed at Execution Block level.
QA0+: A simplified and fast scripted imaging QA. Typically completed 30−90 minutes after each observation
is taken, this is mainly used when the results from QA0 are unclear or marginal and will also be available
in the QA0 report in Cycle 8.
QA1: This involves the measurement of performance parameters and telescope properties by the observatory.
QA2: Full calibration and generation of imaging products.
QA3: Issues found with the data by the PI or ALMA staff after data delivery.
The QA process is handled by the Program Management Group (PMG) and the Data Management Group(DMG) at the JAO with significant contributions from ARC personnel. The process is primarily implemented
using the ALMA Quality Assurance (AQUA) Tool (see Section 11.7) and other software necessary for theassessment of data quality. Responsibility for data quality assurance rests with the Data Management Group
Head within the Department of Science Operations, drawing upon the resources of the Program Management
Group and the Data Reduction Managers (DRMs) at the JAO and ARCs.
The final output of the ALMA QA0 and QA2 processes is a QA Report per ObsUnitSet (Member or Group1 )that summarizes all the relevant QA information for each of the different QA stages up to, and including, thefinal imaging. This report is included in the data package delivered to the PI. The QA3 process is handled
differently (see Section 11.6). A more detailed description of the different stages of QA is given below.
1 Group ObsUnitSet processing, that is, the combination of datasets taken in different configurations/arrays. It is expected thatgroup processing will be implemented as a regular data reduction strategy in later ALMA cycles.

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11.1

CHAPTER 11. QUALITY ASSURANCE

Cycle 8 Quality Assurance Goals

The ultimate goal for ALMA QA is that the delivered products are considered "Science Ready", suitable forpublishing with little need for the user to reprocess. However, ALMA cannot guarantee that all the scheduled
Cycle 8 projects are completed (especially those with grades B and C), or that specific criteria like sensitivity
or angular resolution are precisely met, given the restrictions of the array configurations or system performanceat the time of the observations. The observatory will therefore attempt to meet the sensitivity and resolution
stated by PIs in their Science Goals, within certain tolerances, as described later in this chapter. In principle,
each project component ("Scheduling Block" or SB) is scheduled for the number of executions that are expected
to reach these goals (based on nominal Array performance values). Additional executions may be needed during
the observing cycle if specific executions do not pass QA0 or QA2 (see below).
In Cycle 8 users may need to invest their own time and expertise to ensure that the data products are
suitable to meet their science goals. In rare cases, users may need to re-reduce the raw data if the quality is notsatisfactory. At any time, users may request to visit their ARC or ARC node to obtain help and to be assistedwith the data processing and analysis.

11.2

QA0

The first stage of QA, known as QA0, is a near real-time verification of data quality for each SB execution, or
execution block (EB). It deals with performance parameters on timescales of an SB execution length or shorter,and thus is performed at the time or immediately after each execution. Initial QA0 assessment is performed by
AoDs (Astronomers on Duty) at the OSF, using the software tools AQUA, AosCheck, and QuickLook, based on
the near real-time output from the calibration scans obtained by the ALMA TelCal software. This informationis complemented with reports derived using Monitor and Control display tools to monitor specific parameters
not directly tracked by the calibrations (e.g., total power level variations, weather parameters, etc).
QA0 metrics/parameters have been selected to check the health of the whole signal path from the atmosphere down to the correlators, as well as issues connected with the observation itself. AosCheck examines
the calibration data, looking for significant outliers or out-of-spec results, and other problems (for example,
due to the correlator). Together with additional checks in AQUA itself, these are combined to provide a QA0
assessment for each EB. The parameters checked at QA0 can be grouped into the following general categories2 :Atmospheric Effects: Weather Parameters, Sky Opacity, System Temperature, Phase Fluctuations, WVR
Outputs.
Antenna Issues: Antenna complex Gains, Antenna/pad delays, Relative/Offset Pointing, Geometric Shadowing, Antenna/Pad positions.
Front-End Issues: Bandpass shape & instability, Sideband Ratios, Receiver Temperatures, Phase variations,variations in Tsys spectral shape.
Connectivity Issues: IF Delay Measurements, System Temperatures, unusual relative phase or amplitude
variations between spws, interference spikes.
Correlator Issues: Bandpass spectral shapes, Delay Measurements.
Observation Issues: Calibrator fluxes, incomplete datasets or incomplete mapping.
Tolerances for individual parameters in the above list (for example the maximum range of Trx or the cutoff
for low antenna gain) are defined in AosCheck. These are combined to assess the QA of individual sub-unitsof the EB, such as antennas, spws, scans, periods of time, or targets. An overall assessment of QA0 of the
EB is then made based on combining these results. The overall tolerances for this QA0 assessment that havebeen adopted by ALMA for this Cycle are listed in Section 11.2.1. Additional checks are made in AQUA on
other observatory calibration data, including a recent measurement of the flux of the amplitude calibrator, anda relevant measurement of the antenna/pad position.
Based on these results, each SB execution is classified into three main categories:
2 Some additional hardware problems can occur which are automatically flagged out by the system before they reach the QA0stage, and may not be seen in the data or at QA0 unless this hardware flagging has failed. Examples of these are LO lock problems,
antenna not on-source, or the calibration device not in position.

11.2. QA0

167• QA0_Pass are datasets that comply with all the QA0 criteria and will be used for the final imaging.
• QA0_Semi-pass are datasets that do not fulfill all the QA0 criteria, but contain data that is deemed ofsome scientific value (for instance, the presence of usable bandpass/amplitude calibrator data). QA0_Semipass data are not included in the final data products, but PIs can access those data from the ALMA Science
Archive.
• QA0_Fail datasets are those that are not included in the other two categories. Since they represent
unusable data or data that cannot be calibrated, they are not made available to the PIs through the
ALMA Science Archive nor visible in SnooPI.
In addition, other temporary states can be set at this time, which require further intervention before they
can be re-set to one of the above main states:• QA0_Pending_Other is used if the state based on the initial assessment is unclear; it requires additional QA, using QA0+ imaging as well as possibly further checks (see Section 11.3).
• QA0_Pending_Fluxcal is used if the EB is a Pass but the amplitude calibrator (which is usually also
the bandpass calibrator) has no usable flux measurement within the last 7 days. Once a flux measurement
is available in the archive, these data will automatically be set to Pass.
• QA0_Pending_Correct_ANTPOS is used if an antenna was used in the array which had not been
fully integrated - usually because the antenna positions in the observatory Telescope Monitor and Control
DataBase (TMCDB) have not yet been updated after an antenna move. Once the positions are measured
and updated, these data will be set to Pass.

11.2.1QA0 criteria

Of the antennas available in each interferometric dataset, at least 50% of them (or 22 out of 43 in a 43 element
12-m Array and 5 out of 10 in a 10 element 7-m Array) must be ‘usable’ for the dataset to considered for a
QA0 Pass. If fewer than 50% of the antennas are usable, the EB is normally set to QA0_Semi-Pass (Section
11.3). Datasets with more than 50% but less than 100% usable antennas will normally be QA0 Pass, but willcount less than datasets with 100% usable antennas: this is done through the use of a weighting factor called
the Execution Fraction (section 11.2.2). The antenna restriction does not apply to the TP Array (where theminimum number of usable antennas is 1). The decision as to whether an antenna is ‘usable’ or not depends on
several criteria - both system and weather related. The QA0 criteria that have been adopted by ALMA during
Cycle 8 are the following:- Antennas: Situations that will be considered to render an antenna or spw as not usable include issues
with the antenna or frontend itself, such as Tsys value > a factor of 2 higher than the median of others inthe same spw, an absolute delay in that spw of > 0.5 ns, relative amplitudes on the calibrators <50% of themedian of other antennas/spws, gain calibrator amplitude or phase fluctuations which are significantly
higher (factor of > 3) than other antennas at a similar distance from the array center, or scan-based
phase noise on the bandpass calibrator significantly higher (> 3σ) than other antennas. These criteria aredesigned to identify outliers due to antenna or system problems, as distinct from the effects due to poor
weather conditions noted below.
- Weather: If the atmospheric phase fluctuations on the complex Gain calibrator measured over the whole
execution are such that the antenna-based phase noise3 is larger than 1 radian for a given antenna, thenthat antenna is regarded as ‘unusable’ for QA0 accounting purposes in calculating the Execution Fraction.
Note that these high phase noise antennas are not flagged out at QA0, and will still be reduced in thepipeline.
- Bandpass: A high SNR (>30) must be attained per channel on observations of the bandpass calibrator,
after binning to no fewer than 4 channels. The dataset will be set to either QA0_Semi-pass or Fail if the
3 The antenna-based phase noise is determined in the following way: data from spws and the two polarizations are phased up
and combined to obtain a single phase solution per antenna per Gain calibrator scan. The phase noise for that antenna is thendetermined from the mean value over the whole execution of the difference in phase solutions between adjacent scans.

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bandpass calibrator signal is too weak to attain this SNR depending on the outcome of QA0+ (Section
11.3). The QA0 bandpass results (both amplitude and phase) are used to check that the passband shape
does not show statistically-significant spikes, high spectral rms, or correlator platforming issues. Also the
ATM (Tsys ) calibration observations are used to check for significant passband shape changes during theexecution. If any of these effects are seen, either the relevant channels or the whole spw on that antenna
can be flagged, and will be regarded as ‘unusable’.
- Gain/phase: A SNR (for each antenna) of ≥10 per scan must be attained after averaging all spws. The
dataset will be set to either QA0_Semi-pass or Fail if the gain/phase calibrator signal is too weak toachieve a SNR ≥10 depending on the outcome of QA0+ (Section 11.3). Also note that individual scanson the Gain calibrator are checked for statistically-significant (> 5σ) amplitude drop-outs.
- Execution: More than 20% of the expected time is required on the science target for a given SB execution,and the overall Execution Fraction (see 11.2.2) must be greater than 0.2 to be considered as a QA0 Pass.
The dataset will be set to QA0_Semi-pass if it does not satisfy the above criteria.
- Calibrations: Critical calibrations (bandpass, ATMcal, at least one pair of Gain/phase scans bracketingthe science observation) must be completed. There may also be additional calibration requirements, suchas polarization with >60 degrees of parallactic angle rotation during the session. Datasets which contain
only usable calibrator data shall be set to QA0_Semi-pass.
- Storage: Data must be able to be read from the Archive. Any dataset that cannot be retrieved from theArchive will be set to QA0_Fail.
- Time Sensitive Observations: For Target of Opportunity (ToO) or time critical observations, thedataset must be collected within the time range specified by the PI. For time simultaneous observations
between the ACA and 12-m Arrays, the executions must start at the same time. Observations taken where
the data are not collected simultaneously will be set to QA0_Semi-pass.

11.2.2

Execution Fraction

For operational and scheduling purposes, individual SB executions during Cycle 8 will effectively be weighted
by measuring their data quality. This weighting is quantified by an Execution Fraction (EF), where 1.0 is thevalue predicted per execution by the OT, based on typical observing conditions and number of antennas. An
EF of 0.0 means that the data are not at all usable and the observations should be set to QA0_Fail or semipass,
while an EF > 1.0 means that the EB is better than predicted. The EF is a single number representing thenormalized fraction of the theoretical sensitivity (based on the radiometer equation) that a given execution
should have reached, combined with a measure of the expected image quality (see Section 11.3). It is calculatedusing the number of ‘usable’4 antennas compared with the number that should be in an array in Cycle 8 5 , theactual time on-source compared with expected, the mean Tsys at the representative frequency compared withthat assumed by the OT, and the fraction of antennas with phase noise below the set limit (of 1 radian)3 .
Executions with lower data quality than the reference will have fractional executions between 0 and 1.0,
while those with better quality (such as observations carried out in unusually good weather with lower Tsys ,or with more than 43 antennas), will have an EF value above 1.0. For Cycle 8, the EF on the main array iscapped at 1.5; this allows extra execution time in the case of very good weather (where the EF would otherwise
be significantly higher), to avoid the situation where uv coverage may be important. The scheduler then sumsthe EFs of executions to determine how many more are required for SB completion. Note that datasets with
EF<0.2 will be set to QA0_Semi-pass. For Mosaic observations, if the execution is incomplete (for example if
the SB finished unexpectedly early) and <90% of positions have been observed, the EF will be dropped to 0.2.
The data will then still be reduced, but the execution will not count significantly against the total time.
4 see 11.2.1
5 The requirement for Cycle-8 is forty-three 12 m antennas on the main array, ten 7-m antennas in the 7-m Array, and three 12m antennas in the TP Array.

11.3. QA0+ AND IMAGING QUALITY

11.3

169

QA0+ and imaging quality

QA0+ is an additional stage of QA0 which runs a simplified and (relatively) rapid scripted calibration andimaging pipeline of the channel-averaged data, producing continuum-only images of the science target, phasecalibrator, and check source (when available). The idea behind QA0+ is that if an execution is left in a QA0"Pending Other" state (perhaps because the phase noise is above the QA0 limit, or the QA0 status is unclear for
any reason), the QA0+ images can be used as an additional level of data quality assessment. The EB can thenpotentially be set to "Pass" if the images meet the QA specifications. Typically the QA0+ scripted calibrationand imaging process takes 30-90 minutes to complete. To speed up calibration, it does not run bandpass or thefull Tsys calibration, but uses WVR-corrected data. If QA0 recommends the remcloud option (for wet cloud
removal) it will also run this. It uses flags from the QA0 process (flagging out bad antennas, but not those withhigh phase noise) and combines both polarizations and all spws with bandwidth >400 MHz. For imaging it will
run a single iteration of CASA tclean with a clean box centered on the first science target. For science targets
with SNR >20, it will try self-calibration on a scan-based time interval and will generate a self-calibrated image.
As well as the images, also provided by QA0+ are the beam size and shape for different Robustness parameters (from the phase calibrator), and the science target image, peak and integrated flux, and image RMS.
Note that these are very approximate values, obtained from the mean Tsys, and taking the mean antenna gain
(Jy/K) to obtain the fluxes. As well as the results from the current execution, the data are combined withprevious executions of the same SB, to give the running results so far. Starting in Cycle 8, these values will beavailable to the PI through the QA0 report for each execution in SnooPI.
For EBs requiring QA0+, checks of image quality are performed where possible. The metric used is thepeak to integrated flux ratio for a point source (either a check source or the science target if known to becompact). Also the peak to residual ratio after a single tclean iteration can be used. Both indicate how much
flux from a point source is distributed over the map due to phase decoherence. Whereas completely random
phase fluctuations simply reduce the target flux and scatter power over the whole map, semi-systematic orlarge-scale atmospheric phase changes over the array will distort the image in a semi-coherent way. Thesecan be more egregious during long-baseline or high-frequency observing, and their effect can be monitored byobserving a check-source as part of these observations6 ; QA0+ is then used to assess the image quality.
A perfect image has a peak/integrated value of 1.0; a ‘good’ image has a peak/integrated value > 0.8 and images with values < 0.5 are regarded as "marginal". The QA0+ criterion is that datasets with a peak/integrated
flux ratio on the check source of >0.5 are set to Pass. For those without a check source, in some cases, thescience target is bright enough that the images can be compared with previous executions of the same EB. Thosejudged of similar quality are also set to Pass. For executions where the check source peak/integrated ratio is<0.5, or there is no check source or clear science target, the QA0 status is maintained at (or set to) Pending
Other. These are unclear cases, and require a further stage of checking, usually offline by the full ALMA data
reduction pipeline, before setting the dataset to either QA0 Pass or Semi-pass.

