Doc 6.3, ver. 1.0 | 20 March, 2018

ALMA Cycle 6 Technical Handbook

ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC(Canada), NSC 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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Revision History
Cycle

Version Date

Editors

Remarks

1

1.0

2013-10-01

2

1.1

2013-10-15

3
4
4
5
6

1.0
1.0
1.1
1.1
1.0

2015-03-20
2016-03-22
2016-09-07
2017-03-21
2018-03-20

A. Hales, A. Lundgren, A. Biggs,
J. Di Francesco, B. Vila Vilaro,
S. Leon, D. Barkats, E. Fomalont,
S. Asayama, S. Komugi
A. Lundgren, S. Leon, J. Hibbard,
E. Müller, J. Di Francesco
A. Remijan, M. Adams, R. Warmels
J. Mangum and R. Warmels
J. Mangum and R. Warmels
R. Warmels and A. Remijan
R. Warmels

Cycle 3
Cycle 4
Replace figs 7.9 and 7.10
Cycle 5
Cycle 6

EditorRein Warmels

Authors of this Edition
Tony Remijan - Chapter 1; Antonio Hales - Chapter 2 and Appendix A; James Di Francesco - Chapter 3; Bill
Dent - Chapter 4; Seiji Kameno - Chapter 5; Bill Dent and Eric Villard - Chapter 6; Brian Mason - Chapter 7;
Baltasar Vila Vilaro - Chapters 8; Andy Biggs - Chapter 9; Ed Fomalont and Paolo Cortes - Chapter 10; Eric
Villard - Chapter 11; Neil Philips - Chapter 12; Felix Stoehr - Chapter 13; Kamaljeet Saini - Appendix B

Contributors to this Edition
Eiji Akiyama, Rodrigo Amestica, Yiping Ao, Yusuke Aso, Yanett Contreras, Fumi Egusa, Daniel Espada, Rachel
Friesen, Melissa Hoffman, Liz Humphreys, WooJin Kwon, Andy Lipnicky, Harvey Liszt, Jeff Mangum, Arielle
Moullet, Tony Mroczkowski, Hiroshi Nagai, Kouichiro Nakanishi, Rosita Paladino, Anita Richards, Kazy Rygl,
Masumi Shimojo, Carmen Toribio, Catherine Vlahakis, Al Wootten, Yu-Ting Wu, Kijeong Yim
In publications, please refer to this document as
Warmels, R., Biggs, A., Cortes, P., A., Dent, B., Di Francesco, J., Fomalont, E., Hales, A., Kameno, S.,
Mason, B., Philips, N., Remijan, A., Saini, K., Stoehr, F., Vila Vilaro, B., Villard, E. 2018, ALMA TechnicalHandbook, ALMA Doc. 6.3, 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
12
13
13
14

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
23
24
27
28
29

4 Receivers
4.1 Local Oscillators and IF Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 The Cycle 6 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31
33
34
35
38
41
44
47
50
53
56

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 Online WVR Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Capabilities of the Correlators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Spectral Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59
60
60
61
62
62
64
65
66
66
66

3

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69
70
71
71
72
72

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9 Limitations and Rules for Spectral Setups in Cycle 6 . . . . . . . . . . . . . . . . . . . . . . . . .

75
75
77
77
78
80
81
82
82
83
83
84
84
86

5.6
5.7

7 Imaging with ALMA87
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.2 Cycle 6 Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.3 Shadowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.4 Angular Resolution and Beam Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.5 Snapshots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.6 Large Spatial Scale Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.7 Mosaicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.8 Multi-array and Multi-configuration Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.9 Multi-array and Multi-configuration Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8 Observing Modes
109
8.1 Observing Project Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.2 Execution Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.3 The Observing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.3.1 The Source Selection Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.4 Single Field Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.5 Pointed Mosaic Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.6 Single Dish (Total Power) Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.7 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.7.1 Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.8 Multiple Region Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
8.9 Observation of Ephemeris Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
8.10 Solar Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
8.10.1 Solar Observing Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.10.2 Array Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.10.3 Single-Dish Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.10.4 ALMA Solar Ephemeris Generator Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.11 VLBI Observing Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.11.1 General VLBI Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
8.11.2 ALMA Considerations for VLBI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
8.12 High Frequency Observing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

CONTENTS

59 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.1.4 Ambient Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
9.1.5 DSB Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
9.1.6 System Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
9.1.7 System Temperature (web application and OT GUI) . . . . . . . . . . . . . . . . . . . . . 138
9.2 The Sensitivity Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
9.2.1 12-m and 7-m Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
9.2.2 Total Power Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
9.3 User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
9.4 Total Time Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
10 Calibration and Calibration Strategies
143
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.1.1 Complex Visibility Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.1.2 ALMA Visibility Data Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
10.1.3 True and Measured Visibility Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
10.1.4 Calibration Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.1.5 Reference Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.1.6 Calibrator Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10.2 Initial Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10.2.1 Antenna Surface Setting and Eﬃciencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
10.2.2 Antenna Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
10.2.3 Antenna Primary Beam Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
10.2.4 Antenna Pointing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
10.3 Antenna Integration Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.3.1 Improved Antenna Pointing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.3.2 Antenna Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.3.3 Antenna Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.4 Execution Block Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
10.4.1 Making the Measurement Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.4.2 Flagging Data Based on Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.4.3 Water Vapor Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.4.4 System Temperature Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.4.5 Antenna Pointing Tweaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
10.4.6 Antenna Position Tweaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
10.4.7 Bandpass/Frequency Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
10.4.8 Absolute Flux Density Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
10.4.9 Phase Referencing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
10.4.10 Check Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
10.4.11 Polarization Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
10.5 Additional Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
10.5.1 Self-Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
10.5.2 Astrometric Observations/Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
10.5.3 Calibrator Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
10.5.4 Band-to-Band Phase Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
10.5.5 Band-Width Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
10.5.6 Multiple EB Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
10.5.7 Combining Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
10.5.8 Total Power Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
10.5.9 Solar Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

6

CONTENTS

11 Quality Assurance
165
11.1 Cycle 6 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
11.3.1 Relationship between image quality and phase noise criteria . . . . . . . . . . . . . . . . . 169
11.4 Observatory calibration and QA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
11.5 QA2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
11.6 QA3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
11.7 The Quality Assurance Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
11.8 Overall QA Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
12 Data Flow and Logical Data Structure
175
12.1 Data and Control Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
12.2 The ALMA Science Data Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
13 Data Archiving
179
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
13.2 Data Flow and Archive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
13.3 PI Data and Data Delegation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
13.4 Archive Query . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
13.5 Request Handler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
A Antennas
185
A.1 Design and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
A.2 Antenna Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
A.3 Antenna Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
A.4 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
A.5 Amplitude Calibration Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
A.5.1 Atmospheric Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
A.6 Water Vapor Radiometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
B The LO and IF System
197
B.1 Functions of the LO and IF System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
B.2 Summary of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
B.3 Frequency Generation and Distribution in ALMA . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
B.3.1 Reference and LO Signal Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
B.3.2 LO1 Signal Generation and Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
B.3.3 Line Length Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
B.3.4 The First Local Oscillator (LO1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
B.3.5 LO2 and the IF Processor Units and IF Switch . . . . . . . . . . . . . . . . . . . . . . . . 204
B.3.6 Digitization and Signal Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
B.4 Other functions of the LO/IF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
B.4.1 Delay Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
B.4.2 Sideband Suppression - LO Oﬀsetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
B.4.3 Interference Rejection - 180 degree Phase Switching . . . . . . . . . . . . . . . . . . . . . 207
B.4.4 Sideband Separation - 90 degree Walsh Switching . . . . . . . . . . . . . . . . . . . . . . . 207
C Acronym Dictionary

209

CONTENTS

7

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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.
Cycle 6 operations will include standard and non-standard observing modes. Standard observing modes arethose well characterized, the observations can be calibrated, and in many cases, imaged by the ALMA data
reduction pipeline. Non-standard modes are not as well characterized and may require manual calibration andimaging by ALMA staﬀ. Up to 20% of the principal investigator (PI) observing time in Cycle 6 will be allocatedto proposals requesting non-standard modes. Users should refer to Appendix A (ALMA Capabilities) in the
ALMA Cycle 6 Proposer’s Guide, for the latest information and a description of standard and non-standard
modes.
The Technical Handbook concentrates on the technical aspects of the Cycle 6 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 6 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 is9

10

CHAPTER 1. INTRODUCTION

configured 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 6 is included. Concepts of shadowing, beam shape, and spatial
scale filtering are revisited. Mosaicing and 12-m and 7-m Array data combination are also presented.
Chapter 8 describes the observing modes oﬀered for Cycle 6 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 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 in determining
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.
Credit: ALMA (ESO/NAOJ/NRAO), O. Dessibourg

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 6, ALMA will cover most of the wavelength range from 8.5
to 0.32 mm (35–950 GHz), and when ALMA is completed the coverage will be 50 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 andsub-millimeter 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 Software3 (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 6) will be published in the Capabilities section of the
document ALMA Proposer’s Guide. Complementary background information on ALMA and its capabilities
for Cycle 6 can be found in the document A Primer for Cycle 6. Both documents can be found on the link
http://www.almascience.org/documents-and-tools/.
1 dedicated to the honour of K.-I. Morita

2 http://www.almascience.org/about-alma/weather
3 http://www.eso.org/projects/alma/develop/acs/

11

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.

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
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, and rapid switching between them is possible currently only for observatory calibration (seeChapter 4). Each receiver band (Chapter 4) detects two orthogonal linear polarizations and down-converts thesignals to an intermediate frequency with eight GHz of bandwidth per polarization4 .. Bands 3-8 cartridges aredual 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’) canconduct simultaneous independent observations. Please note that the sub-arrays feature of the 12-m Array is
not yet a capability that is oﬀered. The 8 GHz total IF bandwidth from the selected receiver is divided into four
2 GHz-wide basebands which are digitized at four Gsamples/s, with three-bit resolution, and transmitted on
optical fibres. 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
4 See Section 4.1 for the minimum instantaneous bandwidth available for PI science observations

2.3. THE ATACAMA COMPACT ARRAY

13

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,
although the mean data rate will be considerably less.
The 12-m Array configurations have been designed so that 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 recovered5 . 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 ALMA Common Software (ACS) platform andis operated in a similar fashion to the 12-m Array. To achieve this unified operation, the ACA system is ascompatible 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. Unlike the antennas of the 12-m Array, the 7 m antennas do not contain Water
Vapor Radiometers (WVRs). The 7 m antenna cryostats are fitted with receivers nearly identical to those on
the 12 m antennas, with small diﬀerences in the warm optics. The Local Oscillator signals transmitted to the
7 m antennas are originated identically 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). Each cartridge (see Chapter 4) receives two orthogonal polarizations.
5 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

2.3.2

CHAPTER 2. ARRAY COMPONENTS

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.
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 Proposer’s Guide describes the observing modes
and capabilities oﬀered for the TP Array for each cycle.
Due to the poorer point-source sensitivity of the 7-m Array, during Full Operations, the TP Array will beroutinely used in the calibration observations of the 7-m Array, but this is not yet implemented. Since the 7-m
Array is quite compact, atmospheric phase fluctuations will be smaller than for the 12-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.

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 Plateau de Bure Interferometer(now expanding as NOEMA) 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, I⌫ , is defined as the electromagnetic (EM) power P within arange of frequencies (a bandwidth) ⌫ received from a solid angle ⌦ and intercepted by surface area A:
I⌫ = P/ ⌦ A ⌫,(3.1)

where I⌫ has typical units of W m 2 Hz 1 sr 1 . In addition, the flux density, S⌫ , is defined as the integration

15

16

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

Figure 3.1: The Plateau de Bure Interferometer (top) and the Submillimeter Array (SMA) (bottom) are theprecursors to the ALMA telescope; both are still in full operation and pioneered the science of millimeter wave
interferometry.
of brightness over the solid angle of the emitting source:S⌫ =ZI⌫ d⌦,(3.2)

where S⌫ 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 S⌫ 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 =1I⌫ Ae ⌦.
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.
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 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 /D radians, where is the wavelength of observation and D is the diameter3.2. SINGLE-DISH RESPONSE

17

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.
of 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 zero in ⇠18 arcseconds. The central Gaussian-like feature iscalled the primary beam or the antenna beam size and it has a Half Power Beam Width (HPBW) given by:
HPBW Primary Beam = 1.02 ⇥ /D.

(3.4)

For example, the HPBW of a uniformly illuminated antenna of 12 m diameter at = 0.85 mm is 14.9500 . 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

18

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

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:
FWBN Primary Beam = 2.44 ⇥ /D.

(3.5)

Half the FWBN of the primary beam, ⇠1.22 /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
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 /D and the
FWBN is ⇠2.44 /D. The angle of the first null, i.e., the resolution, is 0.5⇥BWFN = ⇠1.22 /D. Note thatthe HPBW measured from actual ALMA 12-m antennas is ⇠1.13 /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 havemeasured primary beam HPBW values of ⇠1.13 /D.

3.3. VISIBILITIES AND APERTURE SYNTHESIS

19

An equivalent way to consider the antenna power response is in terms of the voltage response, V (✓), whereP (✓) / V 2 (✓). 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 (✓) = J1 (✓)/✓, where J1 (✓) is the Bessel function of the first kind. P (✓) is correspondingly
proportional to (J1 (✓)/✓)2 . The normalized version of the antenna power response, PN , is also known as the
Airy function.
Defining ✓ and ' as orthogonal directional variables (e.g., sky coordinates), I⌫ (✓, ') and PN (✓, ') can be
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:
Prec =

1
Ae
2

ZI⌫ (✓, ')PN (✓, ') ⌦.