11.3.1

Relationship between image quality and phase noise criteria

The quality of images is strongly affected by the phase stability of the atmosphere7 , so measuring the phasenoise provides a good proxy for the final image quality. However, there are cases where it is really necessary tocheck the image directly. ALMA uses nearby phase calibrators to measure and correct for residual sky phasefluctuations (phase referencing). But this correction is not perfect. The image quality of these phase-referenced
observations is affected by spatial differences in the line-of-sight delays to the target and phase calibrator, as
well as baseline errors thought to be due to large-scale, slowly-varying atmospheric structures8 . The spatiallydependent differences between target and phase calibrator are linked to the time-dependent phase fluctuations
through the turbulent structure of the atmosphere, so monitoring just the time-dependent fluctuations canstill give a reasonably good measure of the overall data quality, even without checking the images. Figure11.1 confirms that image quality (measured by the ratio of peak-to-integrated flux on a point source, takenfrom QA0+ results on the check source during the 2017 long-baseline campaign) is correlated with the phasefluctuations (measured by the median phase difference between antennas3 ). The phase is measured in degrees,
6 Check sources are QSOs within a few degrees of the phase calibrator, and are normally observed for a short time during long
baseline or high frequency executions.
7 Although many of these effects can be removed using self-calibration when the target is bright enough - see Section 10.5.1
8 These baseline errors only become significant on the longer baseline observations (of several km or more)

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and therefore just depends on the changing pathlength compared with the wavelength, independent of theactual observing band. As stated in Section 11.3, a perfect image has a peak/integrated value of 1.0; a "good"
image has a peak/integrated value > 0.8 and images with values <0.5 are "marginal". Datasets with phasefluctuations less than 1 radian almost always give reasonably good image quality and can be set to QA0 Pass
immediately. The QA0+ imaging stage is normally used for the marginal datasets; some can then be set to Passas the images are deemed acceptable, but a significant fraction (perhaps 20%) are of very poor image quality.
Time-dependent phase noise is not the only parameter that affects image quality, however, Figure 11.1
indicates that observations where the target-calibrator separations is more than 3deg on the sky tend to haveworse image quality even if the time dependent phase fluctuations are low (<1 radian). This is illustrated
further in Figure 11.2, where the image quality is plotted against the phase calibrator separation. For reasonableconditions (phase RMS <1 radian), generally there is a slow dependence on separation; "good" image quality
is generally achieved when the separation is small (< 4 deg) and phase fluctuations are low (< 1 radian).

Figure 11.1: Check source image quality (measured by peak to integrated ratio) shown as a function of phasefluctuations (the mean antenna-based scan difference on longer baselines, in degrees). Data are taken from 2017
long-baseline observations in Bands 3-7 (no dependence on the band was found). Blue points are QA0 pass,red crosses are QA0 Semi-pass. Encircled symbols indicate that the phase calibrator has a more than 3 deg
separation from the check source. The highest image quality (peak/integrated >0.8) generally occurs for phasefluctuations < 40 deg and for the closest calibrators. The cutoff for an immediate QA0 Pass from AosCheck is< 57 deg (1 radian); higher phase noise datasets are passed on to QA0+ for assessment of image quality.

11.4

QA1: Observatory calibration and QA

In addition to data taken during the SB execution, the observatory tracks array and antenna performanceparameters which vary slowly (typically on timescales longer than a week) and which can affect data quality.
They are measured by AoDs and System Astronomers at predefined periods as “Observatory Tasks”, and after
major interventions including, but not limited to, antenna moves, front-end swaps and subreflector repairs, orif significant deterioration of performance is detected during operations. Typically after such interventions,antennas are set to a non-integrated state and not used for regular science observing. Antenna integration into

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171

Figure 11.2: Check source image quality (measured by peak to integrated ratio) shown as a function of phasecalibrator separation (in degrees on the sky). Data are taken from 2017 long-baseline observations. Blue points
are low phase noise (< 1 radian) and red points are high phase noise datasets (> 1 radian). The blue line showsa linear fit to the low noise datasets weighted by the inverse of the phase fluctuation. The phase-referencing
image quality deteriorates somewhat with larger separations for low noise data, but for high noise data theseparation is less important. Datasets with peak/integrated less than 0.5 are regarded as low quality and arepassed on to QA0+ for assessment of image quality.
the array then requires measurement and ingestion of specific array and antenna parameters (described in moredetail below).
Observations and reduction of such data are done jointly by the AoDs and specialized groups within DMG
and PMG. The end products are a set of parameters that are ingested into observatory databases, in particular
the TMCDB which records hardware status and history. The TMCDB gives the up-to-date view of hardware
parameters which are used by the system during observations. Problems that would significantly downgrade
the quality of the data are solved by, for example, dropping the offending antenna from the active array andfixing, re-measuring and updating the problematic parameters. Particular parameters which are derived fromthese observatory calibrations include:
Array Calibrations: Baseline and antenna position measurements and pad delays.
Antenna Calibrations: Pointing models, focus model curves, surface measurements, beam patterns (including polarization observations), beam squint (offset between polarizations), IF delays (relative delays between basebands and polarizations), front-end delays (relative delays between front ends).
Source Calibrations: Monitoring of solar-system flux standards, and secondary quasar flux standards (e.g.
grid sources, see Sections 10.2.6 and 10.4.7).

11.5

QA2

The QA2 concept refers to the Quality Assurance performed at data reduction level. The ALMA data areprocessed (i.e. calibration and imaging) either with the ALMA Data Reduction Pipeline, or manually, with
the Script Generator. The ALMA Pipeline and the Script Generator are built on CASA, which is the official
software for ALMA data processing and analysis. The ARCs and ARC nodes do not provide support for

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any data processing or analysis done by users on platforms outside of CASA. The ALMA Pipeline and Script
Generator can be run at either the JAO or the ARCs.
The entire data reduction workflow is managed by the Data Management Group (DMG) Head at the JAO,
with support from the Data Reduction Managers (DRMs) at each Executive. It is only during this stage ofdata reduction that the science goals set by the PI can be compared with the actual values in the data products(i.e., noise RMS, angular resolution, SNR and dynamic range).
Like in previous Cycles, during Cycle 8 it is expected that, for the majority of the observing modes, the
ALMA Pipeline (see the ALMA Science Pipeline Reference Manual on the Science Portal9 ) will be used for thecalibration and imaging of the data.
The ALMA Pipeline provides a Weblog page with detailed information on the quality of the calibration,
which provides the basis for QA2. Weblogs are included in the data packages sent to the PIs and are available toall users through the ALMA Archive. For manually-reduced datasets, the QA2 will be carried out with special
purpose scripts whose outputs will be included in the data packages delivered to PIs.
Some datasets can be calibrated by the pipeline, but need to be imaged manually, or with manual intervention
in the pipeline. In these cases, a weblog will be provided for the calibration portion, and an imaging script, or
imaging weblog provided for the imaging. The QA2 metrics which determine the success of an observation are
given below.
A complete description on what the ALMA Pipeline checks is available in the Cycle 8 Pipeline User Guideat the ALMA Science Portal. A short list of the QA2 parameters or issues checked during data reduction(calibration of individual Execution Blocks and joint imaging) are listed below:
Calibration Issues• Bandpass quality: is the spectral profile flat, well behaved and devoid of spectral lines?
• Flux scale calibration: flux accuracy better than 5% for Bands 3, 4 and 5; 10% for Bands 6, 7 and
8; and 20% for Bands 9 and 10• Phase transfer and astrometry: Cycle time and sky separation between phase reference and target;
typical and extreme (unflagged) phase differences between phase reference scans.

QA2 criteria
For Cycle 8, the beam and noise RMS criteria used for the QA2 assessment are the following:• Noise RMS in target images: The predicted value (after data flagging, if necessary) is compared to
the value requested by the PI. The achievement of the requested noise RMS in the images must bewithin 10%, 15% and 20% of the goal for Bands 3/4/5/6, 7/8, and 9/10, in flux units per beam,
respectively. For Solar Observations, this criteria does not apply as there is no blank sky in most of
the images.
• Size of synthesized beam (spatial resolution) for specified weighting scheme, or specific imaging
requirements (if stated by the PI). In order to satisfy the QA2 criteria, for Cycle 8, the beam area,
not the individual beam axes, shall be the figure of merit. The PI requested angular resolution
range shall be interpreted as the geometric mean of the major and minor axes at the PI specified
declination. The beam area must be within the range requested by the PI, taking into account themodifications applied by OT to ensure schedulability of the SB (See Cycle 8 2021 Proposer’s guide).
In addition, those Member Observing Unit Sets (MOUS) that do not satisfy the QA2 requirement ofbeam area will have the execution fraction of the associated Execution Blocks (EB) reduced to 75%
of its current value if failed due to erroneous beam, or by the corresponding fraction if not reached
the required sensitivity.
• Image used for QA2 assessment: The image used to derive both the noise RMS and beam sizevalues mentioned above shall the image whose channel width is the one closest to the representative
9 https://almascience.nrao.edu/processing/science-pipeline

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173

bandwidth selected by the PI in ALMA OT, in the spectral window closest in frequency to therepresentative frequency.

Other criteria used for the final data characterization
In addition to the beam and noise RMS criteria, the following factors will be considered for assessing thequality of the data products:• uv-coverage and time on target (after flagging).
• Spectral resolution and channel ranges used to make sample images.
• Dynamic range limitations.
• Amplitude scale consistency between executions of a multi-execution MOUS.
• Contamination by bright sources outside FOV or aliasing in the ALMA Pipeline task called clean.
• Minimum parallactic angle coverage for full polarization projects.
The data reduction scripts sent to the PI will include any modifications to the standard scripts which were
found to be essential during QA2.
As in QA0, there are three possible QA2 states: QA2_Pass, QA2_Semi-pass or QA2_Fail. In detail:• QA2_Pass implies that the scientific goals, as defined by measurable parameters such as noise RMS,
LAS and angular resolution, have been achieved at the representative spw within the specifications listed
above.
• QA2_Semi-pass refers to those datasets that fall short of meeting the PI requested science goals, but
are otherwise of good quality (or as good as possible with the observations that could be achieved).
• QA2_Fail is a temporary state used during an observing cycle when an observation fails to meet thePIs goals by a significant margin and needs to be scheduled for additional observations. Although theObservatory will try to take a similar quality of data in all spws, those measurable parameters in non
representative spws will not be used for the judgement of QA2_Pass or QA2_Fail.
If there are not enough additional executions of an SB to pass QA2 by the end of an observing cycle and the
SB is not a component of a grade A proposal, the QA2 state is changed from QA2_Fail to QA2_Semi-passand delivered to the PI.

11.6

QA3

QA3 is post-delivery evaluation of the data products delivered to the PIs. It is advisable that PIs check thedata products themselves very soon after delivery. The QA3 process is often triggered by a PI who initiallyfinds some issue in their data. which may reflect an underlying problem with the data, observing procedureor calibration. The issue is then reported to the corresponding ARC for support, typically through a Phase 2
ticket via the ALMA Helpdesk (https://help.almascience.org/) which is then reviewed by the project’s contact
scientist or other ARC personnel. After this initial triage and review, the contact scientist will request the user
to open a formal QA3 ticket through a dedicated department in the Helpdesk only after it has been determined
not to be a user error. The ARC receiving the Helpdesk QA3 ticket will retrieve the data from the archive andevaluate the nature and extent of the problem. The evaluation by the ARC should include an assessment onwhether the problem is present only in a particular dataset or is a more global issue affecting data taken undersimilar set-ups and observing conditions.
If the identified problem reflects a problem with the performance of the array, the calibration or data
reduction processes, or the QA process, the ARC will communicate their findings to the JAO, who will workon solving the problem in collaboration with the ARCs. The result will be communicated back to the reporting
investigator.
An extension of the proprietary period of delivered datasets still within their proprietary period with QA3issues will be granted based on the policies in the Cycle 8 Users’ Policies document. There will be no extension

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to the proprietary period of data already publicly available. During the QA3 evaluation process, which may
include taking additional data for an observing program, the data will not be available through the Archive.
The data will only become available after the issue has been resolved and new data products are ingested into
the Archive.

11.7

The Quality Assurance Reports

The Quality Assurance Reports of QA0 and QA2 will be accessible to the users using SnooPI. These reports will
be generated using the AQUA tool. For Pipeline calibrated datasets, additional reports (Weblogs) will be sent
to the PI as part of the data delivery. For observing modes that require manual data reduction, script-generated
QA2 reports will be delivered.
The QA0 report, which is a summary of the QA0 and QA0+ results, will be available from AQUA (through
SnooPI) after each execution. This report can be used to check the status of ongoing observations. Note that
the QA0+ image results are only very approximate, and only apply to the continuum (channel-averaged) data.
The basic unit of a QA2 Report is the ObsUnitSet, which represents part of the scientific goals stated by the
PI during Phase 1 (project generation and review). An ObsUnitSet will typically contain several executions ofan SB. Each execution only passes to data processing if it has passed QA0. There will be only one QA2 reportfor the whole Member ObsUnitSet10 generated by the JAO/ARCs at the end of the data reduction process.
This report also has to be approved by the DRMs before the data products are delivered to the PI. An interface
between the Pipeline and AQUA permits to generate a complete QA2 report, which is delivered as part ofthe data products package (including the Weblog information). The final report per MOUS delivered to the
PI would in that case be a concatenation of all the relevant QA0 reports per execution with the QA2 report.
Comments on each stage of the QA process (with supporting images, if required) would be added to the Report.
The standard policies for QA0 failures (or QA0 semi-passes) are that the observations of those Execution
Blocks that failed have to be repeated. Failures to pass QA2 may trigger additional observations if the achieved
RMS or imaging parameters do not fulfill the QA2 pass criteria. Additional observations may not be possible
in circumstances, such as projects with very tight weather, very specific configurations, or time constraints. If
the available data are insufficient to reach the required sensitivity, but are otherwise of good quality, they will
be released to the PI at the end of the cycle.