(3.6)

4⇡

In addition, the solid angle of the antenna power response PN (✓, ') is defined by:
⌦A =

3.3

Z

PN (✓, ') ⌦.

(3.7)

4⇡

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 /D. Millimeter/radio wavelength (single-dish)observations have lower resolutions than optical wavelength (single-dish) observations because 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, theJCMT 15-m diameter antenna has an angular resolution at 850 µm of ⇠1400 , and the Arecibo 300-m diameter
antenna has an angular resolution at 21 cm of ⇠30 .
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 as 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:
hP i / h(XVi ) 2 i =XXh( Vi Vk )i.

(3.9)

20

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

Next, this expression can further be rewritten in terms of the sums of element pairs which are the same andthose which are not, i.e.,hP i /X

h Vi2 i +XX
i6=kh Vi Vk i.

(3.10)

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, i.e., multiplying, receiver. Moreover, if the source properties do not change, there isno 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, . In terms of familiar unitsof length, b = L/ , where L is the distance between antennas and is the wavelength in the same unit, e.g.,meters. Both antennas observe a common position so located at an angle ✓ from the meridian. The projected
separation of the two antennas towards so from the perspective of the source is u = b cos ✓. 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 ✓. In other words, emission received by antenna 1
experiences a geometrical delay relative to that received by antenna 2, where the time equals ⌧g = 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.
Moving slightly oﬀ-axis, a small angle from the axis can be described as ↵, and its 1-D sky position as
l = sin ↵, i.e., the direction cosine. At angle ↵, 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 ↵ = ul. All distances can be consideredin this situation in units of the wavelength of the emission, , so that x is the number of wavelengths within agiven distance. The extra path lengths result in phase diﬀerences with ↵ 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:
V2 = V1 e2⇡i(ul) .

(3.11)

Expanding to two dimensions introduces , a direction on the sky orthogonal to ↵. Also, m = sin 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 ✓ and v = b2 cos ' where 'is the angle of the position so on the sky from the reference position orthogonal to ✓. 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= vm. With these changes, the two-dimensional voltage response of antenna 2 is:3.3. VISIBILITIES AND APERTURE SYNTHESIS

21

Figure 3.4: An ideal 1-D two-antenna interferometer consisting of two antennas, 1 and 2, separated by physicaldistance (i.e., a baseline) b. The antennas are both pointed towards a sky location given by so , which is at
an angle ✓ from the meridian. The projected distance between the two antennas in that direction is thus u =b cos ✓. The two antennas are connected to a correlator where the voltages detected from each are combined.

V2 = V1 e2⇡i(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:
hV1 V2 i = hZZV1 (l, m)dldm

ZZ

V2 (l, m)dldmi(3.13)

Under the assumption that signals emanating from diﬀerent parts of the sky are incoherent, i.e., they haveno similarities 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:
hV1 V2 i = hZZV1 (l, m)V2 (l, m)dldmi(3.14)

22

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

hV1 V2 i =hV1 V2 i =ZZZZhV1 (l, m)V2 (l, m)idldm(3.15)hV1 (l, m)2 ie2⇡i(ul+vm) dldm.

(3.16)As V 2 / P (see Equation 3.9), and P / I⌫ (see Equation 3.3),
ZZ

hV1 V2 i /I(l, m)e2⇡i(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:V(u, v) =ZZ

I(l, m)e2⇡i(ul+vm) dldm = Aei .

(3.18)

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

3.4

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

I(l, m)e2⇡i(ul+vm) dldm

(3.19)ZZ

V(u, v)e 2⇡i(ul+vm) dudv

(3.20)V(u, v) =I(l, m) =By measuring the distribution of complex visibilities (in the visibility or (u, v) plane), in principle the skybrightness distribution can be recovered. In essence, an image is a ”sum” (i.e., the Fourier transform) of thevisibilities where each visibility has an amplitude and phase representing the brightness and relative positionof emission on a specific angular scale. The image and its Fourier transform are conjugates of each other, andeach 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 ✓) = /(L cos ✓).

(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3.5. FIELDS-OF-VIEW AND MOSAICS

23

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
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:

V(u, v) =ZZA(l, m)I(l, m)e 2⇡i(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 centre.
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 inpa grid of equilateral triangles spaced by /( 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. 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 theprimary beam of a single pointing but requires a minimum of six other pointings aroundthe single pointing.
p
These six pointings are arranged in a hexagonal pattern with each vertex spaced /( 3D) from each other (andthe single pointing). A single image is produced by combining the visibilities obtained at all pointings into asingle ensemble that is simultaneously Fourier transformed.

24

3.6

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

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 Chapter 7 (“Imaging with ALMA”), 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) =

2M
X

(u

uk , vvk ).

(3.23)

k=1

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)}.

(3.24)

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:
I D (l, m) = b(l, m) ⇤ I(l, m)A(l, m).

(3.25)

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)}, the Fourier transformof 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), whichin the interferometry context is called the primary beam. The image resulting from the Fourier transform of afinite number of visibilities, I D (l, m), is sometimes referred to as the dirty image.
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 the numbers of samples are necessarily finite and discrete, there are invariably gaps in any practicalsampling 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 inthe (u, v) plane and the brightness 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 amplitude. These latter features, also called sidelobes, can complicate the image sincebrightness is distributed via the point spread function throughout the image. The resulting image can havesignificant artefacts depending on 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

3.6. SPATIAL FILTERING

25

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.)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 artefacts 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

26

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

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 = ✓res = k /Lmax ,(3.26)

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 = ✓M RS ⇡ 0.6 /Lmin ,(3.27)

where Lmin is the minimum baseline in the array configuration. Strictly speaking, for an input Gaussian
visibility distribution of FWHM ✓M 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
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 actual ALMA configurations. The
simulations were performed using the Common Astronomy Software Applications (CASA2 ) package, the suiteof data reduction and analysis software used by ALMA. Here, panel a shows an optical image of the galaxy
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 = -40 , a declination easily observable with ALMA. Panels b, c, and dshow 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, and the 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 the compact structures of
its arms. On the other hand, these compact structures are not very discernible in the compact 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. Note that 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.
1 see Wilner, D.J., Welch, W.J. 1994, ApJ, 427, 898

2 For more information on CASA, see http://casa.nrao.edu

3.7. MULTI-CONFIGURATION OBSERVATIONS

27

Figure 3.6: Examples of spatial filtering using the CASA task simobserve and actual ALMA configurations
for Cycle 6. 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 .

3.7

Multi-configuration Observations

As previously discussed, a given configuration with baselines ranging from Lmin to Lmax is sensitive to angularscales from ⇠✓M RS to ✓res . Sensitivity to a broader range of angular scales is possible by combining data obtainedin 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 Array configurationsor the more tightly clustered 7-m Array can be used. Finally, the individual Total Power (TP) Array antennasof the ACA can be used to map the largest angular scales and address the zero-spacing problem. In thissection, we briefly describe so-called multi-configuration observations. Discussion of how ALMA implements

28

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

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.
Otherwise, information on scales covered by lower SNR data is relatively less reliable, making interpretation of
the images diﬃcult. In addition, the accuracies of the astrometry and calibration of the diﬀerent datasets are
crucial. Assuming the SNR of the individual datasets is high, combination is best done in the visibility domainrather than the image domain to minimize the eﬀect of artifacts produced by aliasing, i.e., incomplete (u, v)
coverage, in either dataset. For example, interferometer data obtained from diﬀerent configurations should be
combined in the visibility domain and then the new ensemble should be Fourier transformed to produce a new
dirty image.
Combining single-dish data and interferometer data also works best in the visibility domain, as long as bothdatasets have high SNRs. In this case, the single-dish image can be Fourier transformed into the visibility
domain and the resulting visibilities added to the ensemble of those obtained by the interferometer. The newensemble can be then Fourier transformed en masse to produce a new image. Such data combination works
best if the single-dish and interferometric datasets have significant (u, v) coverages in common. For example, areasonable overlap in (u, v) coverage can provide enough data to reveal amplitude calibration diﬀerences that canbe minimized by re-scaling the single-dish visibilities relative to the interferometric ones. In general, a reasonable
overlap of (u, v) coverage will occur if the single-dish data are obtained by an antenna that has a diameter twice
the minimum baseline of the interferometer, e.g., approximately the interferometer antenna diameter. Multiple
interferometer pointings, i.e., mosaics, can also partially recover missing low spatial frequency information.
In Chapter 7, a specific technique for combining ALMA total power data and 7-m / 12-m Array data called“feathering” is described in some detail.
Single-dish and interferometer data can be done in the image domain as well, and such addition is likely thebest route for combining relatively low SNR datasets.

3.8

Units and Conversions

Finally, this Chapter ends with a discussion of various units used in millimeter and radio astronomy anddescribe some useful conversions. Returning to the concept of specific intensity, this quantity can be describedalternatively in terms of a temperature:I⌫ (✓, ') =2k⌫ 2
TB (✓, ').
c2(3.28)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., h⌫/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, S⌫ (Equation 3.2), where

S⌫ =

2k⌫ 2
c2

Z

TB d⌦.

Assuming the beam is Gaussian, one can then connect brightness temperature to flux density following:(3.29)

3.9. FURTHER READING

✓

T
1K

29

◆

=

✓

S⌫
1 Jy

◆"

13.6

✓

300 GHz
⌫

◆2 ✓

100
✓max

◆✓

100
✓min

◆#

,

(3.30)

where ⌫ is the observing frequency, and ✓max and ✓min 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.

30

CHAPTER 3. PRINCIPLES AND CONCEPTS OF INTERFEROMETRY

Chapter 4

Receivers
The ALMA front end can accommodate up to 10 receiver bands covering most of the wavelength range from
8.5 to 0.3 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 6, 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

mm
mm
mm
mm
mm

90
80

Transmission (%)

70
60
50
40
30
20
10
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 0.3,
0.5, 1.0, 2.0 and 5.0 mm of Precipitable Water Vapor (PWV).
The ALMA receivers in each antenna are situated in a single front-end assembly (see Appendix A, Section
A.4). The front-end assembly consists of a large cryostat containing the receiver cold cartridge assembly for

31

32

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 coverageis ⇠60MHz less (See Section 6.4) 2. Sideband modes: SSB means single sideband receiver, 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.
However, the autocorrelation 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 and lower 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 per polarization, so the total eﬀective bandwidth for each receiver is then another factorof 2 higher. Note that the eﬀects of the anti-aliasing filters have been included (see Section 6.4). 5. In Cycle
6, the maximum bandwidth is approximately double in cross-correlation mode, because both sidebands can beseparated and correlated using 90-degree phase switching (see Section 6.3.4 and Section B.4.4). 6. The maximum
specified SSB receiver temperatures (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 within a 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

33

each band (the CCA, including Superconductor-Insulator-Superconductor (SIS) mixers and Local Oscillator(LO) injection) and the Intermediate Frequency (IF) and LO room-temperature electronics of each band (thewarm cartridge assembly, WCA). The cryostat is kept at a temperature of 4 K through a closed cycle coolingsystem. 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 orthogonal linear polarizations. The designs of the mixers, optics, LO injection scheme, and polarization
splitting vary from 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, the time to fully
thermally stabilize a receiver from an oﬀ state is up to ⇠15 minutes - this is mainly to ensure the optimum
flat bandpass shape. All of the receivers are mounted oﬀ axis in order to avoid extra rotating band selection
mirrors, which necessitates an oﬀset of the antenna pointing to change band. It means that only one receivercan be used at a given time.

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.

34

CHAPTER 4. RECEIVERS

4.2

The Cycle 6 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 LO, TFB LO) by small and opposite amounts, as well as 180-degree phase-switching, theoﬀsets of which depend on the antenna such that the signals from two antennas in the image sideband do notcorrelate (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.
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 6 RECEIVERS

4.2.1

35

Band 3 ReceiverBand 3 is the lowest frequency band available in Cycle 6, covering a frequency range of 84 to 116 GHz (in the
3 mm atmospheric window). The cartridge is fed by a “periscope” pair of ellipsoidal pickoﬀ mirrors locatedoutside the cryostat, which refocus the beam through the cryostat window, allowing for a smaller window
diameter (Figure 4.4). 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, is shownin Figure 4.5. The Cold Cartridge Assembly (CCA) contains the corrugated feedhorn, OMT, SIS mixers andthe low-noise HEMT first IF amplifiers. At room temperature, the Warm Cartridge Assembly (WCA) includes
further IF amplification and the Local Oscillator 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. This includes a 2 K component due to the losses in the external warm
optics. The achieved median performance is typically somewhat better than this, with Trx ⇠37 ±6 K. The OT
is a little conservative, and assumes Trx =45 K. The atmospheric transmission over most of Band 3 is very high,even with a large PWV (Figure 4.6) which means observations in Band 3 can (and do) take place with up to
10 mm or more of PWV. The system temperature (Tsys ) shows the expected rise at the higher end due to theedge of an atmospheric oxygen line (Figure 4.7), so this increase is mostly independent of the PWV.

36

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 forthe 2SB mixers. The Band 3 cartridges were constructed in Canada at NRC-HIA, Victoria.

4.2. THE CYCLE 6 RECEIVERS

37

Transmission in Band 3 at Zenith
100
95

Transmission (%)

90
85
80
75
PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

70
65
60
85

90

95

100

105

110

115

Frequency (GHz)
Figure 4.6: Band 3 zenith transmission for 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. The decrease at the highfrequency end is due to the edge of an O2 absorption line at 118.75 GHz.

Band 3 System Temperature at Zenith
150

T sys

100

50
PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

0
85

90

95

100

105

110

115

Frequency (GHz)
Figure 4.7: Typical system temperature (Tsys ) at zenith for Band 3 with 0.3, 0.5, 1.0, 2.0 and 5.0 mm of
PWV. 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.

38

4.2.2

CHAPTER 4. RECEIVERS

Band 4 Receiver

The Band 4 receiver covers the 125 to 163 GHz spectral window (in 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. Red indicates Band 4 Gaussian beam of 5 times the beam width.

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 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). The OT assumes 51 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 6 RECEIVERS

39

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.

40

CHAPTER 4. RECEIVERS

Transmission in Band 4 at Zenith
100
95

Transmission (%)

90
85
80
75
PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

70
65
60
125

130

135

140

145

150

155

160

Frequency (GHz)
Figure 4.10: Band 4 zenith transmission for 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV.

Band 4 System Temperature at Zenith

100

T sys

80

60

40
PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

20

0
125

130

135

140

145

150

155

160

Frequency (GHz)
Figure 4.11: System temperature (Tsys ) at zenith for Band 4 with 0.3 to 5.0 mm of PWV. Tsys was computed
using only the receiver temperature values adopted in the OT and the atmospheric contribution. No spill-overor background terms have been included. Temperature is given in Kelvin.

4.2. THE CYCLE 6 RECEIVERS

4.2.3

41

Band 5 Receiver

The Band 5 receiver covers the 158 to 211 GHz spectral range (in the 1.9–1.42 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 fulfil 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 realised performance of the receivers are often
better than 50 K over the band. The OT assumes 55 K. The resulting system temperatures (Tsys ) are shown in
Figure 4.15.

42

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 6x multiplier in the WCA, then a 2x cold
multiplier in the CCA (at 110K).

4.2. THE CYCLE 6 RECEIVERS

43

Transmission in Band 5 at Zenith
100

Transmission (%)

80

60

40
PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

20

0
165

170

175

180

185

190

195

200

205

210

Frequency (GHz)

Figure 4.14: Band 5 zenith transmission for 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. 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.
Band 5 System Temperature at Zenith300

PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

250

T sys

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 with 0.3, 0.5, 1.0, 2.0 and 5.0 mm of
PWV. 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.

44

4.2.4

CHAPTER 4. RECEIVERS

Band 6 Receiver

The Band 6 receiver covers a frequency range of 211–275 GHz (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 was 5-10 GHz, but has been extended further for Cycle 6 to allow for
multiple simultaneous line observations with more bandwidth per spw1 ; 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 Tsys isless), 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 three typical 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 overmost of the band. The OT assumes 55 K. The resulting system temperatures (Tsys ) for diﬀerent PWV values
are shown in Figure 4.19.

1 Specifically, the 12 CO/13 CO/C18 O J =2 -1 combination at 230.538/220.398/219.560 GHz, which has a minimum separationof 10.14 GHz. In 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 6 RECEIVERS

45

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. The Band 6 cartridges were built at NRAO, Charlottesville. 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).

46

CHAPTER 4. RECEIVERS

Transmission in Band 6 at Zenith
100
95

Transmission (%)

90
85
80
75
70
65

PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

60
220

230

240

250

260

270

Frequency (GHz)
Figure 4.18: Band 6 zenith transmission for 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. Most of the narrow absorption
lines are from ozone.

Band 6 System Temperature at Zenith

300
250

PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

T sys

200
150
100
50
0
220

230

240

250

260

270

Frequency (GHz)
Figure 4.19: Typical Tsys at zenith for Band 6 with 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV, based on measured
values of the receiver temperatures. 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. Temperatureis given in Kelvin.

4.2. THE CYCLE 6 RECEIVERS

4.2.5

47

Band 7 Receiver

The Band 7 receiver covers the frequency range 275 to 373 GHz (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. 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 75 K over the whole band. The resulting
system temperatures (Tsys ) for diﬀerent PWV values are shown in Figure 4.23. Note that the atmospherictransmission (and hence Tsys ) at frequencies below 300 GHz is considerably better than that of the top half ofBand 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.

48

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 at IRAM in France.

4.2. THE CYCLE 6 RECEIVERS

49

Transmission in Band 7 at Zenith
100

Transmission (%)

80

60

40
PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

20

0
280

290

300

310

320

330

340

350

360

370

Frequency (GHz)
Figure 4.22: Band 7 atmospheric zenith transmission for 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. The deep
atmospheric absorption at 325 GHz is due to water, and the narrower feature at 369 GHz is due to oxygen.

Band 7 System Temperature at Zenith500

PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

400

T sys

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 with 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. Tsys was computed
using only the receiver temperature values adopted in the OT and the atmospheric contribution. No spill-overor background terms have been included. Temperature is given in Kelvin.

50

4.2.6

CHAPTER 4. RECEIVERS

Band 8 ReceiverBand 8 covers the frequency range 385 to 500 GHz (the 650 µm atmospheric window). The cryogenic optics ofthis receiver adopts a single mirror to couple a feed horn in front of an SIS mixer block to the sub-reflector. A
single feedhorn feeds an OMT which splits the two linear polarizations and feeds the 2SB SIS mixers (Figure4.24).

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 wholetuning range. 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 150 K. The resulting system temperatures(Tsys ) for 0.472 mm PWV are shown in Figure 4.27. Note that transmission in the lower part of the band isalmost 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 centre of Band 9.

4.2. THE CYCLE 6 RECEIVERS

51

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.

52

CHAPTER 4. RECEIVERS

Transmission in Band 8 at Zenith100
PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

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 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. The atmospherein the Band 8 frequency range has some deep absorption features due to water and oxygen.

Band 8 System Temperature at Zenith

4000

PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

3500
3000

T sys

2500
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 with 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. Tsys was computed
using only the receiver temperature values adopted in the OT and the atmospheric contribution. No spill-overor background terms have been included. Temperature is given in Kelvin.

4.2. THE CYCLE 6 RECEIVERS

4.2.7

53

Band 9 ReceiverBand 9 covers the frequency range 602 to 720 GHz (the 450 µm atmospheric window). It uses a wire grid inorder 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. 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. In Cycle
6, 90-degree phase switching can also be 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
and warm 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 110 K. Figure 4.31 showsthe expected Tsys for 0.472 mm of PWV, over most of the band given the OT default expected receiver noise,
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

54

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 fibre-optic Line Length Corrector system (see Appendix B.3.3), and means thatthe Band 9 receiver must be available on all the antennas for this to work. The Band 9 receiver was built at
SRON in the Netherlands.

4.2. THE CYCLE 6 RECEIVERS

55

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 Zenith100
PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

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 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. Most of the band is aﬀectedby the wings of pressure-broadened H2 O.
Band 9 System Temperature at Zenith

6000

PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

5000

T sys

4000
3000
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 with 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. Tsys was computed
using only the receiver temperature values adopted in the OT and the atmospheric contribution. No spill-overor background terms have been included. Temperature is given in Kelvin.

56

4.2.8

CHAPTER 4. RECEIVERS

Band 10 ReceiverBand 10 covers the frequency range 787 to 950 GHz (the 350 µm atmospheric window). Band 10 is the highest
frequency receiver of the ten bands envisioned for the ALMA front-end system. The development of 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 been utilized in
the tuning circuit of Band 10 mixers. The Band 10 Nb/AlOx/Nb tunnel junctions with NbTiN-based 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, Cycle 6 allows 90-degree phase switching to be used tocorrelate both USB and LSB simultaneously (see Chapter 6). The IF bandwidth in this receiver is 8 GHz perpolarization (7.5 GHz eﬀective bandwidth after the IF Processor units, see Section 6.4), covering 4–12 GHz. A
block diagram of the Band 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 aÄnd early morning, when the sky is most stable. Also the antenna surface accuracy has
a significant eﬀect on the aperture eﬃciency at this high-frequency band; improvements to the surface accuracyof the 12m 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 6 RECEIVERS

57

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.

58

CHAPTER 4. RECEIVERS

Transmission in Band 10 at Zenith100
PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

Transmission (%)

80

60

40

20

0
800

850

900

950

Frequency (GHz)
Figure 4.34: Band 10 zenith transmission for 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. Transmission of most of
the band is aﬀected by the wings of pressure-broadened lines of H2 O.

Band 10 System Temperature at Zenith

6000

PWV 0.3 mm
PWV 0.5 mm
PWV 1.0 mm
PWV 2.0 mm
PWV 5.0 mm

5000

T sys

4000
3000
2000
1000
0
800

850

900

950

Frequency (GHz)

Figure 4.35: Typical Tsys at zenith with Band 10 for 0.3, 0.5, 1.0, 2.0 and 5.0 mm of PWV. Tsys was computed
using only the receiver temperature values adopted in the OT and the atmospheric contribution. No spill-overor 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 autocorrelation function of each antenna. It delivers complex fringe visibilities which, once
calibrated in amplitude and phase, allow the ALMA users to synthesize astronomical images. The correlator also
provides pre-correlation delay and phase tracking functions to adjust the response to the wavefronts of received
signals in order to maintain the coherence of the complex visibilities. Walsh-switching modulations for sideband
separation (90 phase switching) and spurious-signal suppression (180 phase switching) are demodulated in
the correlator.1
All signals 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), respectively2 . Both correlators run simultaneously
and independently. Thus, while the 12-m Array observes an object using the 64-input Correlator, the ACA
Correlator can be used with the 7-m Array and/or the Total Power Array observing either the same or a diﬀerent
object.
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 TP-Array observations but also for normalization of cross power spectra andmeasurements of system noise temperatures. 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 6 observations. The specifications of the correlators determine a lot of observational performance such as bandwidth, spectral resolution,
time resolution, and polarimetry. The phase tracking performance, including online WVR correction, provides
coherence and improves phase stability in correlated data delivered to users. Imperfect correction for the nonlinear response in the correlators invokes systematic errors in complex visibilities. The response of digital signal
processing is also presented in this chapter.
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 and B.4.4, and also Emerson 2005, ALMA memo No. 537.
2 Crossbar switching allows for some flexibility in this arrangement.

59

60

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 employs a hybrid design, also known as the FXF3 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 a wide bandwidth and acoarse 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 6. Each quadrant
can handle a 2 GHz dual-polarization BB for up to 64 antennas4 . The full set of four quadrants is capableof accepting four BBs to cover a total 8 GHz bandwidth per polarization, that is 16 GHz of 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, sideband ratio measurements, etc. 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 quantization levels from 3- to 2-bits per sample (see Section
5.3).
The TDM mode provides a Spectral Window (spw)5 that consists of up to 256/Npol channels per BB, where
3 F, X and F stand for filtering, correlation and Fourier transform, respectively.

Nant (Nant 1)= 2016 baselines and 64 auto-correlations for Nant = 64.
2
5 An spw is a continuous spectrum composed of uniformly spaced frequency channels.
4

between BB and spw.

See also Chapter 6 about the relation

5.1. THE 64-INPUT CORRELATOR

61

One quadrant to process

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

POL 2

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

At antenna

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).
Npol is the number of polarization products per BB6 . 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.

5.1.2

FDM mode

FDM is adequate 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 an FPGA. (FPGA). In a TFB there are 32 independent 62.5-MHz bandpass filters
or sub-bands. To avoid edge artifacts, sub-band center frequencies are set such that their edges overlap andthe eﬀective bandwidth is thus reduced by a factor of 15/16, that is, 58.59375 MHz of eﬀective bandwidth per
sub-band. Down stream, the correlator software stitches together contiguous sub-bands to output a seamlesscross power spectrum to form an spw with as many as 15
16 ⇥ 8192/Npol channels.
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 bandwidths
6 N

pol = 2 for standard Stokes-I observations that employ XX and Y Y

products, and Npol = 4 for full-Stokes observations.

62

CHAPTER 5. THE CORRELATORS

of 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.
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 is dedicated to observations with the Atacama Compact Array that consists of the 7m 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 FX7 design in which the incoming time-domain data stream is converted intofrequency-domain spectrum via an FFT (Fast Fourier Transform) module before cross multiplication to form
the power spectrum. The FFT part always accepts a full 2 GHz bandwidth and outputs 524288 channel spectrawith a frequency resolution of 3.815 kHz. This design enables flexible spectral handling as shown in Figure 5.3
7 F and X stand for Fourier transform and multiplication, respectively.

5.2. THE ACA CORRELATOR

63

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, a frequency profile synthesis(FPS) is performed in the Correlator Data Processor computer so that the outputs of both correlators arematched (Kamazaki et al. 2008, ALMA Memo 580).

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.
A detailed diagram of the signal processing in the ACA Correlator itself is shown in Figure 5.3. Similar to64

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
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.
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 spectrum8 (hereafter, voltage spectrum) for every BB per
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 detail, 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
8 220 -point FFT produces a 220 -point complex voltage spectrum of a double sideband including the image sideband that will bediscarded.