11.8

QA in Solar Projects

Section 8.10 describes the difference between solar observing modes and those employed for sidereal sources.
Those with implications for quality assurance are as follows:• No WVR observations are possible during solar observing and therefore no antenna-based phase corrections
can be made.
• Observations of the calibrators are made using the so-called MD modes (Bands 3, 5, & 6), which may
yield intrinsically lower SNR. The stepped attenuators are set and held fixed at appropriate levels for both
source and calibrator scans.
• The system temperature may be significantly higher for an MD mode. The antenna temperature is ofcourse much higher as a result of the solar input.
For QA0, the criteria are largely the same as those itemized in 11.2.1. In the case of weather, the phase
RMS criterion is the same for solar observations as they are for non-solar observations (1 rad). Note, however,that this criterion is applied to data that have not had WVR corrections applied and are consequently more
stringent. For fast total power mapping, QA0 criteria are that the calibration sequence and map were completed
for each execution.
Solar observations are currently a mode that cannot be pipeline processed. In the case of QA2 (cf. 11.5),
calibration issues include evaluation of the antenna temperature, which is much higher than non-solar sources.
10 As stated above, processing of group ObsUnitSets will not be done during Cycle 8. PIs should assume that all statements here
apply to Member ObsUnitSets (MOUSs).

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175

In particular, Tant should be 6000 ± 1500K for Band 3 and 5, and 5000 ± 1500K for bands 6 and 7, except forlimb observations. For final data characterization the criteria follow those in 11.5 with the following exceptions
and caveats:• Synthesized beam: check the phase calibrator map for loss of coherence, if any, due to phase variance.
• Spectral resolution and channel ranges: solar modes are fixed - no checks needed.
• RMS noise in target images: n/a for source dominated solar data.
• Combinations of array configurations: n/a for solar observations in Cycle 8.
• Mosaicing and/or contamination by bright sources: Pass if 90% of the mosaic has been completed, Fail if
completion is below 20%, otherwise semi-pass.
• Polarization purity: n/a for solar observations in Cycle 8.
For total power mapping, there should be no artifacts in the map that can be attributable to the (doublecircle) scan pattern or to transient sky absorption.

11.9

QA in VLBI Projects

As discussed in Section 8.11, VLBI observations are executed as polarimetric observations and a portion of
the above-described procedures are applicable with an important distinction. Since VLBI observations are
performed with ALMA’s peer observatories according to a schedule worked out months in advance, it is notpossible to re-observe failed observations (regardless of reason). Thus, the diagnostics provided as part of thenormal QA0 process are examined by the staff, but their utility is restricted to making the limited adjustments
to the observation which are practical. The principal adjustment is to remove antennas which were performing
acceptably at the start of the observing project but develop issues serious enough to degrade the observation.
Such serious issues are relatively rare - antennas that are merely not performing optimally are generally retained.
A version of the QA0+ online reduction is then made and it provides prompt feedback on the performanceof the phasing system. Briefly, it provides time histories of the visibility amplitude and phase for baselines
between the phasing reference antenna or phased sum and the comparison antennas. These reductions are
made principally to verify that the sum signal provides a ∼ sqrt(N ) improvement in performance relative to
the Reference Antenna. If for some reason there are issues, this provides an opportunity to investigate before
the schedule finishes.
Finally, the QA2 process for VLBI is somewhat different than for standard interferometry (polarimetric)
projects. Because VLBI projects will not be re-observed as a result of any imperfections, the focus is on doing
the best reduction possible with the data that were taken. The fruit of this effort is delivered to the PI as with
non-VLBI observations. The second key difference in the QA2 for VLBI is a polarimetric reduction specificallydesigned to allow the linear to circular (PolConvert) transformation of the VLBI-correlated visibilities and anormal VLBI analysis in the circular visibility basis. The details go far beyond the scope of this document, but
the interested reader may consult a full description available elsewhere. (See Calibration of ALMA as a Phased
Array, C. Goddi, I. Martí-Vidal, H. Messias, et al., PASP, 131, 5003.)

11.10

QA in Pulsar Projects

Pulsar data will not undergo the ALMA Quality Assurance process.

176

CHAPTER 11. QUALITY ASSURANCE

Chapter 12

Data Flow and Logical Data StructureThis chapter describes the data flow process from the observations until raw data is ingested into the ALMA
Archive. It includes a brief description of all the main software subsystems involved in the data acquisition andarchiving, as well as a summary of the data structure adopted by ALMA.

12.1

Data and Control Flow

This section describes the overall control of the ALMA system and the flow of data during observations. A
summary of the main actors and operations involved in the observations is shown in Figure 12.1. Each of thelight blue boxes in Figure 12.1 represent an ALMA subsystem involved in the observations. The rest of theboxes, colored according to the actor involved, include labels for the actions performed either by external agents(actors) or by those subsystems.
The software subsystems run within a cluster environment known as a Standard Test Environment (STE),
with the STE used for the real array operation referred to specifically as an ALMA Production Environment(APE). The STE incorporates central server nodes, embedded computers for hardware control, dedicated correlator data processing nodes, and console nodes for user interaction.
A typical observing session would be started by the Telescope Operator interacting with the Executive
subsystem. The Executive subsystem is in charge of starting up the ALMA Common Software (ACS) and its
Common Object Request Broker Architecture (CORBA)-based services and then initializing all of the various
software subsystems involved in the observing and data storage process. Once all the components are ready, theExecutive also handles asynchronous events from several of the subsystems and responds to them accordingly.
Among the events, the Executive also publishes a list of error conditions to the attention of the operator andthe requests for status of the Control, Telescope Calibration, Correlator and Scheduling subsystems.
The actual observations start by the operator creating an array, which means selecting the antennas, photonic
reference and correlator (if needed by the observations1 ) to be used. The antenna selection is largely automatedby filtering based on antenna types, connection to either correlator, and status of the antennas in the ALMA
Dashboard2 . Up to six independent arrays can exist and operate at one time. Once an array is successfully
created, Scheduling Blocks (SBs) can be queued and run on it. SBs can either be manually chosen, e.g. forarray calibration or test purposes, or selected from a ranked list produced by the dynamic scheduler for regularscience operations.
An SB is the smallest, calibratable element of a project. SBs are XML documents which are part of the
ALMA Project Data Model (APDM), and are kept in the archive along with the proposal and other ancillary
information. SBs have an associated state which among other things controls whether they can be executed.
For science SBs to be executable the Phase-2 process3 should have been completed for them, and they should
not have been fully observed or cancelled/timed-out at the end of an observing cycle.
The dynamic scheduling software considerations include the target elevations as a function of time, observing
1 Most ALMA observations use a correlator, either for interferometry or single dish spectroscopy, but single dish continuum
observations can be made using only power detectors in the antennas.
2 Pietriga et al. 2014, SPIE, 9152, 1B
3 For a description of the observing preparation processes, see the Observer’s Guide

178

CHAPTER 12. DATA FLOW AND LOGICAL DATA STRUCTURE

Figure 12.1: Main actors and roles during observations with ALMA. The horizontal direction represents time
evolution.
conditions (PWV and estimated path length variability), actual array configuration, project completion status,
proposal grade and rank, among other things. The dynamic scheduler will also suggest array calibration SBs
at appropriate times. It is intended that by Full Operations the algorithm will be optimized to the point thatthe dynamic scheduler can fully automatically queue SBs during normal operation periods. At present the
Astronomer on Duty will select SBs in the dynamic scheduler GUI to be added to the array’s scheduling queue
for execution.
When an SB reaches the head of the array’s scheduling queue it starts an execution. The SB contains thename of a Python observing script, which is run by the Control subsystem and passed a Python representationof the SB content. The observing scripts, which reside in the Science Software Requirements (SSR) moduleof the software, use the SB content to determine the necessary execution sequence. The observing script
commands the Control subsystem with sequences of scans and subscans. The scan and subscan specifications
specify for each subscan the tuning, phase center and antenna pointing, calibration device position, intent
metadata (to convey the purpose of the scan/subscan), and other parameters that may need controlling fromthe observing script level. Control executes the scan/subscan sequences by commanding all relevant hardware,
the relevant correlator subsystem (Baseline (BL) or Atacama Compact Array (ACA)) and the Total Power
Processor (TPP). Subscans, and most actions performed by the Control and correlator subsystems, start andend on 48 ms (Timing Event) boundaries which are accurately synchronised among the whole system. The
subscans result in raw data files being sent to the archive subsystem incrementally during the observation,and the metadata rows being sent directly to the online Telescope Calibration (TelCal4 ) subsystem through
CORBA-based services. TelCal publishes results from calibration scans it reduces by sending them back to the
4 http://adsabs.harvard.edu/abs/2011ASPC..442..277B

12.1. DATA AND CONTROL FLOW

179

Control subsystem (Data Capture, specifically) as calibration tables, where they are displayed by GUIs to allow
Operator and AoD evaluation of the observation progress, as received by the observing script to apply online
corrections e.g. for antenna pointing and focus. The Control subsystem writes all the metadata tables to thearchive at the end of the observation.
Each run of an SB produces an Execution Block (EB) that is stored into the archive through two parallelpaths: metadata tables compiled by the "Data Capture" component of the Control subsystem, and binary data
files which are streamed directly from the data producers (ie, correlators) via the “Bulk Data” transmission
system. The metadata contains the relevant references to the binary data files to allow them to be exported
from the archive along with the metadata. The metadata tables are defined by the ALMA Science Data Model(ASDM, see Section 12.2)5 . The tables are primarily stored as XML documents, but larger tables are written
in a binary format and stored in the same way as the raw data binary data files. Both the metadata and binary
data are received by an online archive component running on the STE, which provides buffering and handles thecommunication between the STE and the archive for the data storage. For more information on the archiving,please read Chapter 13 of this Technical Handbook.
The Data Capture software is as an interface between the real-time domain of the data taking and the storageside (see e.g., 2006 ADASS contribution by Hafok, Caillat and McMullin). It receives many inputs from otherparts of the Control subsystem, as well as input from the Correlator and TelCal subsystems for each subscan andscan, which it compiles together into the ASDM tables. The Control software itself is also compiling values frommany hardware devices into the information it provides to Data Capture. At the end of each scan the current
table contents pertaining to the scan (an ASDM "slice") are passed to TelCal via CORBA-based services toallow it to produce any necessary calibration results (combined with binary data received directly from the Bulk
Data streams), and when TelCal finishes it passes back results for Data Capture to append to calibration tables.
When the execution finishes, Data Capture sends the finished ASDM tables to the online archive component
for storage (in future the storage may be made more incremental to improve scalability), waiting for the lastscan results from TelCal if needed. Data Capture is also responsible for monitoring the storage of the binary
data to the archive at the end of the execution and reporting when the data is fully archived or if there was anerror.
The archiving at the end of an execution can be carried-out in parallel to further executions, so the next SB
from the queue can start shortly after the last scan of the previous execution. This is achieved by having an
independent Data Capture component run for each execution, which remains alive until all the data from theexecution is archived. At present the array is not allowed to be destroyed until all Data Capture components
for executions in the array have completed archiving.
A summary plot of the main elements involved in data flow is shown in Figure 12.2.

Figure 12.2: Data flow components.
5 see e.g. https://casa.nrao.edu/casadocs/latest/reference-material/the-science-data-model

180

12.2

CHAPTER 12. DATA FLOW AND LOGICAL DATA STRUCTURE

The ALMA Science Data Model

The ALMA Science Data Model (ASDM; Viallefond, F. 2006, Astronomical Data Analysis Software and Systems
XV, 351, 627) defines the collection of information recorded during an observation that is needed for scientificanalysis. The ASDM is a common standard shared by ALMA and the EVLA. As described above it contains
both binary data files (BDFs) and metadata tables. The metadata tables contain links to other tables andreferences to the binary files in the Archive.
The ASDM contains 16 core tables that are common to all observing modes, and up to 23 additional tables
that are only created for specific observations. On top of these, TelCal also creates associated tables wheneverit processes any calibrations. All tables are organized with a similar structure, with the columns listing thecontents and the rows including the actual values. The core tables have been defined to outline some of thefollowing: hardware characteristics, array configuration, antenna tracking, targets, tuning setups and resulting
spectral windows, scan and subscan timing and intents, and flagging information.
The tables produced by TelCal have names prefixed by “Cal” (there is also the CalDevice table which isunrelated to TelCal). The list of these calibration tables expands as new observing modes and calibrations
become available (see Chapter 10).
The ASDM metadata implementation in the ALMA software uses automatic code generation to provide
common libraries for Python, Java and C++ to read and write ASDMs. These are used in the various parts ofthe software, both online and offline, which need to interact with ASDMs.
The BDF format is a mix of XML headers and actual binary data, encapsulated in multipart MIME. Data
recorded in each file can include cross-correlations, auto-correlations, and flags (“BDF flags”). For a typicalsubscan with a correlator, four BDFs are produced for different types of data: spectral correlator integrations,channel-average correlator integrations, Water Vapour Radiometer (WVR) integrations, and baseband Square
Law Detector (SQLD - See Chapter 5) integrations. The BDF structure is designed to support incremental
writing. Currently all but the WVR BDFs are written incrementally. Typically one incremental write includes
data from one integration or all integrations within a second when the integration time is shorter than a second.
BDF file sizes can be up to ∼ 100GB at present.
Most users interact with the ASDMs via the Common Astronomy Software Applications (CASA) data
reduction package. CASA uses a different internal storage format called the Measurement Set (MS)6 . A pieceof software distributed with CASA known as the “Filler” is responsible for producing an MS from an ASDM.
It is invoked either from the command line as asdm2MS or by the CASA task importasdm. The filler uses thesame ASDM libraries as the ALMA software for parsing.