5.4. ONLINE WVR CORRECTION

65

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 with
diﬀerent 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.
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
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

Online 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. The WVR data are recorded together with visibilities. The later can be chosen

66

CHAPTER 5. THE CORRELATORS

to be WVR uncorrected, corrected, or both at the same time. If online correction is selected, then, the correction
happens in real-time every dump duration, based on path length fluctuations in WVR data samples from eachantenna. However, starting from Cycle 6 the online software will only produce uncorrected visibilities, and thecorrection will be applied oﬄine in the CASA pipeline. Recording both WVR corrected and uncorrected results
impacts data rates and storage, 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.

5.5

Capabilities of the Correlators

5.5.1

Polarization

Both correlators oﬀer polarimetry capability by delivering all correlation products of hXX ⇤ i, hXY ⇤ i, hY X ⇤ i,and hY Y ⇤ i where X and Y stand for two linear orthogonal polarization components. These correlations relate
to the Stokes visibilities of I, Q, U , and V as
0
1
0
10
1
I
1
0
0
1
hXX ⇤ i /(GX G⇤X )⇤⇤B Q C 1 B cos 2
B
C
sin 2
sin 2
cos 2 CBCB
C B hXY i /(GX GY ) C ,(5.1)@ U A = 2 @ sin 2
cos 2
cos 2
sin 2 A @ hY X ⇤ i /(GY G⇤X ) A
V
0
i
i
0
hY Y ⇤ i /(GY G⇤Y )where GX and GY stand for complex antenna-based gains in X and Y polarizations and is the parallactic
angle. This formulation doesn’t include cross talk, also known as ‘D-terms’, whose calibration will be discussed
in Chapter 10.
The 64-input Correlator forms 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. Although the ACA Correlator is capable ofpolarimetry, the cross-polarization products of the 7-m Array or the TP Array observations will not be oﬀered
for Cycle 6.

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
listed in Figure 5.5.2 and shown in Figure 5.5.2. 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 5.5.2. The spectral resolution function is given by 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 functions9 are applicable to suppress
9 For a full description, see http://mathworld.wolfram.com/ApodizationFunction.html.

5.5. CAPABILITIES OF THE CORRELATORS

67

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

the spectral sidelobes as listed in Table 5.2. 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 isa trade 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 through the OT if necessary for the science goal.

-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
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 provides a broader spread of correlator functionality between thecurrent TDM (which has only 128 channels in dual polarization) and full FDM (with 3840 channels in dual
polarization mode). It might be quite acceptable for those who need something with more resolution than TDM,
but where the FDM channels at the full resolution are unnecessary. Table 5.2 shows the resolutions (in kHz)for diﬀerent values of N , using Hanning weighting, in the diﬀerent bandwidth modes. The channel spacings arein parentheses. In Cycle 6, the default value is N = 2.
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 thenumber of channels when feasible. This is selected in Phase 2 of the SB creation. However, note that this isa non-reversible operation. For Cycle 6 the default value for spectral averaging will be 2. The proposer mustspecifically request and justify the use of N = 1 for spectral 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.

68

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
6 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

5.5.3

69

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.
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 = 42, 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 18.1 MB/sec.
In Cycle 6, 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 64input Correlator sets Nbyte 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 autocorrelationand 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 be lower
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.
• Integration duration of online WVR Correction

70

CHAPTER 5. THE CORRELATORS

If online WVR corrections are requested by a given spectral configuration, then the integration duration
Tint must be equal to or longer than that of the WVR system (1.152 sec). Given that for Cycle 6 neither
the 7-m Array nor the TP Array uses online WVR, the above restriction applies to the 64-input correlator
only.
A pulsar gating function is not implemented in the ALMA correlators. Timing sensitive analysis must
be taken oﬄine under the time resolution limited by the actual integration duration, Tint , used during anobservation.

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.

5.5.4

Phase Switching

The 180 phase switching capability is implemented to suppress spurious signals and IF cross talks between
the LO1 and the digitizers10 . 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 correlator11 . 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.
The 90 phase switchingThis function aims to separate USB and LSB for the DSB receivers of Bands 9 and 10. When the LO phase of⇡⇡antenna 2 is oﬀset by 90 , the phases of USB and LSB signals in IF will beLO
2 and LO + 2 , respectively.
The 90 -demodulation is taken by swapping real and imaginary parts of the cross correlations in the CDP.
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.
10 Note that this scheme doesn’t work for autocorrelations.

11 See Thompson, Moran, and Swenson, “Interferometry and Synthesis in Radio Astronomy (2nd edition)”, §6.1 and §7.5.

5.6. PRACTICAL PERFORMANCE

State

Ant.

0

1
2

LO

1

1
2

LO

71

LO phaseLO

LO + ⇡

IF signal

Demod.

i LO

S1 e
+N
S2 e i LO + N

00hS1 · S2⇤ i + hN · N ⇤ i

S1 e i LO + N
S2 e i( LO +⇡) + N

0⇡hS1 · S2⇤ iaverage

Cross Corr.

hN · N ⇤ ihS1 · 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.
State

Ant.

LO phase

0

1
2

LO

1

1
2

LO

LO
⇡
LO + 2

IF signal

Demod.

S1,U e+ S1,L e
S2,U e i LO + S2,L ei LO

00S1,U e i LO + S1,L ei LO⇡⇡
S2,U e i( LO + 2 ) + S2,L ei( LO + 2 )

0

i LO

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

i LO

⇡
2

Cross Corr.
⌦
↵ ⌦
↵
⇤
⇤
S1,U · S2,U
+ S1,L · S2,L⌦⇤
S1,U · S2,U

↵

⌦
↵
⇤
⌦S1,U · S⇤2,U↵
S1,L · S2,L⌦⇤
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) quantization12 , and additional re-quantization
processes are applied in the correlators.
In Cycle 6, the 64-input Correlator TDM mode makes use of 2-bit quantization that yields a quantizationeﬃciency of ⌘Q = 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 ⌘Q = 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)13 .
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. ⌘Q = 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.
12 The quantization eﬃciency would be ⌘ = 0.96 if optimal signal levels, threshold voltages, and perfect signal processing wereQ
performed (Thompson 1998, MMA Memo 220).
13 It is reported that the combination of 2-bit quantization, digital filtering, and 2-bit re-quantization yields ⌘Q = 0.81, better
than 0.88 ⇥ 0.88 = 0.77.

72

5.6.2

CHAPTER 5. THE CORRELATORS

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.
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, ⇢. (Right): Departures of the Van Vleck relationship from linear relation using the single factors of⌘4 = 0.881, ⌘8 = 0.963, and ⌘16 = 0.988 for 2-, 3-, and 4-bit quantizations, respectively.
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 coeﬃcients14 . 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
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 it 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
share the 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 spectral windows set up by the proposers inPhase 1 of the OT, and additional spws from observations needed for calibration (pointing, and sometimes
system temperature) set up during Phase 2. Additionally, the WVR data are stored in a spectral window
with 4 channels around the water line at 183 GHz. In the ASDM, except for the WVR spectral window, eachrequested spectral window maps into two output spws in the data: one with the requested dimensions of N
14 The departure from linear relation is⇢/⇢ < 10

3 for ⇢ < 0.2

5.7. FINAL DATA PRODUCT - THE ASDM

73

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 usedby the online telescope calibration system (TelCal) and for realtime diagnostic purposes (QuickLook), and are
typically not used downstream in the data reduction. Overall, this can lead to ASDMs with a large numberof spectral windows. For example, a typical science observation in FDM mode can have more than 25 spectral
windows. Every scan/spw combination has an “intent” associated with it that indicates its purpose (pointing,system temperature, science, etc). The intent can be used in CASA to decode how to utilize each spectral
window in the data reduction process.

74

CHAPTER 5. THE CORRELATORS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 jump to Appendix B. The main change for Cycle 6 is the extension of theBand 6 IF coverage to 4.5–10 GHz, allowing for broader spws convering the J=2-1 12 CO transition and its 13 C
and 18 O isotopologues.
To the ALMA system, a spectral setup includes the hardware LO, IF and correlator settings, such that eachSpectral Window (spws) covers the desired lines and/or continuum frequencies. To the end-user, however, thespectral setup is normally defined in the Observing Tool (OT) just in terms of the desired lines or observing
frequencies, spectral window bandwidths and spectral resolutions: there is normally no need for the user toworry about the details 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 these basebands
it is possible to place up to four Spectral Windows (spws). Each spws forms a final contiguous spectrum, withbandwidths 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 areeﬀectively four diﬀerent LOs set up by the system (Figure 6.1):
1 http://almascience.org/documents-and-tools/

75

76

CHAPTER 6. SPECTRAL SETUPS• 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),• LO4 (also known as the tunable filterbank LO, or TFB LO), which is a digital LO synthesized in thecorrelators allowing positioning of the spectral windows 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 spectral window, one baseband, one polarisation. The Backend IF system is located in each antenna, and the digitised signal for eachbaseband/polarisation 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 realtime 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
picks the best one.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.
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.

6.2. FREQUENCY DEFINITIONS

77

Cycle 6 has similar restrictions on the spectral setups and tuning as Cycle 5 (see Table 6.2 in Section 6.9),
except for Band 6, where the lower end of the IF tuning range has been extended down to 4.5 GHz. The main
limits are that the edges of the 2 GHz-wide basebands cannot lie outside the receiver tuning range listed inTable 4.1, and the edges of the (untruncated) spectral windows cannot lie outside the individual 2 GHz-wide
basebands. The settings of each baseband in the correlator are independent, so the bandwidth, resolution andcorrelator mode as well as the value of LO4 can be diﬀerent for each baseband. For example, it is possible tohave a 58 MHz-wide spws centered on a particular line in baseband 1, and simultaneously use a broadband time
division multiplexing mode (or TDM mode - see correlator chapter) for all the other basebands. It is possible tohave multiple FDM spectral windows within each baseband, described in Section 6.3.2 below; however, currently
the underlying resolution of all spws within the same baseband has to be equal. The spectral setups of the ACA
Correlator and the 64-input Correlator are - to the end user - eﬀectively the same, 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 standard ofrest based on the average motion of the Sun with respect to the solar neighborhood (see Section 6.8).
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 be
diﬀerent 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 spectral windows 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 spws, the other continuum spws frequencies need
to be setup manually; one method of doing this is described in the next section. The selection of secondarylines to be observed can be done using the OT spectral interface. In the case of continuum spws, to maximize
the sensitivity, the widest bandwidth mode should be chosen (i.e. in TDM, or 1.875 GHz in FDM - preferablywith some channel-averaging, see Section 6.4). Also the continuum spws should cover as much of the IF bandas possible. Not only will this maximize the continuum SNR on the science target, but these continuum data

78

CHAPTER 6. SPECTRAL SETUPS

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 infrequency, since the input signal is the same in the overlap region; the OT uses the unique aggregate bandwidthin calculating the sensitivity, taking any spws overlap into account. However, for sources with known high line
density ( 1 spectral feature per 10 MHz), PIs are encouraged to set up all the spectral windows in FDM mode.
This will allow a more robust determination of the line-free channels used to form the aggregate continuum
during data processing and imaging.

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 continuum is selected;
these are noted in Table 6.1 and illustrated by the red in Figure 6.2.

Figure 6.2: ALMA bands available in Cycle 6 (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

6.3. SPECTRAL SETUPS

79

Band/setup

Species/transition

Freq. (GHz)Sideb.

bandwidth

3a
3b*
-

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

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

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

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

1

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 in Cycle 6. This includes the standard 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, so this frequency
is not actually covered if both sidebands are used. See Figure 6.2. * Based on a template spectral setup released
with Cycle 6 version of the OT.

80

CHAPTER 6. SPECTRAL SETUPSf (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)• 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 - if possible, adjustment of thecontinuum BBs (for example, choosing whether the opposite sideband is LSB or USB) should be done using the
OT spectral display, to avoid deep atmospheric absorption 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 in adiﬀerent 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 thesame spws, and use the other basebands in TDM mode to maximize the total (aggregate) bandwidth for phasecalibration. 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, can be
moved around, but only within the two sidebands. The spectral windows are also shown, labelled by the name ofthe primary spectral line or continuum. In this example, baseband 1 is set for a TDM spws covering the whole 2
3 Note - this case assumes one spws per BB

4 although, as before, spws in diﬀerent basebands can have diﬀerent channel widths

6.3. SPECTRAL SETUPS81

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 spws, 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 spws has 234 MHz bandwidth and 0.28 MHz resolution (with 2 channel-average) and one spws 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 spws, as this can free an additional TDM spws
for improved continuum sensitivity. Many combinations of spws and basebands can be set up in this way.

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 spectral
windows (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 thecurved line represents the nominal atmospheric transmission for the chosen PWV. The bandwidths of the spws
are illustrated 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.