6 see e.g. https://casa.nrao.edu/casadocs/latest/reference-material/measurement-set

Chapter 13

Data Archiving
13.1

Introduction

The ALMA Archive is composed of three subsystems, the ALMA Frontend Archive (AFA), the ALMA Science
Archive (ASA) and the Calibrator Source Catalogue (SC).
The ALMA Frontend Archive is at the center of the ALMA data flow (Figure 13.1). It provides the corepersistence functionality. The AFA is a combined database and binary data storage system that is accessedby the different software subsystems through the same software layer. The AFA stores all metadata and dataof ALMA including the user accounts, proposals, antenna configurations, monitoring, raw data, and reduced
science data. The storage architecture is based on the Next Generation Archive System (NGAS) with Oracle
technology for replicating the metadata.
The ASA makes the science data and metadata available to PIs and archival researchers for query anddownload following ALMA’s data access policy (http://almascience.org/documents-and-tools/latest/alma-userpolicies). An ALMA Science Archive Manual is available from the ALMA Science Portal1 . The ASA holds asmall subset of metadata in a relational database and provides access to external interfaces like the Archive
Query interface and Virtual Observatory (VO) tools.
The SC provides access to measurements of calibrator observations.
Each of the three ALMA Regional Centers (ARCs) in North America, Europe and East Asia holds a copyof the entire ALMA Archive subsystems for backup, user support and data distribution to the ALMA PIs andarchival researchers. The ARCs provide a completely identical user experience to their communities and a user
can download data from any ARC.

13.2

Data Flow and Archive

Data from the correlator, together with monitoring and weather data, are sent via dedicated optical fiber links
to the OSF, where they are archived. A peak data rate of 66.6 MB/s can be sustained for short periods oftime, i.e. days. This peak rate is a technical limitation of the data capture and data flow systems and will be
imposed by the Observing Tool at the proposal validation stage.
The Pipeline processing system and Archive storage system have been designed to cope with an averagedata rate of 10% of the peak rate, i.e. 6.6 MB/s leading to a yearly amount of 200 TB of data. The volume ofdata products from the pipeline are expected to approximately equal the raw data volume, resulting in about
400 TB/yr being ingested into the ALMA archive.
As soon as data are taken and have passed (or semipassed) the QA0 quality control step (see Section 11.2),
their metadata are harvested from the AFA into the ASA and made available for search. This allows archival
researchers to see which data will become public in the future. Harvested metadata include all the informationneeded to describe the observations, including date and time, source coordinates, frequency settings for each
spectral window, and spectral and spatial resolution.
The ALMA Archive at the OSF is designed to provide up to a year of temporary storage for the instrumental
data (in the form of files in the “ALMA Science Data Model”, or ASDM, format) and the monitoring data. The
1 http://almascience.org/documents-and-tools/latest/science-archive-manual

182

CHAPTER 13. DATA ARCHIVING

instrumental data are then transferred to the main archive at the SCO, where the pipeline is run and from
where the data and pipeline products are distributed to the three ARCs. At this stage, a sizeable fraction of
the data are processed at the ARCs and then mirrored back to SCO. The process of copying the data to anyof the archives involves a replication of the metadata (support data) and of the bulk data (ASDM and FITS
files). All data transfer is done over the network. Metadata replication from SCO to the ARCs happens withina few seconds, transfer of bulk data can take longer (up to several hours), depending on the amount of data totransfer to the individual ARC.

Phase I Manager
OT Phase I

Pro

PI

OT Phase II

al

pos

Source Catalogue

Scheduling

ALMA Frontend
Archive

Pr
od
u

cts
ALMA Science
Archive

Calls
Meta-data

Array Operations
Software

AQUA
QA2

Bulk data

Quicklook
QA0
Pipeline
CASA(virtual) project flow

Figure 13.1: The ALMA Frontend Archive is in the center of the ALMA data flow. The ALMA Archive
subsystems are shown in green.
Once the pipeline has processed an ObsUnitSet (hereafter OUS, see Chapter 8 for details on the OUS
structure) and the science products have passed QA2 they are ingested into the ASA.
PIs of large programs are expected to return processed data products to the project as described in the
Cycle 8 2021 Proposer’s Guide. These data will be transferred to JAO from where they will be ingested into
the ASA.

13.3

Calibrator Source Catalogue

The Calibrator Source Catalogue (SC) contains information about more than 3000 ALMA calibrators, including position, flux density, structure and polarization. It is updated with measurements from Calibrator
Survey observations, and used mainly for the selection of calibrators for bandpass, flux, phase, and polarization
calibrations, either through the OT in project preparation or the Online Software during observations.
At https://almascience.org/alma-data/calibrator-catalogue the SC database can be accessed through a webbased user interface (see Figure 13.2).
Combined search options are available for sky position (radius or RA/Dec ranges), band or frequencies, flux
density, time or polarization to facilitate the selection of calibrators. The search results are presented in a table
and a downloadable format, and zoomable views are available for the sky positions and flux density history of
the selected calibrator sources.

13.4

PI Data and Data Delegation

The unit of data delivery to the PI is the OUS. As soon as an OUS has passed QA2 and the data products havebeen replicated to the user’s home ARC, PIs will receive an email notification containing a link to their data and13.4. PI DATA AND DATA DELEGATION

183

Figure 13.2: Example of a search for polarized calibrators in an RA/Dec range with recent measurements anda flux density limit for a set of ALMA bands

supporting information. This sending of the notification to the PI triggers the start of the proprietary period of
12 months for standard proposals and 6 months for Director’s Discretionary Time (DDT) proposals. Extensionsof the proprietary period can be granted under certain circumstances (see Section 8.4.4 of the ALMA Users’
Policy). When a Group OUS consisting of several Member OUSs is processed (for example, a combined TP,
7-m and 12-m Array observation), the Group OUS products are released separately, with their own 12-month
proprietary period.
The data deliveries consist of one or more bundles of raw (ASDM-format) data and one "products" bundle
tar file which includes the FITS files, logs, scripts, QA information and calibration tables.
Often PIs want to make their proprietary data available to collaborators, e.g. Co-Is. To this end, a datadelegation service is available so that PIs do not have to give away their Science Portal password to anyone.
Instead, PIs can give access rights to the data of a project to any registered ALMA user. To do so, PIs need tolog into the Science Portal, go to their user profile page in the top right corner of the Science Portal page andthen add delegates in the "Project delegation" tab.

184

13.5

CHAPTER 13. DATA ARCHIVING

Archive QueryAt http://almascience.org/alma-data/archive users can query the holdings of the ASA (Figure 13.3). They thencan download the data corresponding to their queries, if those data are public or if the users are authenticatedand have the proper access rights to those data.

Figure 13.3: The ALMA Science Archive Query Interface
Queries can be made by physical quantities along the Position, Energy, Time and Polarisation axes. Helpon how to query is provided in the tooltips of the query fields as well as through the "Query Help" link. Query
constraints using standard operators for strings (*, ?) and numbers (>, <, .. ) can be placed into the form
fields. There is also a name resolver available for non-solar system objects (Sesame), which queries the Simbad,
NED and Vizier databases. No operators can be used in the name resolver field.
By default, the Archive Query Interface (Figure 13.3) will present users with the metadata of the observations, although they can choose to also see the metadata per project or per publication. Users can sort andsubfilter the results and add or remove columns from the result table to narrow their search. The sky coverageand the spectral coverage of the observations are visible in a graphical windows.
The interface also offers to download the results in VOTable, TSV (Tab-separated values) or CSV (Commaseparated values) format for further processing in tools like topcat2 . Astroquery3 can be used to encapsulate
and simplify programmatic access to the ASA. Neither Topcat nor Astroquery are part of the offical ALMA
software, and support of users of these tools will be limited to best efforts.
ALMA offers Virtual Observatory (VO) access through the TAP (Table Access Protocol) and SIAPv2 (Simple
Image Access Protocol Version 2) at the locations https://almascience.org/tap and https://almascience.org/sia2.

13.6

Request Handler

Once data of interest are defined, they can be selected via checkboxes on the interface and submitted to the
ALMA Request Handler for download. The data are displayed in the full OUS hierarchy. This allows users tocheck immediately if there are data from other Member OUS or higher-level Group OUS products available.
By default, only data products (i.e. images and cubes as well as ancillary processing documentation) will beselected for download. Users who want to download the raw data as well are asked to select “include raw”
before hitting the Download button or to select the desired data manually. The sources row can be expanded
to show all the source names that are part of the package. Furthermore, a readme file is provided summarising
the structure of the data and providing the full links to the OUS. For recent observations, data files can be
downloaded either as complete tar files or individually, file by file. A small arrow in front of some tar-files allow
the user to list the contents.
2 http://www.star.bris.ac.uk/~mbt/topcat/
3 https://astroquery.readthedocs.org/en/latest/alma/alma.html

13.6. REQUEST HANDLER

185

Five possibilities exist for the download itself:• The first option is to use the download script. This script runs under Linux and MacOS and downloads
files in parallel streams and is also adapted for downloads to a processing environment where no web
browser is available.
• The second option is to use the download manager applet with the FireFox browser. This method is very
convenient and allows for parallel downloads, too. It requires a Java Browser Plugin.
• It is also possible to use the download manager through Java Webstart technology.
• Moreover, a page with the links to all selected files can be displayed which then can be conveniently
downloaded, e.g. using a browser plugin like "DownThemAll".
• Finally, it is possible to just use the right-click and "Save as ..." functionality of the web browser.
Only the data deliveries that users have permission to download can be selected. If they are not authorised toaccess any data delivery in the request, no "Download selected" button appears.
If the user is authenticated before requesting data for download, the request will be stored. This allows
users to go back to previous requests. Note that these requests are stored only at the ARC the user is currently
accessing. If data should be downloaded from a different ARC, then a new request has to be issued. For verylarge data requests PIs or archival researchers have the possibility to ask via the ALMA Helpdesk for datadelivery on hard media i.e. USB hard-disks. The ARCs may have different policies regarding the details of theshipping of the hard-disks.

186

CHAPTER 13. DATA ARCHIVINGAppendix A

Antennas
A.1

Design and Properties

ALMA is composed of a total of 66 antennas, 54 with a diameter of 12 m and 12 with a diameter of 7 m.
The four 12-m antennas used for total power observations and the twelve 7-m antennas together form the
Atacama Compact Array (ACA). The ALMA antennas are manufactured by three different contractors. These
are VertexRSI (North America) which provided 25 12 m antennas, Alcatel Alenia Space European Industrial
Engineering MT Aerospace (AEM, Europe), which also provided 25 12 m antennas and Mitsubishi Electric
Corporation (MELCO; East Asia), which provided the four 12 m total power antennas and the twelve 7 mantennas (Figure A.1).
All antennas have been designed to meet very stringent ALMA performance criteria, and to successfully
operate under the extreme environmental conditions at the Array Operation Site (AOS), i.e. strong winds,
large temperature ranges and gradients, solar irradiation and snow. The primary operating conditions are thefollowing:• Range of Ambient Temperatures: -20 ◦ C ≤ Tamb ≤ +20 C• Gradient of temperature: Delta(Tamb ) ≤ 0.6/1.8 ◦ C in 10/30 minutes• Wind Velocities ≤ 6/9 m/s (day/night)• Full solar loading
The antennas have the following specifications within the Primary Operating Conditions:
Antenna Surface: RMS deviation of 25 (20) microns or less for 12-m antennas (7-m antennas) relative to an
ideal parabola.
Pointing: Absolute pointing ≤2.0 arcsec all-sky. Offset pointing ≤0.6 arcsec within a 2 degree radius on thesky.
Primary Beam: The total power pattern response of each ALMA antenna shall be determined to a measurable
and repeatable precision better than 1% at frequencies <400 GHz and 2% at frequencies >400 GHz.
Subreflector: 6 degrees of freedom to allow for alignment with the corresponding receiver beam.
Subreflector Motion: Maximum horizontal (X) and vertical (Y) displacements of ±5 mm. Maximum focal
displacement (Z) of ±10 mm. The maximum rotation around the axes is 1.2 degrees. Positioning mustbe accurate to 5 microns.
Antenna Location: The phase center position of the ALMA antenna shall be determined to a radial precisionof 65 microns (including the antenna structure and pad), stable over two weeks.
Configuration: The ALMA antennas shall be relocatable.

188

APPENDIX A. ANTENNAS

Lifetime: a minimum of 30 years.
Antennas used by ALMA have both 12 meter and 7 meter diameters, with the receivers mounted at thesecondary (Cassegrain) focus. The 12-m antennas have a focal length of 4.8 meters, but the distance from thesecondary focus to the plane of the subreflector of the 12-m antennas is 6000 mm, giving an effective focal ratio
f/8, with an effective secondary focal length of 96 m and a plate scale of 2.15 arcsec per mm. The subreflector
has a diameter of 750 mm. The 7-m antennas have a focal length, to the primary focus, of 2.572 meters. Givenan effective focal ratio f/8, an effective secondary focal length is 56 m. The subreflector has a diameter of 457
mm.
The main reflectors of the ALMA 12-m and 7-m antennas are composed of individual panels. The size andnumber of panels varies between the different types of antennas:
VertexRSI: 264 panels spanning 8 rings with 12 (rings 1 and 2), 24 (rings 3 and 4), and 48 (rings 5 through8) individual panels which are roughly a half-meter-square in area.
AEM: 120 panels spanning 5 rings with 8 (ring 1), 16 (ring 2), and 32 (rings 3 through 5) individual panels
which are roughly one-meter-square in area.
Melco 12-m: 205 panels spanning 7 rings with 5 (ring 1), 20 (rings 2 and 3), and 40 (rings 4 through 7)
individual panels which are roughly one-meter-square in area.
Melco 7-m: 88 panels spanning 5 rings with 4 (ring 1), 12 (ring 2), and 24 (rings 3 through 5) panels which
are each roughly one-meter-square in area.

Figure A.1: The four different ALMA Antenna designs: Vertex 12-m, MELCO 12-m, AEM 12-m, and MELCO
7-m (from left to right).
Each panel has up to 5 adjustment screws, which can be used to optimize the surface accuracy of theindividual antennas (based on holographic measurements). The surface of the panels are etched to scatter
optical and near infrared solar radiation.
The antennas are equipped with a movable aluminium subreflector. Subreflector adjustment is used tomaximize the transfer of power into the receivers by compensating for changes in the focus position due togravitational- and temperature-induced deformations. The backplane of the subreflector is attached to a hexapod that controls its position and orientation. The hexapod has six degrees of freedom, displacement and tilt
around the three axes, horizontal (X), vertical (Y) and along the optical axis (Z).
All antennas have a Cassegrain cabin that is kept at a constant temperature of 20 degrees Centigrade andcontains the receivers, the amplitude calibration device and associated electronics.
A shutter protects the inside of the Cassegrain cabin when the antenna is not operating. A membranetransparent to the frequencies that can be observed with ALMA is located below the shutter to prevent airflow
from the cabin to the outside when the shutter is open. The current design uses a 0.5 mm thick Goretex
membrane.

189

A.2. ANTENNA FOUNDATIONS

Vertex
Melco 12-m
Melco 7-m
AEM

BUS

Number PanelRings/ MatePanels rial

Quad
type1

Cabin

Drive
System2

Metrology System3

CFRP
Al
Invar
CFRP
Steel

8/264

Al

+

Steel

Gear

7/205
5/88

Al
Al

+
+

Steel
Steel

DirectDirect5/120

Nickel x
Rhodium

CFRP

Direct4 linear displacement sensors + 1
two-axis tiltmeter (above the azimuth bearing)
Reference Frame metrology
Thermal (main dish), Reference
Frame metrology
86 thermal sensors + 2 tiltmeters inyoke arms

CFRP
Invar

Table A.1: Design Properties of the Different ALMA Antennas.
Notes: 1 Shape of the quadrupod supporting the subreflector as seen looking along the optical axis of theantennas when they are pointed to the viewer. 2 A gear drive consists of a main motor driving a series ofconnected reduction gears (i.e., gearbox) that do the actual precision work. A direct drive system does not
require such gears and takes the power directly. The direct drives used in ALMA antennas are magneticallysupported. 3 Jointly used to correct in semi-real time the pointing of the antennas, under a wide range ofenvironmental conditions, to meet the ALMA specifications.
The different antennas use a combination of steel, aluminium, Carbon Fiber Reinforced Polymer (CFRP)
and Invar to achieve the best compromise between stiffness, robustness, smoothness, and low thermal expansion(see Table A.1 for a summary of properties). Common to all antennas is that they have a steel pedestal.
All antennas have built in metrology systems which allow thermal and wind deformations to be computedand corrected. For these purposes, the antennas are fitted with thermal sensors, linear sensors and inclinometers(tiltmeters).
The Vertex antennas have a drive system that is gear-driven whereas the AEM and MELCO antennas havemagnetically supported direct drives.
The antennas are controlled using the ALMA Control Software (ACS). ACS sends instructions to the Antenna
Bus Master (ABM) computer, which are then sent to the Antenna Control Unit (ACU) through a CAN bus.

A.2

Antenna Foundations

The antennas are placed on specially-designed concrete pads to guarantee stable orientation and location (FigureA.2). All antennas are attached to the pads at three points at the vertices of a triangle. The three points (inserts)
are located on a circle centered at the antenna pad with a spacing of 120 degrees.

Figure A.2: Structure of an antenna pad (actual pad at the OSF) (left) and detail of antenna anchored to apad (right).

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APPENDIX A. ANTENNAS

This interface guarantees a position repeatability error of the antenna, considered as a rigid body, notexceeding the values below:• X/Y plane < 2 mm (peak to peak)• Rotation around Z < 30 arcsec (peak to peak)• Parallelism with respect to Z +/- 10 arcsec with respect to Zenith
The minimum stiffness which the foundation must exhibit at each insert is:• Vertical stiffness (Z) > 13 x 109 N/m• In X/Y plane > 9 x 109 N/m
Stiffness includes the inserts, the concrete pad and the soil. This does not include the kinematic mountlower part nor the foot of the antenna. The position of the pads are measured to a precision of 65 microns,
and then monitored for stability for over two weeks. The pads are equipped with two vaults that contain the
power, communication, Local Oscillator (LO) and data transmission cables that are connected once the antennais placed on the pad.

Figure A.3: The ALMA array with eight 12-m antennas (left), and an antenna being transported to the AOS(right).

A.3

Antenna Transportation

Antennas are moved from one pad to another using a specially-designed transporter (Figure A.3, righthandpanel). ALMA has two of these vehicles. They are 20 meters long, 10 meters wide and 6 meters high, and eachhas 28 tires. The transporter positioning system performs a fine positioning of the antenna before setting it
down on the foundation in the 3 in-plane degrees of freedom (x, y, rot -z) and 2 in-tilt (rot-x, rot-y). Adjustment
in each of the 5 adjustment axes can be done independently. The adjustment range of the antenna positioning
system compensates for the inaccuracy of the vehicle position with respect to the antenna foundation (whichmust be smaller than 10 cm) to achieve the required antenna positioning accuracy. The antennas can bepositioned to within a few millimeters, ensuring accurate placement on the antenna foundation pads. Moreinformation on the transporters can be found on the ALMA EPO pages1 .
1 http://www.almaobservatory.org/en/technology/transporters

A.4. CRYOSTAT

191

Figure A.4: Side view of ALMA front end showing cryostat assembly, with room temperature unit below.

A.4

Cryostat

The ALMA front end consists of a large closed-cycle 4 K cryostat containing individual cold cartridge assemblies(CCA) with mixers and LO injection for each band, along with room temperature electronics for the IF and
LO for each band (the warm cartridge assembly, WCA) and fore-optics and entrance windows for each band.
The water vapor radiometer (WVR) is mounted to one side of the cryostat using a pickoff mirror to direct theantenna beam into the WVR. The Amplitude Calibration Device (ACD) is mounted above the front end, andis described in Section A.5. Figures A.4 and A.5 show overviews of the front-end unit, with the cylindricalcryostat on top and the room temperature electronics beneath.
All of the receiver cartridges are in the same cryostat, with the mixers thermally-coupled to the same 3stage Sumitomo cryocooler (Figure A.6). The three stages have nominal temperatures of 4 K, 15 K and 110
K. To avoid overloading the cooler, only three bands can be switched on at a time. It takes about 1 minute toswitch between any of the bands that are switched on at a given time. For bands that are off, the time to fully
thermally-stabilize them from an off state is 15 minutes – this is mainly to ensure a flat bandpass shape. All of
the receivers are mounted off-axis to avoid extra rotating band-selection mirrors, which necessitates a pointing
offset of the antenna to change band. The band pointing offsets are known and well-measured; the reference
band for pointing is Band 6, and all offsets are with respect to this band. The four higher-frequency bands(Bands 7-10) are mounted close to the central boresight to minimize aberrations.

192

APPENDIX A. ANTENNAS

Figure A.5: Bottom view of ALMA front end, showing WCAs.

A.5

Amplitude Calibration Device

The ALMA specification for relative amplitude calibration repeatability2 has been set to be better than 1% forfrequencies below 300 GHz and better than 3% for all other frequencies covered by the ALMA Front End. To
achieve this goal, ALMA has adopted a two-load amplitude calibration approach.
The Amplitude Calibration Device (ACD) is located above the cryostat. It consists of a robotic arm attachedto the top plate of the front end (Figure A.7). The arm holds two calibration loads, one at ambient (i.e., receivercabin) temperature and the other one maintained at 80 ◦ C (353 K). In addition, this arm also holds a solar
filter to attenuate solar radiation during observations of the Sun. The arm is designed to allow the two loads
to be placed in the path of any of the receiver beams (Figure A.8). Typically it takes 2 seconds to move thearm from the park position to the position where one of the loads is in the beam, and also 2 seconds to change
between loads.
To accurately calibrate radio astronomical data to a temperature scale, the actual brightness of the twoloads has to be precisely known. Critical to this calibration precision is the coupling of the load to the beamof a given band. This coupling must be very good at any telescope elevation and free of reflections of the load
emission. This is because any reflection from the loads back into the cryostat would be terminated at a different
temperature and would cause standing waves. Both loads have thus been designed so that the actual effective
brightness temperature and that computed from the measured physical temperature (with sensors embedded
2 “Calibration Repeatability” means being able to make repeated measurements of the same flux densities (or brightness temperatures) for the same source under different conditions (weather, telescope elevations, front-end status, etc.).

A.5. AMPLITUDE CALIBRATION DEVICE

193

Figure A.6: Views of cryostat assembly, showing different windows (top) and the portholes for the WCAs foreach band (lower view).

194

APPENDIX A. ANTENNAS

Figure A.7: Lateral view of the ACD on top of the ALMA front ends.

Figure A.8: Top view of an ALMA front end showing the robotic arm of the ACD retracted during normal
observations or on top of one of the front-end inserts for calibration. The current design has been improved byplacing all the loads in a wheel.

195

A.6. WATER VAPOR RADIOMETERSin the loads) using known emissivities differ by, at most, ±0.3 K and ±1.0 K for the “ambient” and “hot” loads,
respectively. This requirement also sets a limit to the fluctuations and departure from the set temperature thatare allowed for the “hot” load. Furthermore, the return loss specifications for these loads are -60 dB and -56
dB, respectively.

A.5.1

Atmospheric Calibration Procedure

The ACD is used to measure the receiver temperature and the sky emission by comparing the signals on the sky,
ambient and hot loads. This is known as atmospheric calibration (ATM calibration), and is required to correct fordifferences in the atmospheric transmission between the science and the celestial amplitude calibrators. Normally
ATM calibration is done during observations, both near the science target, as well as near the amplitude
calibrator.
Traditionally, most mm and submm observatories have used the single-load calibration method, but several
simulations have shown single-load calibration is not capable of reaching the relative amplitude calibration
accuracies required by ALMA at all of its observing frequencies. However, that method has the very desirable
feature that it is only weakly dependent on the opacity of the sky at the time of the observations. A method,using the two calibration loads within the ACD, has been devised in the past to try to achieve the same weak
dependence on the opacities at the time of the observation. This method (“the α method”) uses the voltage
outputs from the observations of both loads to simulate a single load with a brightness temperature close tothat of the atmosphere at the observing frequency. This fictitious single load is defined as a weighted sum of thevoltages of the “hot” and “ambient” loads so that the temperature calibration factors are almost independent of
the optical depth. The fictitious load voltage output, VL , is defined as:
VL = αVL1 + (1 − α)VL2(A.1)

where α is the weighting factor, and VL1 , VL2 the output voltages when the two loads are measured. From thisdefinition and some algebra, one can find the optimum weighting factor needed to minimize opacity dependency,
and the corresponding resulting calibration factors are:

α

=

TCal

=

ηJM + (1 − η)JSP − JL2
JL1 − JL2
(JMs − JBGs ) + gη eτs −τi (JMi − JBGi )

(A.2)
(A.3)

where η is the forward efficiency of the antenna, g the sideband ratio, τ the opacity, and JM , JSP , JL1 , JL2
and JBG are the emissivity temperatures of the average sky, the spill-over, the two loads and the backgroundradiation, respectively. The subscripts s and i represent the signal and image bands, respectively. The systemtemperature is then derived using the formula:
TSys = TCalVSky
VL − VSky(A.4)

For ALMA it has been found that with the current system, the non-linearities are the dominant source oferror for this calibration. The system electronics and SIS mixers are not fully linear and dominate the relative
amplitude calibration accuracy.

A.6

Water Vapor Radiometers

In the mm and submm regions, variations in the water vapor distribution in the troposphere that move across aninterferometer cause phase fluctuations that degrade the measurements. ALMA uses the so-called “Water Vapor
Radiometry” technique to correct for these phase fluctuations. Water Vapor Radiometry involves estimating
the excess propagation path amount due to water vapor along a given line-of-sight by measuring the brightness
temperature of the sky at frequencies near the atmospheric water vapor resonances. These temperatures canthen be transformed into a path length and the difference between any pair of antennas in the array gives the
final phase fluctuations to be corrected for a given baseline. ALMA has implemented this technique by placing
a Water Vapor Radiometer (WVR) on each 12-m antenna (the 7-m antennas do not have WVRs). For the196

APPENDIX A. ANTENNASWVRs to be effective, the measurements have to be taken with a cadence that is fast enough to map the actual
variations in the atmosphere. The relevant shortest timescale is the antenna diameter divided by the wind speed
as the path delay is averaged over the whole antenna beam and cannot therefore be corrected at any finer time
resolution than that. The effective diameter is about 10 m for the ALMA antennas and the relevant windspeed
is usually 10 m/s or a bit less so the fastest necessary sampling speed is 1 Hz. On timescales shorter than this
1 Hz timescale, the water vapor path fluctuations are expected to lead to small apparent pointing fluctuations
which are analogous to the seeing effects in single-aperture optical telescopes. ALMA selected the 183 GHz line
because it is quite bright and allows a more compact design than would the 22 GHz water line. It was decided
to measure the temperature of the 183 GHz line in four regions offset from the center using filters of different
bandwidths. The positions of the filters are indicated as blue boxes superimposed on the profile of the water
vapor line in Figure A.9. The sensitivity specification for the WVRs is 0.08–0.1 K per channel RMS.

Figure A.9: WVR filters superimposed onto the 183 GHz water vapor emission line.
It is very important that the WVR illuminates the same area of the sky as the ALMA band receivers in
the near-field region. This is because the origin of the water vapor fluctuations is usually located in the lower
troposphere (i.e., near the observatory), with one to several layers of water vapor clumps encompassing a wide
range of sizes. Since the ALMA backends are located at the Cassegrain focus, an offsetting optical system (seeFigure A.10) had to be designed to allow the WVR to measure along the optical axis of the antennas.
The WVRs are only able to detect the variations in atmospheric brightness temperatures due to the “wet”
atmosphere (i.e., the precipitable water vapor). There are also variations due to the changes in bulk ambient
temperature at different heights above the observatory. It is expected that these could become significant during
day time and some techniques are being currently studied to try to measure them (including thermal soundersof the atmosphere that use the profiles of the emission of the oxygen molecules). The brightness temperature
variations of the sky that the WVRs have to detect are sometimes quite small, so the quality of the receiving
system becomes very important. In fact, the current specification for the ALMA WVRs is that they need toallow corrections of the path fluctuations (in µm):
w 
10µm + 0.02δLraw .
(A.5)
δLcorr ≤ 1 +1mm
where w is the precipitable water vapor (PWV) content in mm along the line of sight, and Lraw the total
fluctuations observed at any given time. Therefore, this formula includes the expected error of about 2% inmeasuring the total fluctuations, and states the total resulting path errors after correction (Lcorr ). For a 1
mm PWV, the residual term in the formula would be 20 µm. The stability specification for the WVRs is very
stringent (0.1 K peak-to-peak over 10 minutes and 10 degree tilts). To achieve this, a Dicke-switching-radiometer
approach was adopted. The input into the mixer is switched periodically (5.35 Hz) between two calibrated loads

A.6. WATER VAPOR RADIOMETERS

197

Figure A.10: Offset optics used to collect the sky emission along the optical axis of the antenna into the WVR.
(the “cold” and “hot” loads at 293 K and 351 K, respectively), and the sky using a rotating vane embedded in
the light path as shown in Figure A.11.
Calibration of the measurements is done following the usual method for a 2-load system. The ratios of theoutput powers when observing the “hot” and “cold” loads can be used to determine the receiver temperatures.
Furthermore, these output powers from the loads are also used to extrapolate to a virtual load that has abrightness temperature similar to that of the atmosphere. The specification for the absolute accuracy of thecalibration is 2 K (maximum error). The mixer system is an un-cooled DSB Schottky diode pumped by an
LO at 15 GHz that undergoes 2 stages of multiplication. The receiver noise temperature is about 1000 K.
After amplification, the IF signal is split into four complete chains (one per filter) and a bandpass filter isapplied to select the four desired sampling regions in the profile of the water vapor emission line. In each
IF chain, the signal is detected with diodes and after a Voltage-to-Frequency conversion, sent to the Control
section for accumulation and control. There is a possibility of LO leakage out of the WVRs that could affectthe ALMA receivers in the same antenna and others nearby. To avoid coherence, all the WVRs are tuned to afrequency slightly different (offsets by consecutive integer multiples of 10 kHz up to the total number of WVRs
available). The final products sent to the ALMA Control system are time-stamped, calibrated measurementsof the brightness temperatures in the 4 filter regions. The path length error due to the PWV can be calculated
from these brightness temperature measurements and used to correct the data. Corrections at the scales of thesampling rates of the WVRs are possible at the correlator and refinements for longer timescales can also bedone offline in CASA using the wvrgcal tool. Currently both streams of data are being recorded (WVR phasecorrected and WVR non-corrected) in order to rigorously assess effectiveness.