82

6.3.4

CHAPTER 6. SPECTRAL SETUPS

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 - 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, butobserve 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
In Cycle 6 it is possible to double the continuum bandwidth by simultaneously recording both sidebands fromthe 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 per polarisation (2x 2 GHz per baseband)- particularly helpful in these high-frequency bands as it can improve the continuumpsensitivity by ⇠ 2, as well as making available the lines in the opposite sideband. The actual improvement
however, depends on the atmospheric transmission in the opposite sideband, which in Bands 9-10 can result inimage system temperatures 20% (or more) higher or lower than the main signal sideband. Even though thisdoubles the number of spectral windows there is no loss of correlator spectral resolution, so the correlator data
rate is doubled. This may cause correlator data rate limitations in FDM mode, which could be mitigated bylonger integration times, lowering resolution by increasing the channel-averaging factor, and/or using TDM in
the continuum-only basebands. For Cycle 6, there is a restriction that this mode can only be used with TDM or
the maximum-bandwidth (1875 MHz) FDM configuration, and the spws can only be centered on each baseband.
It also requires that 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
2 GHz nominal, the correlator outputs a bandwidth of 1.875 GHz. Thus in FDM wideband, the filters do nottruncate the spectrum, and the full available correlator bandwidth in wideband 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 (indouble-polarization) or 8 (single-polarization) channels are removed or flagged manually oﬄine. This results inapproximately the same usable bandwidth in both TDM and FDM modes and is illustrated in Figure 6.4. Notethat if the centers of two basebands are separated by 1.875 GHz it is possible to set up spws that can be joined
in data reduction to yield a contiguous 3.75 GHz spectrum.

6.5. SPECTRAL RESOLUTION AND CHANNEL-AVERAGING

83

Figure 6.4: Comparison of TDM (left) and FDM (right) autocorrelation 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).

6.5

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 the correlator Section 5.5.2. The default FDM setup from the OT in Cycle 6 uses Hanningsmoothing with a channel-averaging factor of 2 (see Section 5.5.2). This is changed from previous Cycles, which
had a channel-average factor of 1, and has been introduced to reduce the size of the FDM datasets with negligible
loss of spectral resolution. 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 theadvantage of halving the data rate. If the line is well resolved, with 3 channels covering the linewidth, thenthis 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 size of the final product; thisis more critical where fast dump times are needed, e.g. for long baseline observing. If the extra 15% resolution
is required or the line is expected to be marginally resolved, a justification for using channel-average=1 should
be made. Note that for TDM mode, Hanning smoothing without channel-averaging (1) is the default.

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. If more than 5 tunings are required to cover the range, additional
science goals need to be created.

84

6.7

CHAPTER 6. SPECTRAL SETUPS

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
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 on-line 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 neighbourhood.
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 runtime, 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, =30 for
epoch 1900.0) will be included. This means that the LO solutions are slightly diﬀerent at runtime 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. Note that velocities can be defined inthree diﬀerent ways, resulting in diﬀerent conversions to frequency. These diﬀerences only become significant
at high velocities.
5 Although the WVR LOs have small oﬀsets which are diﬀerent for each antenna, which helps to reduce their cross-correlated
signal
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 spectral windows outside the 2 GHz-wide basebands atruntime, to allow 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 FRAMES85

The velocity formulae are:Radio v = c(foOptical v = c(fof )/fo . This is the default.
f )/fRelativistic v = c(fo2f 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?"
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 and 4. However, note that three basebands in one sideband and one baseband in the othersideband 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 in Cycle 6).
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 spectral windows.
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.

86

6.9

CHAPTER 6. SPECTRAL SETUPS

Limitations and Rules for Spectral Setups in Cycle 6

The correlators already allow for a broad flexibility of spws in a single observation, however, the full capabilities
are gradually being introduced and tested by the observatory before release. The current rules for spectral
setups are given in Table 6.2.

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:
A(l, m)I(l, m) =Z Z

V(u, v)e2⇡i(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 (u, v) plane Vk (uk , vk ) wherek = 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 . 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 or more for ALMA.
One implication of the van Cittert-Zernike theorem, which will be discussed in more detail elsewhere in thischapter, 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 “(u, v) coverage”
of an observation, and the PSF is called the “synthesized” or “dirty” beam. In practice it is often useful todefine a weighted visibility function V W (see Briggs, Schwab & Sramek, 1999) that enables the properties of thesynthesized 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 (uuk , vvk )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 (u, v)
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 (u, v) “density” weight that can be

87

88

CHAPTER 7. IMAGING WITH ALMA

used to oﬀset the high concentration of measurements near the center of the (u, v) plane, typically increasing
angular resolution and reducing the large-scale sidelobes caused by abrupt gaps in the (u, v) coverage density.

Figure 7.1: This Science Verification image is one of the sharpest images ever taken by ALMA (ALMAPartnership 2015). It shows the protoplanetary disc surrounding the young star HL Tauri. These observations reveal substructures within the disc that have never been seen before and even show the possible positions of planets forming in the dark patches within the system. The data, calibration andimaging scripts used to create this image are available from http://almascience.org/alma-data/scienceverification and http://casaguides.nrao.edu/index.php?title=ALMA2014_LBC_SVDATA. Credit: ALMA
(ESO/NAOJ/NRAO)
The following sections describe: the ALMA configurations (Section 7.2); the eﬀects of antenna shadowing(Section 7.3); the factors that eﬀect angular resolution and beam shape (Section 7.4); the special case of
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

Cycle 6 Configurations

In Cycle 6, depending on the range of angular scales required, an ALMA Science Goal will obtain data fromeither: 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 angularscale of interest 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
to connect these spatial scales as required.
During Cycle 6 the 12-m Array will be arranged in ten diﬀerent configurations. As discussed below, operational factors impact the actual configuration achieved in a given observation, so these ten configurations
are called “representative configurations”. The representative configurations for Cycle 6 are identical to thoseused in Cycle 5. Each 12-m Array configuration will have at least 43 antennas. The maximum baseline will
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.

7.2. CYCLE 6 CONFIGURATIONS

89

be 16.2 km for Bands 3-6, 8.5 km for Band 7 and 3.6 km for Bands 8-10. The 7-m Array will be available
in only one configuration, with at least ten antennas. Four extended configurations will be available in Cycle 6: C43-7, C43-8, C43-9, and C43-10. The most extended configuration - C43-10 - will be oﬀered alone; itcannot be combined with other configurations. All other configurations are oﬀered in combination with otherconfigurations.
Tables 7.1 and 7.2 give the basic properties of the 12-m Array and 7-m Array configurations. Each configuration is characterized by a maximum recoverable (spatial) scale ✓M RS and an angular resolution ✓res . Generally
these are taken to be determined by the shortest and longest baselines in the configuration, respectively. As
discussed in Section 7.4 and Section 7.6, the ALMA project uses the somewhat more robust 5th and 80th percentile baseline lengths instead. Figures 7.2, 7.3, and 7.4 show antenna locations for the configurations of the
12-m and 7-m Arrays. The three TP Array single-dish 12-m antennas will be in fixed positions, although theirrelative spatial locations do not substantially aﬀect their imaging characteristics.

Configuration
7-m
C43-1
C43-2
C43-3
C43-4
C43-5
C43-6
C43-7
C43-8
C43-9
C43-10Band
Frequency (GHz)

3
100

4
150

5
185

6
230

7
345

8
460

9
650

10
870

✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)✓res (arcsec)✓M RS (arcsec)

12.5
66.7
3.38
28.5
2.3
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
0.0278
0.412
-

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 (✓res ) and maximum recoverable scale (✓M RS ) for the 7-m Array and 12-m Array configurations available during Cycle 6 as a function of a representative frequency in a band. The value of ✓M RS is
computed using the 5th percentile baseline (L05) from Table 7.2 and Equation 7.7. The value of ✓res is the mean
size of the interferometric beam obtained through simulation with CASA, using Briggs (u, v) plane weightingwith robust=0.5. The 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).
12-m Array configurations in particular are impacted by a variety of “real-world” factors including, but
not limited to, the availability of specific antenna pads2 , and necessary, ongoing antenna relocations. To help
accomodate these factors, “hybrid” configurations are often used. These operational considerations will oftenchange the resolution and maximum angular scale that are achieved by executing a given scheduling block.
The scheduling subsystem 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
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.

90

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

Configuration
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

C43-5
14.6
90.9
623.8
1397.9

Table 7.2: Basic parameters of the 7-m Array configuration and the ten 12-m Array configurations oﬀeredduring Cycle 6. The baselines are projected for a transiting source (HA = ± 1h) at a declination of 23 . Notethat C43-9 and C43-10 will not be available for Bands 7-10, and C43-8 will not be available for Bands 8-10.
required angular resolution (✓res ) and largest angular scale (✓LAS ) are specified in the OT, and projects areobserved using array configurations that will achieve the specified science goals. Since Cycle 5 it has also beenpossible for PI’s to specify an acceptable range of ✓res . More details about array combination are provided in
Section 7.8.

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 firstantenna. This phenomenon is known as shadowing. Given ALMA’s location (latitude= 23.02917 ), targets
as far North as declination +47 can in principle be observed, corresponding to a maximum source elevation
at Chajnantor of ⇠ 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”) whensources of various declinations are observed in the most compact ALMA configurations. As can be seen, theshadowing fraction can be as large as 55% for sources observed with the most compact 12-m Array configuration(C43-1). Image quality and time on source will necessarily be limited for such northern sources. Given the shortbaselines in the ACA, sources with declinations less than 70 or greater than +25 are subject to significant
shadowing. For the 12-m Array, shadowing becomes significant (> 5 %) in the most compact configuration forsources with declination lower than 65 or higher than +20 .
Note that independent of shadowing, observations at low elevation often result in elliptical (u, v) coverage
and, therefore, elliptical synthesized beams.

7.4

Angular Resolution and Beam ShapeThe angular resolution ✓res of an array can be estimated with the following equation:✓res =k[radians]
Lmax

(7.3)

where ✓res is the FWHM of the main lobe of the synthesized beam; k is a factor that depends on the (u, v)
plane weighting function; 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 circumstances cansometimes result in unrepresentatively long baselines3 for a given configuration, the single longest baseline
3 For example, there could be one or two baselines much longer than the next longest baselines; these would provide very poor

7.4. ANGULAR RESOLUTION AND BEAM SHAPE

Figure 7.2: Representative 12-m Array compact configurations for Cycle 6.

91

92

CHAPTER 7. IMAGING WITH ALMA

Figure 7.3: Representative 12-m Array extended configurations for Cycle 6.

Figure 7.4: Representative 7-m Array configuration for Cycle 6.
Lmax is a somewhat fragile indicator of angular resolution. Consequently ALMA uses the 80th percentile of the(u, v) distance as a more robust proxy to angular resolution. Using the ALMA representative configurations,(u, v) coverage and commensurately useless imaging.

7.4. ANGULAR RESOLUTION AND BEAM SHAPE

93

Figure 7.5: Shadowing fraction (%) for the most compact configurations as a function of declination (for a
1-hour observation at transit).
the following equation was determined:✓res ⇡

0.574
L80[radians](7.4)

where again is the observing wavelength in meters, and L80 is the 80th percentile of the (u, v) distance inmeters (see also Table 7.2).
One important consideration in imaging is the choice of (u, v) plane weighting scheme, in particular the(u, v) density weighting scheme. Two commonly used, limiting forms of density weighting are natural weighting
and uniform weighting. These are controlled by the density weight Dk (see Eq. 7.2):• 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 (u, v) plane.
• Dk = Ns1(k) is called uniform weighting, where Ns (k) is the number of visibilities in a region centeredon the k th visibility. It removes the dependence of spatial-scale sensitivity on the density of visibilities(samples) in the (u, v) 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 C43-4 configuration at 100 GHz using robust values between 2 and 2. As can be seen, the angularresolution varies from 0.700 (robust = 2) to 1.200 (robust = 2). In general, the angular resolutions presented inthis chapter were computed using CASA simulations with Briggs weighting and robust = 0.5.
The synthesized beam shape, which is the Fourier transform of the (u, v) plane sampling during the observation(s), is a function of the source declination. In addition to shadowing, sources that must be observed at
low elevations also have shorter projected North-South baselines and thus the shape of the (u, v) plane sampling
distribution becomes more elongated and the beam shape more elliptical. For example, Figure 7.7 shows thediﬀerent beam shapes for sources observed at declinations of 70 (similar to the SMC and LMC) and 30 .
Also, Figure 7.8 shows the (u, v) coverage for these sources, revealing the elongation of the (u, v) plane sampling

94

CHAPTER 7. IMAGING WITH ALMA

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 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.

distribution, together with the large fraction of shadowing, for the more southern sources. To mitigate thiseﬀect, one can convolve the resulting images to a more circular (albeit larger) beam after deconvolution.
Figure 7.9 shows the minor and major axes of the synthesized beam widths (✓res ) for each array configuration
as a function of source declination for a 2-hour observation at 100 GHz. Figure 7.10 shows the geometrical meanof the major and minor axes of ✓res at the same frequency. The beam width scales with , but bear in mind that
not all configurations can be used with the higher-frequency bands, e.g., C43-8 and more extended configurations
are not available at Bands 8-10.
Note that in the OT, the angular resolution and sensitivity are now computed consistently, assuming Briggs
weighting with robust = 0.5. If the imaging requirements of a project are particularly scientifically critical, thenfor purposes of proposal preparation it is advisable to carefully evaluate the expected performance using CASA
simulations that employ the representative configurations, target declination, and expected (u, v) coverage ofthe proposed observations. In this case it is also advisable to include realistic noise and to CLEAN4 the images
carefully in order to realistically assess the results that can be expected. For a given real dataset, and/or
for planning special imaging observations, it may be desirable to vary the value of robust and other imaging
parameters.
As will be discussed in Section 7.9, combining data from compact configurations with those from more
extended configurations primarily has the eﬀect of compensating for negative sidelobes in the synthesized beamand thereby improving the interferometer’s response to larger angular structures on the sky. Such combination,
however, does also slightly degrade the resolution. This degradation can be mitigated by moving towards
uniform density weighting using “robust”.
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.