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APPENDIX A. ANTENNAS

Figure A.11: Optical layout within the WVR encasing, showing the loads, the chopper vane and the input feedto the mixer.

Appendix B

The LO and IF System
In this Appendix, the signal path, LO chain, and the relation between these systems and the observer’s spectral
setups are described. To the system, a spectral setup effectively consists of the settings of the local oscillatorsand correlator in the system such that each spectral window (spw) covers the desired lines and/or continuum
frequencies. To the end-user, the spectral setup is normally defined in the Observing Tool (OT) just in terms of
the observing frequencies and spectral resolutions, and there is no need to worry about the details of each LO
setting. For full details of the OT and how to use it, see the OT User and Reference Manuals, available fromthe ALMA website1 (and also in the OT itself).
The following sections show how the LO system works. For those only interested in the spectral setups andnot the details of the components in ALMA, please see Chapter 6.

B.1

Functions of the LO and IF System

In the signal path from the front end to correlator, ALMA uses three frequency conversions. The associatedLO and IF systems perform multiple functions:
1. Down-conversion of the sky frequencies to basebands in the range 2–4 GHz, which then alias down to 0–2
GHz for digitization.
2. Amplification and adjustment of the correct power levels into the digitizers.
3. Adjustment of the spw center frequencies (in the Correlator FDM modes) within the basebands. This isactually done in the correlator using the TFB LO, but can effectively be treated as a 4th stage of the LO
system.
4. Application of frequency corrections for fringe rotation, and compensation for the slight differences in the
Doppler shifts at each antenna due to the differential line-of-sight velocities with respect to the target.
5. Provision of geometric delay corrections.
6. Separation of the signal and image sideband. In the case of DSB receivers, selection of the wanted
sideband(s). This is done through frequency offsets and phase modulation at each antenna using Walshpatterns.
7. Suppression of spurious signals and reduction of the effects of DC drifts in the samplers. This is doneusing phase modulation of the LOs using Walsh patterns.
Frequency down-conversion therefore effectively occurs in four stages: two hardware Local Oscillators (LO1and LO2), a 4 GHz sampler/LO and a digital LO synthesised in the tunable filterbanks (TFBs) in the Correlator2 . Chapter 6 shows how to setup the system to observe spectral lines (particularly multiple spectral lines)
1 http://almascience.org/documents-and-tools/
2 Note that the ACA correlator is designed to appear like the 64-input Correlator to the end user, although it does not use TFBs
in the same way as the BLC

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APPENDIX B. THE LO AND IF SYSTEM

and continuum. Some other aspects of frequency setups are then discussed, including the usable bandwidth,
spurious signals, and rules and limitations pertaining to this observing Cycle. An overview of the LO and IF
operation in ALMA is given in Sections B.2 and in Section B.3, the hardware and how the LO frequencies aresynthesised and distributed around ALMA are described.

B.2

Summary of Operation

Figure B.1: Overview of ALMA frequency downconversion, LO mixing and delay corrections. This takes placein the front end, back end, and correlator. Example frequencies are given for an observation at a sky frequencyof 100 GHz seen in the USB. Some LOs (e.g. LO1) are continuously tunable; others have quantized tuning steps,
such as LO2 (which can be changed in a multiple (“N”) of 125 MHz plus or minus a finely-adjustable offset of“fts”), the TFB LO (which uses a multiple “L” of 30.5 kHz) and the Bulk Delay Correction (which has steps of
250 ps, with a factor of “P”). See text for descriptions of each stage.
Figure B.1 shows a simplified block diagram of the ALMA LO/IF system, showing example setups for an
observing frequency centered on 100 GHz. Referring to this diagram, the system operates in the following way:
1. The front-end mixer uses LO1 to downconvert the observing frequency into an IF range covering up to
4-12 GHz. This wide range is needed to cover the IFs of all the ALMA bands, since the mixers for Bands
3, 4, 7 and 8 have an output IF of 4-8 GHz, Band 6 a range of 5-10 GHz and Bands 9 and 10 a range of
4-12 GHz. Over most of the front-end tuning range, LO1 and the front-end mixer can be used in upper orlower sideband; although at the edges of the tuning band, only one sideband is possible. LO1 consists of acommon reference component for all antennas, plus a smaller offset component generated in the FLOOG(First LO Offset Generator) which is different for each antenna (see LO1 Section B.3.4). The FLOOG isused to perform coarse fringe tracking (i.e. rough correction for the small offsets in the observing frequency
at each antenna), to offset the LO1 frequencies slightly to suppress internally-generated interference, andfor sideband separation or selecting the sideband. It is also used to offset the LO1 phase in conjunction

B.3. FREQUENCY GENERATION AND DISTRIBUTION IN ALMA

201

with a Walsh switching pattern on the antennas. A 180 degree phase offset is used to remove spurious
signals and DC offset while a 90 degree phase offset is used for sideband suppression and, in the future,for sideband separation on the DSB receivers (Bands 9 and 10).
2. In the back end (BE), the IF processor (IFP) splits the IF into basebands, each with a frequency range of
2-4 GHz, via a set of filters and tunable second LOs (LO2) (see IFS/IFP in Section B.3.5). LO2 is used tooffset the individual baseband frequencies within the IF range. The LO2 and second mixer only operates
in LSB, with a possible LO2 tuning range of 8-14 GHz. The LO2 signal itself is generated by a course
synthesiser which can be set only in steps of 125.0 MHz, plus or minus a second fine-tuned synthesiser(fts) which provides an offset in the range 20.0-42.5 MHz (marked as “fts” in Figure B.1). The limited fts
range and the 125 MHz quantization means that LO2 setting is not fully contiguous; consequently there
can be up to ∼30 MHz difference between the desired and the set value. With a single baseband, this canbe compensated by a suitable offset of LO1, but with multiple basebands this is not always possible. So
without additional correction, setups with multiple basebands could have the requested lines offset fromthe spw center by up to 30 MHz. However, the remaining differences in the different spws are compensatedby applying an opposite offset to the TFBLOs (LO4 - see below.)3 . An algorithm used by the OT andthe realtime system generates the best LO tuning “solution” for LO1, LO2 and LO4 which minimizes theoffset of the requested observing frequencies from the centers of the spws. Other uses of LO2 are thatthe finely-tunable fts is used for fine fringe tracking and LO2 can also be used to offset the frequencies in
conjunction with LO1 to suppress interference and select the sideband.
3. The 2-4 GHz analog IF signal from the second mixer in the IFPs is digitised (or sampled) with a 4.0 GHz
clock (DGCK). A fine delay (or time) offset is applied to this clock in units of 1/16 of the clock period(250 ps) (the “fine delay correction”).
4. In the FDM correlator mode, up to 32 digital filters (known as TFBs, or "Tunable Filterbanks") areapplied to each digitised baseband signal, each of which can be individually adjusted across the baseband
frequency (the TFB offsetting). This is effectively applying a digital LO (the TFBLO, or LO4), which isadjustable in steps of 30.517578125 kHz4 and allows the spws to be moved around within the basebands.
At Phase 2, the TFB is centered on the baseband if the TFB “offset” is set to the default of 3000.0 MHz;
it can be moved up to +/-900 MHz from that frequency, the range depending on the spw bandwidth.
The TFB outputs are resampled and sent to the correlator. The TFBLO can also be used to offset
the frequencies in conjunction with LO1 to suppress interference and select the sideband. Finally thecorrelator software is used to perform the finest level of residual delay correction.

B.3

Frequency Generation and Distribution in ALMA

Figure B.2 shows a summary of the main units involved in the LO generation and distribution. The LOs are
generated by the Central LO (CLO) (Section B.3.1) in the AOS Technical Building (lower half of diagram).
A fiber-optic system is used to distribute these signals out to the antennas (Section B.3.1) incorporating a
realtime path length correction system (Section B.3.3). In the antennas, the important outputs are LO1 (FE
1st LO) (Section B.3.4), LO2 in the IF Processer (Section B.3.5) and the digitizer clock (DGCK). All of these
are required in each antenna, shown in the upper part of Figure B.2. In the following subsections, some of thesecomponents are described.

B.3.1

Reference and LO Signal Generation

The Central Local Oscillator (CLO) generates and distributes the reference, timing and LO signals to all ALMA
components to ensure that antenna movement, electronics, and data acquisition are synchronized. These signals
are distributed to the antennas through optical fiber using the light of three infrared lasers. The ALMA frequency
and phase standard is a Hydrogen maser (installed in 2014), known as the Master Frequency Standard (MFS,
lower right), which produces a signal at a frequency of 5 MHz. This is fed into the Central Reference Generator
3 This is done automatically when the OT generates a spectral setup in an SB from a proposal. However, it is repeated at runtime.
See https://safe.nrao.edu/wiki/pub/ALMA/AlmaLamaMemos/lamaMemo808.pdf for more details on the tuning algorithm
4 The Phase 2 OT has an "adjust" button which quantizes the value entered by the user by this unit

202

APPENDIX B. THE LO AND IF SYSTEM

Figure B.2: Summary block diagram of the LO distribution system. The components in the lower section of the
diagram (below the dashed-dotted line) form the Central LO (CLO), located in the AOS Technical Building.
The components above are located in each Antenna (only one antenna is depicted in this diagram). These arelinked by the exterior buried fibers linking the Technical Building with the antenna pads (shown middle-left ofthe diagram). Thin lines with arrows represent cable distribution, thick lines represent fiber-optic distribution.

B.3. FREQUENCY GENERATION AND DISTRIBUTION IN ALMA

203

module, which produces several signals at multiples of the 5 MHz signal. The 125 MHz signal becomes one of
the standards used by many components in the ALMA system. At the AOS Technical building it is used by
the Slave Lasers in the Laser Synthesizer modules (Section B.3.2). At the antennas, it is fed into the FLOOG,
the Digital Clock (DGCK, see Section B.3.6), the IFPs, and the LO2 Synthesizers. The 2 GHz signal goes into
the DTS cards at the antennas. All the reference signals are modulated onto a 1532 nm IR laser in the Central
Reference Distributor (CRD) module. The CRD has an internal 48 ms (known as a TE, or Timing Event)clock that is also modulated into the same signal, and is used to synchronize many of the hardware events inthe observatory. The modulated 1532 nm signal is sent to an optical distributor (with 80 outputs), the Low
Frequency Reference Distributor (LFRD), that feeds it into the Sub Array Switch (SAS) modules, where it ismerged with the signals from the Master and Slave lasers (see Section B.3.2). The reference and LO signals are
fed to the antennas through the fiber-optic distribution system (see Section B.3.3).

B.3.2

LO1 Signal Generation and Distribution

LO1 is distributed through fiber-optics and regenerated photonically in each antenna front end by mixing thetwo infrared laser carriers (known as the Master (ML) and Slave Lasers (SL)) to produce a fixed frequency
for all the antennas. Figure B.3 shows a block diagram of this part of the LO system. There are five usable(production grade) Slave Lasers (Laser Synthesizers, LSs), each containing four tunable units, that can produce
six different LO1 frequencies which allow simultaneous observations at different frequencies with different subsetsof the array (multiple arrays or sub-arrays), and may be used for observing modes that will benefit from rapid
switching between frequencies (e.g., band-to-band transfer or spectral scans).

Figure B.3: LO block diagram, showing the Central LO (CLO) and the LO section in the WCA in each front
end. Yellow lines represent common synchronization and reference signals fed to all antennas, blue lines are LO
signals which are individual to each antenna. For a description of acronyms, see text.
The laser frequencies are generated in the CLO in the following way:
• The Master Laser (ML) generates a 1556 nm fixed optical reference signal, which feeds the Master Laser
Distributor (MLD) – essentially a 6-way splitter.
• The Central Reference Generator (CRG) produces the 125 MHz IF, and the Central Variable Reference
modules produce the tunable reference signals that are fed to the five Laser Synthesizers (LS) used togenerate the phase locked laser tone offset by 27 – 121.7 GHz with respect to the Master Laser, and combine
the two into a single fiber. The offsets between the ML and SL signals provides the beat note which isused to generate the LO1 frequency in the photomixers in the Warm Cartridge Assemblies (WCAs) in thefront end (B.3.4). It is used by the software to set up the front-end observing frequency. With five LSs it
is possible to generate five separate LO1 frequencies.
• The Photonic Reference Distribution (PRD) feeds the optical signals to the Sub Array Switch (SAS)module (one per antenna), which chooses the sub array to connect to.

204

APPENDIX B. THE LO AND IF SYSTEM

Figure B.45 shows the three laser signals after combination in the Sub Array Switches (SAS). The Masterand Slave laser signals have wavelengths of about 1556/1557 nm and the laser carrier signal for the reference
signals from the CRD has a wavelength of 1532 nm. The signals are distributed via a single-mode fiber optic
line to each of the antennas. The fibers are distributed in buried trenches, and fed into the Cassegrain cabinon each antenna through dedicated Az and El fiber wraps. All are fed through Line Length Correctors (LLCs),
which are used to correct for changes in the optical fibers. The LLCs are described in B.3.3 below.

Figure B.4: The ALMA fiber signals. The 1532nm carrier contains the frequency reference signals, and the1556/1555 nm carriers are used to remotely generate LO1. Within each antenna, the optical signals are split
and fed to both the LO Reference Receiver (LORR) for the demodulation of the reference/timing signals, andthe LO Photonic Receiver for the LO Reference signals.