7.4. ANGULAR RESOLUTION AND BEAM SHAPE

95

Figure 7.7: Beam shape for configuration C43-1 with a 2-hour observation of a transiting source at a declinationof either 70 (left) or 30 (right).

Figure 7.8: (u, v) plane coverage for 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% of visibilities
are expected to be flagged due to shadowing.

96

CHAPTER 7. IMAGING WITH ALMA

Figure 7.9: Cycle 6 angular resolutions as a function of source declination. Each stripe shows, for a particularconfiguration, the range of the major and minor axes of the synthesized beams expected from a 2-hour observation at 100 GHz and at transit. 12-m Array configurations are arranged with C43-1 at the top and C43-10
at the bottom.

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. 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.

7.5. SNAPSHOTS

7.5

97

Snapshots

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

(7.5)

vk )

k=1

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 functions and its Fourier transform is a central peak surrounded by
a complex pattern of sidelobes. This “dirty beam” response is a consequence of the gaps in the (u, v) plane, thesidelobes becoming increasingly prominent as the gaps increase (following the Gibbs phenomenon). Conversely
as there are fewer gaps in the (u, v) plane— i.e. better the (u, v) coverage— the PSF sidelobes becomes lessprominent.
Because the baseline lengths and orientations as seen from the source change as a function of time due to the
Earth’s rotation, the (u, v) 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 (u, v) taper , i.e. down-weighting of the visibilities on longer baselines, during theimaging process. The (u, v) taper is represented as the set of taper weights Tk in Eq. 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 array configurations. The levels are indicated with three diﬀerent weighting schemes used for theimaging.
Table 7.3 gives the level of sidelobes for each configuration, for a 1-hour observation of a source at Dec= 23 .
Figures 7.11 and 7.12 show examples of a (u, v) plane sampling distribution and cleaned image for a snapshotof 1-minute duration and a longer integration of 1-hour duration expected with the configuration C43-1. As
shown in Figure 7.11, the (u, v) coverage in 1 minute is quite uniformly sampled, but much less dense thanthat of the 1-hour integration. In addition, the cleaned images of the snapshot and the longer integration (seeFigure 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 with relatively strong
point sources, is to perform CASA simulations using a component list of the strongest sources together withthe actual array configuration. This test allows one to estimate the sidelobe fingerprint left by the strong point
sources after deconvolution (cleaning), although the residuals will likely be higher in practice due to imperfectcalibration. It is worthwhile to use the interactive mode during the deconvolution so that residuals can bemonitored.

98

CHAPTER 7. IMAGING WITH ALMA

Figure 7.11: (u, v) plane sampling distributions of a model ALMA observation with 1-minute integration (left)
and 1-hour integration (right), using the C43-1 configuration to observe a source at a declination of 23 .

Figure 7.12: Images obtained from a model ALMA observation with 1-minute integration (left) and 1-hour
integration (right), using the 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.

7.6. LARGE SPATIAL SCALE RESPONSE

7.6

99

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 (u, v) 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 angular 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 toa point source and so it has large amplitudes up to a baseline of 180 m. Meanwhile, the most extended disk haslarge amplitudes only up to ⇠40 m. Therefore, an array with baselines larger than 40 m will not be sensitive toemission on angular 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
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.
The maximum recoverable scale (✓M RS ) is the largest angular structure to which a given array is sensitive.
It is in principle determined by the length Lmin of the shortest baseline in the array, which measures spatial
scales (i.e. Fourier modes with a period) of /Lmin . In practice the sensitivity of this measurement to suchlarge structures is not very good, so a smaller value of ✓M RS is typically adopted. The exact filtering depends
on the details of the large-scale structure as well as the short-baseline (u, v) coverage and is best determined bysimulations. ALMA has adopted a criterion of measuring 10% of the total flux density of a uniform disk, which
for well-constructed array configurations yields:✓M RS ⇡

0.6
[radians]
Lmin

(7.6)

where is the observing wavelength in meters, and Lmin is the shortest baseline in meters. For reasons similar
to those explained in Section 7.4, the ALMA project uses the 5th percentile shortest baseline L5 instead of thevery shortest baseline Lmin to calculate ✓M RS ; using simulations of configurations the following equation wasdetermined:
0.983✓M RS ⇡
[radians](7.7)
L5
where is the observing wavelength in meters, and L5 is the 5th percentile of (u, v) distance in meters. This is
the equation used to measure MRS for purposes of choosing configurations during proposal preparation. Table
7.1 lists the ✓M RS for the Cycle 6 array configurations. If the scientifically required ✓res and ✓M RS 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 (u, v) 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.
Figure 7.14 shows the annularly averaged visibility amplitudes vs. (u, v) distance of an example astronomicalsource, M51. This example is taken from an H-↵ image, but it is used to indicate the spatial structure expected
at 100 GHz. The amplitudes of the visibilities can be approximated as a power law of (u, v) distance with anegative index. This distribution indicates that most of the power is located in larger scale structures and thatpower decreases rapidly at smaller scales. This result shows that the flux that would be received by the 7-m
Array would be much higher than that received by the 12-m Array with extended configurations (e.g., C43-6).
The only case where flux is independent of the sampling in the (u, v) plane is for point sources, which havethe same amplitude for all visibilities (i.e., the Fourier transform of a Dirac function). In our M51 example,
the visibility amplitude detected by the 7-m Array (at kuv ⇡ 5k ) is ⇠23 Jy, whereas that detected by theconfiguration C43-6 (kuv ⇡ 200k ) is only ⇠0.9 Jy. Ideally, ALMA users should use simulations to estimate the

100

CHAPTER 7. IMAGING WITH ALMA

Figure 7.13: Annularly averaged amplitudes of the expected visibilities of three model uniform disks (annularaverages) at 100 GHz as a function of (u, v) distance.
distribution of power at diﬀerent length scales 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
illuminated, 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 tradeoﬀ is a fundamental aspect of radio telescope design. The resulting
F 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
can be corrected as the last step of imaging. In addition to correcting the sky distribution of the signal to its
correct value, this correction, however, 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 tothat at the primary beam center. Moreover, beyond a certain map size, the antenna is not sensitive and it isnecessary to observe several adjacent pointings, i.e., a mosaic, to recover the sky emission.
Observing a mosaic with ALMA is needed if a map size larger than approximately the F W HM of the
primary beam is required. The default mosaic pointing pattern used by ALMA is a fully sampled hexagonal
grid with equilateral triangles whose vertices are separated by ✓hex = Dp3 = 0.511 ⇥ F W HM . With thisspacing, the mosaic will sample the emission at the Nyquist
spatial frequency. Note that a hexagonal mosaic
p
has spacing ✓hex along a row (e.g., in right ascension) and 23 ✓hex between rows (e.g., in declination). Figure 7.16
gives an example of such a mosaic. To estimate the number of pointings (Np ) necessary to cover an area of
LX ⇥ LY using this hexagonal pattern, the following expressions can be used:

7.8. MULTI-ARRAY AND MULTI-CONFIGURATION OBSERVATIONS

101

Figure 7.14: Image of H↵ emission from M51 used as a model of emission at 100 GHz (left) and the expectedvisibility amplitudes with (u, v) distance (right). Note that M51 cannot be observed from ALMA.
NX

=

NY

=

Np

⇡

LX
(int) ⇣0.511F
W HM + 1.

2⇥LY p+ 1.
0.511F W HM 3
(2NX 1.) ⇥ N2.Y

(int)

⌘

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
antennas, the FWHMs are commensurately larger (F W HM = 1.13 D also 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 primarybeam response pattern. Another frequently used mosaic
ppattern has pointings separated by F W HM/ 2 (see for example the NVSS survey); this pattern covers area
more eﬃciently but with little gain in sensitivity over a single pointing. Generally the Nyquist sampled hexagonal
pattern (the default on ALMA) is a good choice for smaller mosaics and the constant noise hexagonal pattern
is most often used for larger mosaics. The ALMA Observing Tool (OT) can be used easily to set up a mosaic ofadjacent pointings with a user-definedpspacing, 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, ✓res , which
are a function of the longest baselines of the configuration. Similarly, the maximum recoverable scales , ✓M RS ,of each configuration depend on the shortest baselines present. To achieve the requirements entered by the PI
in the OT, ✓res and ✓LAS , multiple configurations may be needed. Note that ✓LAS is a property of the sciencetarget, while ✓M RS is a property of an array configuration. In particular, the most compact configuration for a
project must ensure that ✓M RS is larger than or equal to the ✓LAS of the science target.
Based on the user-entered values of ✓res and ✓LAS for a given Science Goal, the OT will automatically attempt
to choose configurations that will produce a final image with the requested scientific goals5 . In order to provide
5 The entire suite of potentially 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

102

CHAPTER 7. IMAGING WITH ALMA

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).

7.8. MULTI-ARRAY AND MULTI-CONFIGURATION OBSERVATIONS

103

good image quality, there are some restrictions on which arrays and configurations can be combined (based
mostly on the (u, v) coverage each provides). For example, at most two 12-m Array configurations are allowed
and the most extended configurations (C43-10) cannot be combined with any more compact configurations. If
such restrictions result in the requested ✓LAS not being achievable, the OT will return a validation error and ✓LAS
must be modified. 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 notpossible to request observations that only require the TP array.
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 ✓res .
2. If the ✓M RS of this array configuration is less than the requested ✓LAS , 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 ✓M RS of the most compact configuration included thus far is still less than the requested ✓LAS , add
a 7-m array component.
4. If ✓M RS is still < ✓LAS , add a TP array component if possible. Single dish continuum, band 9, and band
10 observations are not currently supported so there is a fundamental limit to how large a source can bereliably imaged in these cases.
This procedure is carried out automatically by the OT and is entirely dependent on the values of ✓res and ✓LAS
that are entered by the user. A detailed list of the allowed combinations is given in Table 7.4. Fig. 28 of the
Cycle 6 ALMA Primer gives visual representation of required array combinations as a function of ✓res and ✓LAS .
Note: if the PI specifies a range of ✓res there may be multiple 12-m array combinations which could achieve
the Science Goal. For instance, C43-5 or C43-4 could serve for the extended 12-m configuration. This would
imply C43-2 or C43-1, respectively, for the compact 12-m configurations; but C43-5 plus C43-1 is not an allowed
combination. In this situation the initial observations will collapse the space of possibilities such that subsequent
data will be taken in the most “compatible” array combinations. In this example, if C43-5 data are collected
first, then every eﬀort will be made to collect all of the extended array data in C43-5, and subsequent, compact
configuration observations will be taken in a C43-2-like configuration. For purposes of total time calculations
in Phase 1 the most 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 (u, v) tapered to give the same angular resolution as the more compact configuration. Thisapproach is an incremental improvement to the approach used in previous Cycles, 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 often impractically large for the
7-m and TP Arrays when the most compact 12-m Arrays are in use. 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). In Cycle 6, a less restrictive cap of 7 for adjacent arrays
or configurations is adopted, but in practice this choice only aﬀects the 7-m Array time ratio with respect
to C43-1 and C43-2. Furthermore, all 7-m:12-m Array time ratios are rescaled by the factor by which the
7-m:C43-1 time ratio was reduced from its ideal value. This approach has the eﬀect of more uniformly applying
MOUSes.

104

CHAPTER 7. IMAGING WITH ALMA

✓res (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

✓LAS (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
C43-10
C43-9
C43-9 + C43-6
C43-8
C43-8 + C43-5
C43-7
C43-7 + C43-4
C43-6
C43-6 + C43-3
C43-6 + C43-3 + 7-m
C43-6 + C43-3 + 7-m + TP
C43-5
C43-5 + C43-2
C43-5 + C43-2 + 7-m
C43-5 + C43-2 + 7-m + TP
C43-4
C43-4 + C43-1
C43-4 + C43-1 + 7-m
C43-4 + C43-1 + 7-m + TP
C43-3
C43-3 + 7-m
C43-3 + 7-m + TP
C43-2
C43-2 + 7-m
C43-2 + 7-m + TP
C43-1
C43-1 + 7-m
C43-1 + 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 {✓res , ✓LAS } 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.

the operational constraint across diﬀerent arrays and configurations with a modest and consistent impact on
image characteristics.
Two additional considerations can impact the required integration times. First, the OT enforces a minimum
on-source integration time in order to ensure that the telescope is used eﬃciently. The minimum allowed onsource time is taken to be the greater of 5 minutes and half of the integration time spent on the bandpass
calibrator. Finally, the 7-m Array needs integrations of at least 1 hour to provide suﬃcient (u, v) coverage forgood image quality. Snapshot observations with the 7-m Array are therefore strongly discouraged (see also
Section 7.5).

7.9. MULTI-ARRAY AND MULTI-CONFIGURATION IMAGING

105

As previously noted, the configuration in which a given SB is executed may diﬀer from the ideal “representative” configuration(s) that the OT assigned. One reason for this diﬀerence is that, to meet its demanding
configuration schedule, ALMA antennas are almost daily being moved from one pad to another. Fundamentally,
ALMA covers a very wide range of spatial scales (and wavelengths), and reconfiguring several dozen antennas
is both operationally challenging and time consuming. Unanticipated proposal pressure distributions, periodsof bad weather weather, and hardware problems can require further flexible adaptation. In response to thesecircumstances it is not uncommon to merge two adjacent configrations into a single “hybrid” configuration thatprovides adequate if not optimal coverage of both of the two configurations. The scheduling subsystem accounts
for the actual array configuration and matches projects with it based on their requested ✓res and ✓LAS , allowing
for the performance margins that ALMA’s Quality Assurance (QA2) process dictates. For observations thatneed a second, more compact 12-m Array configuration, observations of the second configuration are scheduledconsidering Angular Resolutions and (u, v) overlaps corresponding to the combinations of arrays listed in Table 7.4. Some flexibility in QA2 is provided by the use of Briggs’ weighting for QA2 imaging, a scheme whichallows a tradeoﬀ between angular resolution and sensitivity. This flexibility in scheduling and analysis is vitalto achieve PIs’ science goals eﬃciently.

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 fromeach will be processed separately and delivered if they pass quality assurance. 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 Guide6 for detailed guidance ondata combination.
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 6 will be directly combinable7 .
If total power data are part of a project, then there is a second step to the combination procedure, where
the 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.
5. The results from 3 and 4 are added and Fourier transformed back to the image plane.
6 https://casaguides.nrao.edu/index.php/M100_Band3

7 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
the data 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.

106

CHAPTER 7. IMAGING WITH ALMA

Figure 7.17: Expected (u, v) coverage for C43-1 (1 hour) and 7-m observations (5 hours)

Figure 7.18: Radial density of (u, v)-coverage with (u, v)-distance using 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. An excellent
discussion of feathering and a comparison to other techniques for combining single dish and interferometer data
is given in Stanimirovic (2002).

7.9. MULTI-ARRAY AND MULTI-CONFIGURATION IMAGING107

As an example, the (u, v) coverages and (u, v) plane sampling distributions for a 1-hour observation with
the 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 6 7-m Array configuration with ten 7-m antennas provides (u, v) measurements in therange 8-32 m and overlaps the 12-m Array configurations in the range R(u,v) < 15 m. Using the H↵ emissionof M51 as a hypothetical model (see Figure 7.14)

Figure 7.19: Images obtained using C43-3 (top left; 1 hour), C43-3 + C43-6 (top right; 1 + 3.3 hours) and C43-3+ C43-6 + 7-m (bottom left; 1 + 3.3 + 1.3 hours) Array combinations, and the image model itself (bottom
right).
Figure 7.19 shows the images resulting from observing with a C43-compact configuration (C43-3) only; acompact plus extended 12-m configuration (C43-3 + C43-6); and finally of also adding the 7-m Array. Naturalweighting was used and deconvolution was performed using the CLEAN algorithm. 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, the angular 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 (u, v)-coverage and108

CHAPTER 7. IMAGING WITH ALMA

weight of the array configurations in the combined dataset.
These simulations illustrate two general features of multi-configuration/array observations. First, they areeﬀective 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 (u, v) weighting, e.g., via the robust parameter, at the expenseof sensitivity.
One final eﬀect to be aware of when combining data from multiple arrays or configurations is the flux bias
which can result by the mismatch between the clean and dirty beam areas. This eﬀect is discussed by Jorsater& van Moorsel (1995), who present an analytic correction and also note that it can be mitigated by deeper
cleaning.
References[1] ALMA Partnership, Brogan, C., Perez, L., et al. 2015, ApJ 808, L3[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] Jorsater, S. & van Moorsel, G. 1995, AJ 110, 2037
[6] Mason, B. & Brogan, C., 2013, Relative Integration Times for the ALMA Cycle 1 12-m, 7-m, and Total
Power Arrays, ALMA memo 598[7] Moriarty-Schieven, G. ed., 2013, Observing with ALMA: A Primer for Early Science, ALMA Doc. 2.1, ver.
1[8] 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

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 SB). 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 stage of the project lifecycle. 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, the positions and velocities ofthe science targets, details of the correlator setup, the integration and cycle times of the diﬀerent calibrations,etc. 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 ofobservation 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 the calibrations 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 welldefined science goals have been reached as specified in the Science Parameters section of the SB. An SB cannot
be stopped and re-started mid-way. Therefore, an SB either runs to completion, fails mid-way, or is terminatedby the Astronomer on Duty (hereafter AoD). Given the limited duration of the SBs, it is often necessary to
1 For a description of Phase 1 and Phase 2 see the Cycle 6 Proposer’s Guide
2 SBs can also be created in an ad-hoc manner for commissioning purposes

109

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CHAPTER 8. OBSERVING MODES

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).

8.2. EXECUTION STRUCTURE

111

observe them several times to achieve the sensitivity required by the PI. The current maximum execution time
for a 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
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 a single
SB until a certain goal has been reached (see detailed description later on). Sessions have the added benefit thatsome of the calibrations can be shared among the diﬀerent executions, which increases the overall observing
eﬃciency. For Cycle 6, sessions are primarily used for polarization observations 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.
All SBs in a Science Goal have to be processed together 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 be grouped 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 (seeChapter 13 for more details). 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 otherevent that triggers data reduction is 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 non-standard modes)
observations do not currently fit this scheme, the data reduction will 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 thatis 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 shown in Figure 8.1. The SSR subsystem constructs a sequential series of scans for each of the required
calibrations and commands Control to execute them. 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 of subscans). Although commands are issued at the scan/subscan level, thecorrelator output corresponds to a particular integration. In general, each calibration observation consists of ascan containing several subscans (e.g. the 5 data points of a pointing calibration constitutes a scan with five
3 There are two types of OUS, the Member OUS and the Group OUS. Member OUS is the set of all SBs needed to achieve (partof) a Science Goal, and usually it is associated to a specific array configuration. Group OUS contain all Member OUS neededto achieve the science goals of a complete science proposal, and it can include Member OUS 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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CHAPTER 8. OBSERVING MODES

subscans (see Chapter 10. Similarly, the integration time on a single science source between phase calibrations
consists of one scan comprised of a number of subscans. To optimize the execution, scans may be organized inscan sequences which are passed to Control for execution. Scans and scan sequences can be of arbitrary length,
depending on the characteristics of a given observation. But subscans are recommended to be 30 seconds orless in most cases. Integrations tend to be on 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 andthe length of the correlator integration time and dump 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 where one example is an antenna pointing result. The SSR and the Control subsystem are responsible
for the creation of all the metadata needed downstream 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 6 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 are 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 observation sequence. Unless otherwise prefixed, the sources are selected at run-time by
the SSR query algorithm using the parameters defined in the SB as input. If sources of suﬃcient quality forcalibration 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. In
the particular case of pointing calibration, it is usually verified before the amplitude and bandpass calibrators
are observed, and again before the main observations of the science target and phase calibrator cycle. Withina group, the Science targets are each observed in turn until observation of the primary phase calibrator (thecalibrator with shortest 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 is repeated 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 scheduling block. Fora description of what each calibration 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 recommendedmode.
- 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.
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. One example is the polarization calibration.

8.4. SINGLE FIELD INTERFEROMETRY

8.3.1

113

The Source Selection Algorithm

The ALMA system calibration for a given Scheduling Block is usually done using astronomical sources selected atruntime (exceptions are Long-Baseline and High-Frequency observations where some calibrators are pre-selected
and hard-coded into the SBs, or SBs with User-Defined calibration where calibrators are pre-selected and hardcoded 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 proximity to the representative frequency, science target and timesince the last measurement present in the source catalog.
• Expected SNR is calculated from flux and SB observing setup• The returned list of sources that passed the signal to noise criteria are ranked based on SNR, 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 bandwidth (usually 2 GHz), or the aggregate
bandwidth when only narrower spectral set-ups are specified. Unless a value is set up in the SB, a searchradius of 15 degrees from the query center is used as default (smaller cycle times and radii are used forthe highest frequencies and longest baselines, as described in Chapter 10).
• Flux calibrator: A Solar System Object is searched in the first instance for flux calibration purposes.
Otherwise, a search is performed among Grid Sources (see Chapter 10 for further details). The firstobservable grid source is picked up. A detailed list of the Solar System objects and grid sources used forflux calibration is available 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
6 The reader should refer to Chapter 10 for further details on all the diﬀerent system calibrations.

114

CHAPTER 8. OBSERVING MODES(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 the observed flux of a wellknown source, such as a solar system object. The observed flux will be used to compare with the establishedflux 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 beam so as not to resolve
the source structure and add uncertainties in the flux calibration. In practice, many solar system objects may
be moderately resolved. In such cases, only a subset of the baselines may be used to estimate 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 system object is observable, theSSR will pick the first available grid source.
The interferometer is a device for measuring the spatial coherence function (e.g., Clark 1999), so 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 the phase 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 Sections 10.4.3 for further details).

8.5

Pointed Mosaic Observations

Pointed mosaic observations are also oﬀered for this Cycle. This mode enables a single Science Goal 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 to 150 pointings are possible in a single SB. This limitation isset 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 their bandpass, amplitude and phase calibrations which are done
as single fields. For larger fields that cannot be covered by 150 pointings, multiple Science Goals may need to
be defined. The mosaic is arranged as a single scan composed by a number of subscans corresponding to theindividual rows in the mosaic (see Section 5.5). Both the science target 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 a Rectangular
Field in the OT. If the user wishes to execute several small mosaics within an SB, the custom-mosaic under
Multiple Pointings should be selected (see details in the OT guide).

8.6

Single Dish (Total Power) Observations

The purpose of adding data from single-dish observations using autocorrelations 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. 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 6, only spectral-line observations are oﬀered in this mode.
The observing script that executes this mode is called standard single-dish script. As with standard interferometry (see section 8.3), this script uses the SSR capabilities to perform some of the calibrations observations

8.7. POLARIZATION

115(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 rectangular area on the science target for line mapping with periodic
oﬀsets to a certain reference position observed for calibration purposes. For the OTF and reference position
integrations, only the autocorrelation 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 poining
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.
The OTF map is observed as a series of raster rows, scanning in the coordinate system specified in the SB. In
Cycle 6, 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 in absolutecoordinates or as oﬀsets from the map center. 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 come incalibrated 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 ⌘mb and the beam size ✓. These are measured
separately for each project by obtaining a continuum map of a bright quasar or a planet with known flux8 .
These “amplitude calibration” maps are reduced in the same way as the science observations, and the emission
is compared with their model or observed flux (taken from the most recent calibrator survey measurements inthe case of quasars) to calculate the Kelvin to Jansky/beam conversion factor, which is then applied to thescience observations.

8.7

Polarization

The ALMA antennas have receivers with linearly polarized feeds followed by a waveguide with a polarization
splitter.9
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 XX, YY, XY, and YX (or Vxx , Vyy , Vxy , and Vyx ).
These four cross-correlations, as a function of the Stokes parameters, are ideally given by

Vxx = I + Q(8.1)

Vxy = U + iV

(8.2)

Vyx = UiV

(8.3)

Vyy = IQ

(8.4)

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 It is expected that during Cycle 6, these measurements will only be needed for the high-frequency ALMA bands, while forbands up to Band 7, the values will be automatically derived from fits to the aperture eﬃciency of each antenna as a function oftime, elevation, outside temperature, surface accuracy, etc., which will be regularly monitored by the observatory.
9 For the ALMA receiver bands oﬀered in polarization mode for Cycle 6, 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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CHAPTER 8. OBSERVING MODES

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 VyyQ=
2
Vxy + Vyx
U=
2
Vxy Vyx
V =
2i

(8.5)

I=

(8.6)
(8.7)
(8.8)

From here, it is easy to see that the total intensity is in Stokes I (function of the parallel hands XX andYY), and the linear polarization is described by Stokes Q and U ; while circular polarization is described by
Stokes V . However, there are a number of issues that prevent directly using the measured cross-correlation inthis simple way:
1. The splitting of the incoming radiation into orthogonal components is not perfect and small projectionsof 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 andthe band (cartridge design and external optics). Additionally, this quantity is measured in the frame of
the antenna which is an elevation and azimuth frame (Alt/Az) and thus, it rotates with respect to theframe of the sky. This rotation introduces an angular dependance into the visibilities as a function of theparallactic angle ( ). By design, the instrumental polarization is small (a few percent), but not negligible.
2. The 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. It has also been observed that theusage of the diﬀerent local oscillators also introduces an oﬀset in the XY-Phase.
3. The usual oﬀ-line calibration procedure arbitrarily sets the phase of a reference antenna to zero; thisresults in the inverse of its X-Y oﬀset being imprinted on the cross-hand phases of the other antennas.
4. Other eﬀects, such as position within the primary beam (oﬀ-axis polarization), are still under commissioning. Thus, only on-axis polarization is oﬀered for Cycle 6 (see below for a detailed explanation.)
By taking into consideration the instrumental polarization and the parallactic angle dependence, the equations 8.1–8.4 for the visibilities can be re-written as

VXX = (I + Q ) + (U + iV )d⇤Xj + dXi (UVXY = (I + Q)d⇤Yj + (U+ iV ) + dXi (UiV ) + dXi (IQ )d⇤Xj

iV )d⇤Yj + dXi (I

(8.9)

Q )

(8.10)Q )d⇤Xj(8.11)VY X = dYi (I + Q ) + dYi (U + iV )d⇤Xj + (UiV ) + (IVY Y = dYi (I + Q )d⇤Yj + dYi (U + iV ) + (UiV )d⇤Yj + (IQ )(8.12)

where dXj are the D terms as a function of polarization and antenna, the asterisk denotes complex conjugates,
and U and Q are the Stokes parameters as a function of the parallactic angle. Figure 8.2 shows an example
of D terms in Band 3. The D term level is typically a few percent at Bands 3, 4, 5, 6, and 7 on axis
with some variations over frequency10 . 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. The cross-hands output will be purely D terms since Stokes Q, U, and V will have nosignal. However, bright unpolarized sources are rarely found.
10 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.