B.3.3

Line Length Corrections

The LO Reference signals are generated at the AOS Technical Building and need to be distributed via opticalfibers to all the antennas. In order to guarantee that the phase of the LO signals is stable during the observations
for fibers of up to 15 km in length, compensation for changes has to be done in real time. The method adopted
by ALMA is based on a round-trip optical interferometer. Phase fluctuations for an optical fiber transmission
system are mainly caused by thermal expansion of the fiber and mechanical stresses, which produce birefringent
effects and changes in the absolute polarization of the signals. These changes, in turn, cause differential grouppropagation delays (DGD) that show up as LO phase jitter. The method implemented by ALMA to correct
for this is known as the Line Length Corrector (LLC). Part of the LLC can be seen in Figure B.3, and a moredetailed block diagram of the system is shown in Figure B.5.
The two-wavelength laser synthesizer signal (master and slave lasers) is adjusted in polarization, combinedat the Laser Synthesizer (LS) and then passed through a 3-port polarizing beam splitter assembly (PBS). The
polarization is aligned so that all the light passes through the beamsplitter. It then passes through a piezo-driven
fiber stretcher assembly and the fiber to the antenna. At the antenna end there is a 3-dB coupler, so that half ofthe light goes to the turnaround assembly and half to the photomixer in each WCA. The turnaround assembly
consists of a fiber frequency shifter (located in the LO Photonic Receiver module) and a Faraday Rotator mirror
located within the WCA of specifically the Band 9 cartridge in each front end. The frequency of the signal
traveling back to the AOS technical building thus receives a frequency shift of 25 MHz twice, therefore it comesback offset by 50 MHz from the original. The Faraday rotator reflects the signal but turns its polarization
angle by 90 degrees to the incident polarization. This means that the outgoing and returning light is orthogonal
everywhere along the fiber between the PBS and the Faraday Mirror. Back at the PBS, the returning signal
is sent to a third port where it is mixed with a sample of the Master Laser reference signal in a low-frequency
photodetector. This results in an output at the 50 MHz offset frequency. This output is compared in a phasedetector with a 50 MHz reference signal and the phase of the whole loop is kept constant by a servo driving thefiber stretchers.
The current stretchers can cover ranges up to 5 mm in two modes. A “slow” mode (about 10Hz) copeswith the large deformations (about 3 mm, allowing for some headroom at the ends of the ranges) and a “fast”
response mode (about 1 kHz) copes with the small range variations (about 0.1 mm). The LLCs are reset to
5 This figure needs an update. The Slave Laser (variable) wavelengh is ∼1557 nm.

B.3. FREQUENCY GENERATION AND DISTRIBUTION IN ALMA

205

Figure B.5: Block diagram of the Line Length Corrector system for ALMA. The FRM (Faraday Rotation
Mirror), shown upper right, is located in the Band 9 cartridge of every front-end. It rotates the polarisation of
the incoming light, and the resulting reflected signal is fed back though the buried optical fiber, to be comparedwith the outgoing signal. This allows the optical path length to be adjusted in a closed loop using the fiber
stretchers.
mid-range at the start of every SB execution.

B.3.4

The First Local Oscillator (LO1)

The reference signal required to tune LO1 in the receivers is obtained as the difference of the wavelengths oftwo phase-locked infrared lasers, the Master and Slave lasers. The Master Laser (ML) has a fixed wavelength of1556 nm and the tunable Slave Laser (SL) is offset from this; both are generated in the CLO (see Section B.3.2).
The offset frequency can be anywhere in the range 27 to 38 and 65 to 122 GHz. The beat note from the twolasers constitutes the Photonic LO Reference; the LO1 reference signal is generated from this by photomixers
located in the Warm Cartridge Assembly (WCA) of each receiver. This reference signal is used to drive a YIG(Yttrium Iron Garnet) oscillator operating at frequencies around 10–30 GHz (the exact range depending on theband), via a Phase Locked Loop (PLL) circuit. This produces LO1 for the SIS mixers via two sets of multipliers(see example Figure B.6 for Band 7). The same photonic reference signal is distributed to all antennas in thesame sub-array. However, to correct for different delay rates required in different antennas, the First LO Offset
Generator (FLOOG) in each antenna generates a small but variable (and different) offset frequency in the range
20–45 MHz which is also fed into each PLL. The FLOOGs for all the antennas are continuously tracked during
an observation.

B.3.5

LO2 and the IF Processor Units and IF Switch

The output of each front-end cartridge is connected to an IF Switch unit (IFS) situated in the front end, which
selects between bands, provides some amplification, and has variable attenuators to set the output levels. The
four (or two) outputs from the IF switch unit are fed into two IF Processor units (IFP), one per orthogonal
polarization. Figure B.7 shows a basic block diagram of one IF Processor (only one polarization channel isshown). The Bands 3, 4, 6, 7 and 8 receivers are dual-sideband (2SB), where both the upper and lower sideband
signals are provided separately and simultaneously. So there are four outputs from each receiver cartridge inthese bands, two sidebands times two polarizations. Each output has an IF bandwidth of up to 4 GHz. For
Bands 9 and 10, the receivers are double-sideband (DSB), where the mixer produces a downconverted output

206

APPENDIX B. THE LO AND IF SYSTEM

from signals in both USB and LSB. These bands have only two outputs, one per polarization, but the signal IF
bandwidth of these DSB receivers is 8 GHz per output.

Figure B.6: Block diagram showing generation of LO1 in a WCA - in this case Band 7 (diagrams for the otherbands are shown in the description of the individual bands). Note that an additional multiplier, not shown
here, is used to generate the LO1 frequency at 282.9 – 365.1 GHz (in this case, an x3 multiplier). The photonic
LO signal (green) feeds a photomixer which creates a beat signal between the ML and SL frequencies. Thisis mixed with a fraction of the LO from the YIG (x6), and the difference frequency is used in the PLL. The
FLOOG also generates a small offset frequency for the PLL, which is different for each antenna. See text for
details.
The IF processors divide the incoming IF bands from both sidebands into four 2 GHz basebands anddownconvert them to the 2-4 GHz range using the second LO (LO2). Since each baseband is fed by a separate
LO2, it is possible to locate them at different frequencies within the IF bandwidth of the receiver (see Chapter 6
and Table 6.2 for limitations). The LO2s are common to both mixer polarizations which means that bothpolarizations will have the same spectral setups.
The LO2s are digitally-tuned YIG oscillators with a range of 8-14 GHz. LO2 is generated from a harmonicof 125 MHz, plus a fine-tuned synthesiser (fts) of range 20-42.5 MHz, added or subtracted depending on thelock sideband selected by the software. Note that this does not give continuous LO2 coverage, and has to becompensated elsewhere in the LO system.
The IFP unit has 0.5 dB stepped attenuators and Total Power detectors for tuning/optimization of the
IF power levels into the digital samplers; these levels are set up at the start of each scan. It is important tonote that the switch network layout in the IFP means it is NOT possible to select IF configurations with one
baseband in one sideband and three in the other (except for DSB receivers, where this is done using sideband
selection). The IFP has anti-alias filters, one set of which is switchable depending on whether the IF range in
use is in the upper or lower part of the IF band. As well as downconversion, the LO2s can also be used forsideband separation when combined with the first LO (Section B.1).
The IF processor also has anti-aliasing filters, which define the 2 GHz baseband width and remove out-ofband signals (Section B.3.6). This results in the higher noise levels on the upper and lower 50-100 MHz ofchannels in the TDM correlator mode (see Section 6.4). These filters cause a decrease in the effective IF range
to approximately 1.875 GHz.

B.4. OTHER FUNCTIONS OF THE LO/IF

207

Figure B.7: Block diagram of one polarization channel of the IF Processor. This has two IF inputs (at left),and feeds 4 baseband (BB) outputs to the digitizers (to the right of the diagram).

B.3.6

Digitization and Signal Transmission

The outputs of the IF Processor units are fed into the Data Transmission System Transmitter (DTX), that
includes digitizers and formatters to convert the signals to optical wavelengths for transmission via opticalfibers. There are four DTX units per antenna, each one handling data for a given baseband pair (i.e., thesame 2 GHz baseband from each of the two orthogonal polarizations). Each baseband is digitized by a separate
digitizer at 4 GHz (i.e., Nyquist sampling for a 2 GHz bandwidth), quantizing each sample into 3 bits (8 levels)
per polarization, so that a total of 6 bits must be transferred per baseband pair. The digitized signal is thentransferred to the formatter part that packages the data in frames of equal size. The output of each DTX
module is fed to three optical fibers, each transporting 2 bits, and the signal leaves the antenna after passing
through a Fiber Optic Multiplexer (FOM). All DTX modules are fed with reference/timing signals from anassociated Digital Clock (DGCK), which is also used to do the fine delay tracking.
The outputs of the DTX are sent, via the optical fibers, to the AOS Technical Building where the process isinverted (conversion from optical to digital signal) at the DRXs (Data Transmission System Receiver modules),before the signals are sent to the correlator. Delay corrections due to changes in the length of the opticalfibers are done using metadata information to realign the frames sent from the transmitting side at the antenna(DTX) and the receiving side at the Technical Building (DRX). Figure B.8 shows a block diagram of a single
DTX module.

B.4

Other functions of the LO/IF

In addition to frequency downconversion, the LO/IF performs several other tasks, detailed below.

B.4.1

Delay Corrections

ALMA handles delay corrections via the “Delay Server” software package. It computes the corrections for all
the different components involved with a cadence of one minute and distributes them buffered. The three main
components along the data flow chain where the corrections are applied are: the First LO Offset Generator(FLOOG), the Digital Clock (DGCK) and the correlator (see Figure B.1). Fringe tracking is done at the
FLOOG by slightly offsetting the frequency of the LO1 signal. Currently, the delay handled by the FLOOG isin steps of 250 ps. The FLOOG is also used for phase and frequency switching for suppression and separationof sidebands, and for rejection of internally-generated interference, described in the next subsections.
Fine delay corrections are handled by the DGCK that feeds the corrections into the four DTS modules ineach antenna. The delay correction resolution of the fine delay is 1/16 of the 4GHz ADC clock. The bulk delay
correction is handled by the Correlator in integer multiples of the 250 ps units. On top of these corrections,the correlator also handles the “residual” delay corrections at much higher temporal resolution (<250 ps/16)
by applying a linear phase gradient across the passband after correlation. Also, the correlator applies relative

208

APPENDIX B. THE LO AND IF SYSTEM

Figure B.8: The Data Transmission System Transmitter (DTX) module, as used in each antenna.
delay corrections between all the basebands and polarizations of a given ALMA band receiver. Currently, thefirst baseband of the X polarization is used as reference.

B.4.2

Sideband Suppression - LO Offsetting

Some of the ALMA receivers (e.g. Bands 3, 4, 6, 7, and 8) are inherently single sideband (SSB), either throughhaving a mixer or quasioptic design which rejects the unwanted sideband6 . Their intrinsic sideband rejection istypically only about 10-15 dB, which, although adequate for rejection of the unwanted sky noise, is not enoughto remove strong lines from the other (image) sideband. Others receivers (Bands 9, 10) are double sideband(DSB), and the relative response of the two sidebands may not be equal, significantly affecting calibration.
Accordingly, additional schemes are necessary for more effective removal of the unwanted sideband (known as
sideband suppression), and for correlation of both sidebands independently (or sideband separation - see next
section). Sideband suppression in ALMA is done using the FLOOG, and either LO2 (2LO offsetting) or a
combination of LO2 and LO4 (3LO offsetting). A small frequency offset Fo is added to LO1 and subtracted
from the other LOs, so that while the signal sideband remains at the same frequency, the image sideband is
shifted 2Fo away from its nominal value. A different value of Fo is applied at every antenna (the offsets aredefined using a Walsh pattern), so that all signal sidebands are at the same frequency, but all image sidebands
are at slightly different frequencies and no longer correlate.
Note that each of the basebands has an independent LO2 and LO4. So by setting the sign of the offset in(LO2+LO4) differently, each baseband can be set up to observe in a different sideband.
For single-dish observing, such interferometric sideband rejection methods cannot be used, and a frequency
scanning method is under development which will allow image rejection.

B.4.3

Interference Rejection - 180 degree Phase Switching

The FLOOG is additionally used to reject spurious signals prior to digitization by applying 180 deg phaseswitching according to orthogonal Walsh function patterns, with a pattern cycle time of 16 ms. The Walsh
6 Although they have mixers to allow both sidebands to be observed separately and simultaneouslyB.4. OTHER FUNCTIONS OF THE LO/IF

209

pattern is different on each antenna, and is demodulated by a sign change within the DTS; as a result, thewanted signals correlate, and the unwanted signals are canceled out. This rejects spurious signals generated
in the system between the receiver and the sampler, and also suppresses sampler DC offsets. 180-Walsh is a
default setup for all observations. For further details please see Section 5.5.4.

B.4.4

Sideband Separation - 90 degree Walsh Switching

It is possible to apply a 90 deg phase switch in the FLOOG and in the correlator processing, allowing correlationof the upper and lower sidebands separately. For Bands 9 and 10 (DSB) it will effectively double the bandwidthfrom 8 GHz to 16 GHz per polarization from the DSB receivers. For further details please see Section 5.5.4.

210

APPENDIX B. THE LO AND IF SYSTEM

Appendix C

Acronym Dictionary
2SB
AIA
ACA
ACD
ACS
AFA
ALMA
AoD
AOS
APDM
APE
APP
APS
AQUA
ARC
ASA
ASC
ASDM
ASIC
ATC
ATM
AZ
BB
BDF
BE
BL
BLC
BWFN
BWSW
CASA
CCA
CCC
CDP
CFRP
CIP
CLO
CLT

Dual Sideband
Atmospheric Imaging Assembly (SDO)
Atacama Compact Array
Amplitude Calibration Device
ALMA Common Software
ALMA Frontend Archive
Atacama Large Millimeter/Submillimeter Array
Astronomer on Duty
Array Operation Site
ALMA Project Data Model
ALMA Production Environment
ALMA Phasing Project
ALMA Phasing System
ALMA Quality Assurance software
ALMA Regional Center
ALMA Science Archive
ALMA Sensitivity Calculator
ALMA Science Data Model
Application Specific Integrated Circuit
Advanced Technology Center, NAOJ
Atmospheric Transmission at Microwaves
AzimuthBasebandBinary Data Format
BackendBaseline
BaseLine Correlator
Beam Width between First Nulls
Bandwidth Switching
Common Astronomy Software Applications package
Cold Cartridge Assemblies
Correlator Control Computer
Correlator Data Processor
Carbon Fiber Reinforced Plastic
Correlator and Integration Processor
Central Local Oscillator
Chilean Local Time212

APPENDIX C. ACRONYM DICTIONARY

CORBA
CRD
CRG
CSV
CW
DC
DEC
DFP
DGC
DGCK
DMG
DRX
DSB
DSO
DTS
DTS-Rx
DTX
EB
EHT
EL
EM
EPO
ES
ESO
FDM
FE
FFT
FITS
FLOOG
FOM
FOV
FP
FPGA
FPS
FT
FWHM
FWHP
FWBN
FX
FXF
GMVA
GOUS
GPS
GUI
HA
HEMT
HPBW
IF
IFP
IRAM
JAO
JCMT
JPL

Common Object Request Broker Architecture
CentralReference Distributor
Central Reference Generator
Commissioning and Science Verification
Continuous Wave
Direct Current
Declination
DTS-Rx and FFT Processor
Differential Gain Calibrator
Digital Clock
Data Management Group within DSO
Data Receiver module
Double Sideband
Division of Science Operations
Data Transmission System
Data Transmission System Receiver
Data Transmitter module
Execution Block
Event Horizon Telescope
Elevation
Electromagnetic
Education and Public Outreach
Early Science
European Southern Observatory
Frequency Division Mode
Frontend
Fast Fourier Transform
Flexible Image Transport System
First LO Offset Generator
Fiber Optic Multiplexer
Field of View
Focal Plane
Field-Programmable Gate Array
Frequency Profile Synthesis
Fourier Transform
Full Width Half Maximum
Full Width to Half Power
Full Width Between the Nulls
Fourier transform correlation type correlator
Filtering, Correlation, and Fourier transform type correlator
Global Millimiter VLBI Array
Group Observing Unit Set
Global Positioning System
Graphical User Interface
Hour Angle
High Electron Mobility Transistor
Half Power Beam Width
Intermediate Frequency
Intermediate Frequency Processor
Institut de Radioastronomie Millimetrique
Joint ALMA Observatory
James Clerke Maxwell Telescope
Jet Propulsion Laboratory

213

LAS
LFRD
LLC
LO
LO1
LO2
LO3
LO4
LORR
LS
LSB
LSRK
LTA
MCI
MD
MFS
MIT
ML
MLD
MOUS
MRS
MS
NAOJ
NGAS
NRAO
NVSS
OMC
OMT
OSF
OST
OT
OTF
OUS
PBS
PDM
PI
PLL
PMG
PRD
PSF
PWV
QA
QA0
QA1
QA2
QA3
QL
RA
RF
RMS
SAS
SB
SCO
SD

Largest Angular Resolution
Low Frequency Reference Distributor
Line Length Corrector
Local Oscillator
First LO
Second LO
Digitizer Clock LO, Third LO
Tunable Filterbanks LO, Fourth LO
LO Reference Receiver
Laser Synthesizer
Lower Sideband
Local Kinematics Standard of Rest
Long Term Accumulator
Monitor and Control Interface
Mixed De-Tuned or Mixed De-Biased mode
Master Frequency Standard
Massachusetts Institute of Technology
Master Laser
Master Laser Distributor
Member Observing Unit Set
Maximum Recoverable Scale
Measurement Set
National Astronomy Observatory Japan
New Generation Archive System
National Radio Astronomy Observatory
NRAO VLA Sky Survey
Operator Monitoring and Control
Ortho-mode Transducer
Operations Support Facility
Observation Support Tool
Observing Tool
On the Fly
Observing Unit Set
Polarization Beam Splitter
Propagation Delay Measure
Principal Investigator
Phase Lock Loop
Program Management Group within DSO
Photonic Reference Distribution
Point Spread Function
Precipitable Water Vapor
Quality Assurance
Quality Assurance Level 0
Quality Assurance Level 1
Quality Assurance Level 2
Quality Assurance Level 3
QuickLook pipeline
Right Ascension
Radio Frequency
Root Mean Square
Sub Array Switch
Scheduling BlockSantiago Central OfficeSingle Dish214

APPENDIX C. ACRONYM DICTIONARY

SDO
SED
SEFD
SG
SIS
SL
SNR
spw
spws
SQLD
SRON
SSB
SSR
STE
STI
TA
TDM
TE
TelCalTFB
TFB LO
TMCDB
TP
TPP
Tsys
Trx
USB
VLA
VLBI
VOM
VO
WCA
WVR
XF
XML
YIG

Solar Dynamics Observatory
Spectral Energy Distribution
Source Equivalent Flux Density
Science Goal
Superconductor-Insulator-Superconductor mixer
Slave Laser
Signal-to-Noise Ratio
Spectral Window
Spectral Windows
Square Law Detector
Stichting Ruimte Onderzoek Nederland (Netherlands Institute for Space Research)
Single Sideband
Science Software Requirements
Standard Test Environment
Site Testing Interferometer
Technical Assessment
Time Division Mode
Time Event
Telescope Calibration subsystem
Tunable Filter Banks
Local Oscillator at the Tunable Filterbanks; LO4, Fourth LO
Telescope Monitor and Configuration DataBase
Total Power
Total Power Processor
System Temperature
Receiver Temperature
Upper Sideband
Very Large Array
Very Long Baseline Interferometry
VLBI Observing Mode
Virtual Observatory
Warm Cartridge Assembly
Water Vapor Radiometer
Correlation-Fourier Transform Type Correlator
eXtensible Markup Language
Yttrium-Iron Garnet Oscillator

Index(u, v) plane, 22
uv taper, 94
uv-coverage, 89
12-m Array, 9, 11
64-input Correlator, 9, 12, 57, 58
7-m Array, 9, 11, 13

response, 16
specifications, 187
surface, 187
transportation, 190
transporters, 11
types, 188
AOS Technical Building, 201
ACA Correlator, 9, 60
Aperture, 16
Airy function, 18
synthesis, 19
Alcatel Alenia Space European Industrial Engineering Application Specific Integrated Circuit, 62
MT Aerospace (AEM), 187
Array
ALMA
performance, 173
Calibrator Source Catalogue, 181, 182
Array Operations Site (AOS), 11
Common Software (ACS), 177
Astrometry, 160
Frontend Archive (AFA), 181
Astronomer on Duty, 107, 166
location, 11
Atacama Compact Array, 9, 11
Science Archive (ASA), 181
Atacama Large Millimeter/Submillimeter Array, 9
Science Data Model (ASDM), 179, 180
Atmosphere
ALMA Common Software (ACS), 11
opacity, 133
ALMA Project Data Model (APDM), 107
Atmospheric calibration (ATM), 195
ALMA Regional Center (ARC), 181
Atmospheric transmission, 29
ALMA subsystem, 177
Auto-correlation, 19
Control, 177
Executive, 177band-to-band, 162
Telescope Calibration, 177, 178
Bandpass
Amplitude, 15, 21, 141
calibration, 150
Amplitude Calibration Device, 31
calibrator, 150
Amplitude Calibration Device (ACD), 192
Barlett weighting, 65
Angular resolution, 84, 90
Baseband(s), 12, 13, 57, 71
Antennadesired center, 73
delay offset, 146
Baseline, 20
integration, 145
Baseline calibration, 142
pointing, 145, 149
Baseline Correlator, 57
position, 146, 150
Beam shape, 90
positions, 146
Bessel function, 18
power response, 18
Binary Data File (BDF), 180
Antenna(s)Binary Data Format, 66
beam size, 16Brightness, 15
CM, 12temperature, 28
design and properties, 187
Brightness temperature, 28
foundations, 11, 189
Calibrationpads, 189
atmospheric, 112
panels, 188
bandpass, 111, 150
performance specifications, 12, 187
flux, 111
PM, 12phase, 111
power response, 18

216polarization, 157
system-defined, 110
user-defined, 110
Calibration observation, 109
Calibration-astrometry, 160
Cartridge assembly, 31
Cassegrain focus, 188
Chajnantor, 11
Chajnantor Plateau, 10
Cittert-Zernike theorem, 22
Clock rate, 60Complex visibility, 21
distribution, 22
cone-searches, 154
Configurations, 84
Contact scientist, 173
Correlator
64-input, 12
ACA, 12, 57
capabilities, 64
FX, 13, 60
XF, 12
Correlator and Integration Processor, 62
Correlator Data Processor, 60
Correlator mode
FDM, 201
Cosmic Microwave Background, 134
Cross-correlation, 19
Cryostat, 191
Cycle 0, 9
Datadelegation, 183delivery, 183
download, 185
replication, 182
Data and Control Flow, 177
Data Capture module, 179
Data Management Group, 165
Data rate, 12
average, 181
peak, 181
Data receivers, 62
Deconvolution techniques, 25
Delay
artificial, 20
geometrical, 20
Digital Transmission System Receiver, 61
Digital Transmitter, 62
Digitizers, 62
Director’s Discretionary Time, 183
Dirty
beam, 24
image, 24

INDEX

Dirty beam, 83
Doppler shift, 199
Doppler tracking, 80
DTS and FFT processor, 61
Dump rates, 12
Early Science
Operations, 9Earth rotation, 22
EB calibrations, 147
Electromagnetic power, 15
Ephemeris file, 80, 118
Execution Block (EB), 109
Feathering, 102
Field of view, 23, 97
Field programmable gate array, 59
Flux density, 15, 28
Flux-scale, 150
Fourier transform, 15
Fraunhofer approximation, 18
Frequency
center offset, 73
definitions, 73
generation, 201
rest, 73sky, 73
synthesizer, 72
Frequency and phase standard, 201
Frequency Division Mode (FDM), 58
Frequency Profile Synthesis, 60
Fringe, 22
rotation, 199
spacing, 22
tracking, 200
Frontend, 29, 191
Full Width Between Nulls, 17
Full Width Between the Nulls, 17
FXF, 58
Gibbs phenomenon, 94
Grid source, 112
Group Observing Unit Set (GOUS), 109
Half Power Beam Width, 16
Hanning function, 64
Helpdesk, 173
Hot load, 148
Image fidelity, 24
Imagingsimultaneous, 73
Integration time, 100
Interferometer
resolution, 25

217

INDEX

two-antenna, 20Interferometry
single field, 111
Intermediate frequency, 31, 71
Jansky, 16
Joint ALMA Observatory (JAO), 11
JPL Horizon format, 118
Koh-ichiro Morita, 14
Lasers, 201
LO and IF systems, 199
operations, 200
Local Oscillator, 31, 57, 71
offsetting, 77
Local Oscillator (LO), 12
Long Term Accumulator, 60
Lower sideband, 71
Maximum recoverable scale, 13, 25, 96, 98
Measurement set, 147
Member Observing Unit Set (MOUS), 109
Metadata, 180
Metrology, 189
Mitsubishi Electric Corporation (MELCO), 187
Morita Array, 9Mosaicing, 23, 97, 112
Multiple Region Modes, 118
NED, 184
Next Generation Archive System, 181
non-dispersive, 142
Observations
on-the-Fly Mapping, 112
total power, 112
Observingproject, 107
proposal, 107
script, 107, 110
session, 109
Observing mode(s), 9
Observing session, 177
Observing Unit Set, 174
Observing Unit Set (OUS), 109
On-the-fly scan (OTF), 13
Operation Support Facility (OSF), 11
Ortho mode transducer, 33
Output radiance, 133
Pampa la Bola, 11
pcal-sens, 154
Phase, 15, 21, 141zero, 143
Phase referencing, 153

Phase 1, 71, 107Phase 2, 71, 107Phase calibration, 76
Phase calibrator
image, 154
Phase center, 21
Phase slope, 146
Phase switching, 79
phase-frequency relationship, 142
Pointing referencing, 150
Polarization, 16, 78, 113
instrumental, 114
off-axis, 114
Position switching, 13
Precipitable water vapor, 63
octiles, 133
Precipitable water vapour
octiles, 134
Primary beam, 97
Primary beam, 16
correction, 23
Primary focus, 188
Program Management Group, 165
Proposer’s Guide, 9, 109
Proprietary period, 183
PWV, 148
Quality Assurance, 165
categories, 166
classification, 165
report, 174
Quantization, 57
efficiency, 69
Radiometer
Dicky-switching, 196
Rayleigh resolution, 17
Rayleigh-Jeans limit, 28
Receiver(s)2 sideband, 136
double sideband, 136
heterodyne, 135
Rectangular field, 112
Reflector
secondary, 18
Robustness, 90
San Pedro de Atacama, 11
Scan, 109, 178
Scheduling Block, 166
Scheduling Block (SB), 107
Sciencegoal, 107, 112
parameter(s), 107
Science Pipeline, 171

218

Science Software Requirements, 109
Self-calibration, 157
Sensitivity, 74, 133
point-source, 137
surface brightness, 138
Shadowing, 26, 86
Shutter, 188
Sidebanddouble, 30, 77
double (DSB), 12
dual, 12, 30
Sidelobes, 17, 25, 83, 94
Simbad, 184
Sky brightness distribution, 15, 22
Sky frequency, 71
Snapshot, 94
Solar observations, 120
Solar system objects, 118
Spatialfiltering, 23, 95
frequency, 15, 21
Specific intensity, 15, 28
Spectral setup, 71, 73
Spectral window (spw), 58
Spectral window (spws), 71
Stokes parameters, 113
Sub-arrays, 12
Submillimeter Array (SMA), 16
Subreflector, 145, 188
Subscan, 178
Subsystems
QuickLook, 110
Control, 110
Scheduler, 109
Telescope Calibration, 110
Synthesized beam, 24
Technical Handbook, 9
TelCal, 146
Telescope
filled-aperture, 20
Telescope operator, 177
Temperaturesky, 133
system, 133
Tiltmeters, 189
Time Division Mode (TDM), 58
Tools
AosCheck, 166
AQUA, 166, 174
Monitor and Control, 166
QuickLook, 166
TelCal, 166
Total Power Array (TP Array), 11

INDEX

Total Power Array (TP Array), 9, 13
Transporter, 190
Tunable Filter Bank (TFB), 12, 58, 59, 199
Tuning range, 77
Upper sideband, 71User Policies, 173
Van Vleck relationship, 69
Velocity definition
Optical, 80Radio, 80
Relativistic, 80
Velocity reference, 80
Barycentric, 80
LSRK, 80
Topocentric, 80
VertexRS, 187
Virtual Observatory, 184
Visibility, 15
Visibility function
weighted, 83Vizier, 184
Voltage response, 18
VOTables, 184
Walsh-switching, 57, 79
Water Vapour Radiometer (WVR), 12, 63, 195
Weblog page, 172
Weightingnatural, 90
uniform, 90
WVR Correction, 63
Zero phase, 143
Zero spacing, 112
Zero-point fluctuations, 135
Zero-spacing problem, 13, 25