8.7. POLARIZATION

117

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.
ALMA therefore normally uses an unresolved quasar as a polarization calibration source. These are monitored to ensure they are bright enough, and the exact polarization is determined during data reduction provided
that the source is observed over a wide enough range (> 60 ) of parallactic angles to separate the eﬀects of thesource polarization, the D terms and the cross-hands phase spectra and delay. Fig 8.3 shows that the rateof change of parallactic angle is fastest near transit and slowest for low elevation sources. The D terms may
have a slight elevation dependence, and therefore it is favorable for the polarization calibrator to be close to
the science target. The ALMA Observatory will select appropriate calibrators for each science target, but theusers must take into account these limitations when planning the observation.
With the current calibration scheme, linear polarization imaging of a compact source on-axis, at the level of
0.1% in fractional linear polarization is feasible in TDM mode (see below). The accuracy of absolute polarization
position angle will be nominally 6 degrees (based on initial polarization mode verification results), with acontribution of 2 degrees coming from the specification on the orientation of the receiver feeds, and an additional
scaling of the error with the number of antennas contributing to the final image. Of course, these levelsof accuracy will only be reached if there is suﬃcient signal-to-noise in the polarised emission. For circularpolarization we have determined that the minimum detectable degree of circular polarization, defined as threetimes the systematic calibration uncertainty, is currently 1.8% of the peak flux for both TDM and FDM
observations. This level of accuracy is currently only on-axis, as oﬀ-axis circular polarimetry is still beingcommissioned. Thus, the users should consider this current level of accuracy when proposing.
As the D term component also arises from the oﬀ-axis geometry of feed horn, antenna illumination, andthe alignment of optics, it will also vary across the primary beam pattern (see Chapter 4). Generally, theD term level becomes larger when increasing the oﬀset from the beam center. This is the so-called oﬀ-axis
instrumental polarization. In Cycle 6, the oﬀ-axis instrumental polarization calibration will not be employed.
The expected minimum detectable degree of linear polarization, defined as three times the systematic calibration
uncertainty, is 0.1% (1%) for compact sources (i.e., within the inner 1/3 of the primary beam FWHM) and
0.3% (3%) for extended sources for TDM (FDM) observations, respectively. The minimum detectable degree ofcircular polarization is 1.8% of the peak flux for both TDM and FDM observations. Note that the systematic
calibration uncertainty can degrade by a factor of ⇡2 depending on the choice of calibrator, parallactic angle
coverage, etc. With the current calibration scheme, linear polarization imaging of a compact source on-axis in
TDM mode is feasible at the level of 0.1% (3 sigma) fractional polarization for the very brightest calibrators,
and 0.2% (3 sigma) level for a typical observation. Users must justify that their science goals can be met bysources exceeding these lower limits.

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CHAPTER 8. OBSERVING MODES

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 ( ) plot as a function of hour angle for the declination of 30, 10, -10, -30, and -50
degrees.
Spectral line polarimetry is also oﬀered in Bands 3, 4, 5, 6, and 7 at arbitrary frequencies. In the case of
circular polarization, the current minimum detectable fractional polarization of 1.8% also applies to FDM mode.
This should be considered for Zeeman-like experiments. Figure 8.4 shows the D-term solutions of a representative
antenna (DV22) 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 andno spur-like structure is seen even in highest frequency resolution mode (30.5 kHz at the right bottom panelof Figure 8.5). Figures 8.4 and 8.5 clearly demonstrate that the instrumental polarization is mostly spectral
resolution independent for these datasets. No mosaic, ACA, and TP Array observations are oﬀered. Further, aminimum execution time of 3 hours will be imposed to ensure suﬃcient parallactic angle coverage for calibration.

8.7.1

Sessions

Though not directly related to polarization itself, sessions are the observing scheme designed to observe polarization projects with ALMA. In order to allow the execution of long programs and to avoid the execution oflong scheduling blocks (more than 2 hours), the concept of a session was implemented into the SSR. Given thecurrent stability of the system, it was considered an unnecessary risk to have more than 1.5 hours scheduling
blocks, because in the event of a system failure all data may be lost. Thus, a session scheme was designed as
an alternative. A session is defined as the continuous execution of the same SB until the scientific criteria aremet. A session will manage the cycle time of each of the calibrators from the starting point of the session, i.e.
the first execution of the SB. In this way, calibrations are only executed when needed, avoiding unnecessary
observations and giving an additional level of optimization for ALMA. By default, calibrations such as flux
calibration will be done once per session and bandpass calibration every hour, thus saving observing time. Also,
the phase calibration science target loop will be interrupted (preserving phase calibration) when an additional
calibration is-needed (e.g. polarization)11 The mode that currently exploits the session scheme in ALMA is
the observation of polarization projects. Because for an Alt/Az antenna the frame of the sky rotates, the calibration of the instrumental polarization requires sampling a strong compact source as a function of parallactic
angle approximately every 30 minutes. The session will remember the last time the polarization calibrator wasobserved and interleave the calibration when needed. In general, one can achieve the required parallactic angle
coverage by running the polarization SB 2 or 3 times, which results in between 3 to 4 hours of observation,
which is a perfect example of the session scheme. Other cases in which the session scheme might be useful arelarge mosaics, surveys (multi-target), and large single dish raster maps, but those cases are not yet oﬀered insession mode for Cycle 6. The implementation of sessions is done by keeping information about the previous
execution of the SB into the runtime memory.
11 The cycle time parameters are user controlled and can be explicitly specified in the OT target parameters section.

8.8. MULTIPLE REGION MODES

119

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).

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 spectral windows covering a number of disjointed spectral
regions. This is called the Multiple Region Modes. The constraints are:
• The spectral window width must be a multiple of 62.5 MHz.
• The aggregate width of these spectral windows must be equal to that of the original bandwidth selected.
• The spectral windows must all fit within the 2 GHz baseband used.
• The other parameters (resolution, polarization and sensitivity options) must be the same for all spectral
windows.
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 6, a maximum of four spectral windows 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 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:

120

CHAPTER 8. OBSERVING MODES

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).
*******************************************************************************
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

Solar observing was part of the original science case for ALMA. It has recently been thoroughly tested andverified and released for PI science observations. In Cycle 6, solar observing with ALMA will be supported,albeit with limitations. In particular, the following conditions apply to solar observing in Cycle 6:• Only Band 3 and Band 6 continuum observations using the following default frequencies are oﬀered:*******************************************************************************
LSB
USB
Band
LO Freq.
BB1
BB2
BB3
BB4
*******************************************************************************
3
100 GHz
92-94 GHz
94-96 GHz
104-106 GHz 106-108 GHz
6239 GHz
229-231 GHz 231-233 GHz 245-247 GHz 247-249 GHz• Interferometric observations must be done using the TDM mode (see section 5.1.1); frequencies are fixed
to 2 GHz-wide spectral windows 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 with Bands 3 and 6 are not oﬀered: each execution block can only include one
band.
• Observations will be carried out while the array is in a compact configuration corresponding to C43-1,
C43-2, or C43-3.

8.10. SOLAR OBSERVATIONS

121• Because the WVR receivers are saturated when the dishes point at the Sun, on-line WVR phase correction
will not be applied and oﬀ-line 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 dishes and will beprocessed with the baseline correlator (Section 5.1).
• To minimize shadowing of 7-m antennas, observations will be carried out between 13:00 UT and 20:00
UT.
• 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 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 6.
• 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 7 minutes
for Band 3 and 10 minutes for Band 6.

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+2 mm dB with a return loss of -25 dB (-20 dB for ⌫ > 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 and Band 6 for Cycle 6. These are referred to as solar observing modes MD1 and MD2.

122

CHAPTER 8. OBSERVING MODES• 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 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.
The MD1 mode is considered to be a “quiet Sun” mode (coronal holes, the solar limb, quiescent filaments, prominences, quiet areas outside of active regions) whereas the MD2 mode isrecommended 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 (seeChapter on Antennas). The Primary Beam is filled with complex emission when pointing at the Sun, as are
the beam sidelobes. The ALMA array ultimately measures the brightness temperature contrast relative to thebackground Sun, which is resolved out by the array. As noted earlier, in order to recover the absolute brightness
temperature of 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.
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 spectral window bandpass response between source
and calibrator scans as a result of attenuator settings. Careful testing has shown that this should not be asignificant concern. While these tests show that phase shifts caused by the attenuation level changes do inpractice diﬀerence out, verification that this is the case cannot be checked from observing data obtained using
the standard solar Scheduling Block. As a check, the observatory will carry out a test observation of a calibrator
source using normal and MD attenuation levels before solar observations begin on a given day or at least once
before a campaign program.
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, the8.10. SOLAR OBSERVATIONS

123

normalized 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 )

(Pof f(Psky Pzero )(Thot
Pzero )(Phot Pcold )Tcold )

The autocorrelation 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 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.
While various types of scan patterns have been developed and tested for ALMA dishes, Cycle 6 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

124

CHAPTER 8. OBSERVING MODES

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.
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.
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 Soler 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 and submillimeter wavelengths. Since Cycle 4, ALMA VLBI mode observing has been oﬀered in8.11. VLBI OBSERVING MODE

125

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
ALMA Cycle 6 Call for Proposals (http://almascience.org/proposing/call-for-proposals/).
For all VOM observations in Cycle 6, ALMA will be operated as a phased array of 12 m antennas (expected
to contain up to 39 phased antennas). With 39 12 m antennas, phased ALMA is equivalent to an antenna of
diameter of 75 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. Since Gain ⌘ Ae↵ /(2kB ) where kB is the Boltzmann
constant and SEFD ⌘ Tsys /Gain. Coppesponding estimates for these quantities are:
Gain
SEFD
Gain
SEFD

=
=
=
=

0.71⇡(372 )/(2kB ) ⇥ 10 26 = 1.13 K/Jy
62 Jy
0.68⇡(372 )/(2kB ) ⇥ 10 26 = 1.06 K/Jy
94 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 will be shipped to common sites(MIT Haystack Observatory and MPIfR Bonn) for correlation 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; 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 theindividual telescopes that comprise the global array. In practice, for the ALMA VLBI observer there will bevery little diﬀerence between planning an observation in the two observing bands, aside from details such as
diﬀering bandwidths and frequencies.
Successful 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 theseschedules, 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.
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).
Since all VLBI science targets for Cycle 6 are required to be suﬃciently bright to permit phase self-calibration( 500 mJy), observations of a gain calibrator will be required only every 20-30 minutes to allow calibration of
the amplitudes.
It is important to recognize that most VLBI stations currently record circular polarization (either left,right, or dual), in contrast to ALMA which records dual linear polarizations. Consequently, every VLBI mode
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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CHAPTER 8. OBSERVING MODES

observation with ALMA must be treated as a polarization observation in order that a transformation fromlinear to circular polarization can be made correctly during post-correlation processing. A special softwaretool, PolConvert, is available for this purpose. Robust execution of PolConvert requires a minimum session
duration of 3 hours (session length, not time on science target) in order to achieve adequate parallactic angle
coverage on the polarization calibrator sources for the computation of polarimetric “leakage” or D terms (seeSection 8.7). Visualization and display panels enable user to pan and zoom in/out the region of interest.
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 in Cycle 6 were 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, 98.268 and 100.268 GHz,
respectively. In Band 6 (at 1 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. For the first time in Cycle 6, the EHT is planning to oﬀer 64 Gbps recording at all sites and istherefore expected be able to record all four bands and match for the first time ALMA’s full frequency coverageand bandwidth. However, stations of the GMVA are limited to 2 Gbps recording rates. The GMVA sites will
therefore be tuned to a 256 MHz band centered at 86.124 GHz, so only the first ALMA baseband is available
for VLBI.
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 network, so recordings(onto disk modules) of the antenna baseband signals are forwarded 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 delivery of the correlated
VLBI data products to the observer, as discussed in Section 8.11.2. Correlation is currently preformed 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 added “in phase”. The necessary signal processing for this takes place within
special cards and circuitry within the ALMA correlator as well as with special software within the ALMA
control system which 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, PASP, in press. Detailsof this are also presented in the following sections, with particular emphasis on those aspects which are essential
either for the proposer or data analyst. The discussion begins with a description of the VOM Scheduling Blockin the next section. Section 8.11.2 discusses the scan sequences used by the VOM. That is followed by a section
with some important details about how the APS works (Section 8.11.2). Finally, Section 8.11.2 makes a few
comments about the analysis of VLBI data (a full discussion is outside the scope of this document).
15 http://www.atnf.csiro.au/vlbi/dokuwiki/doku.php/difx/start
16 An NSF MRI/ALMA North America Development Project.

8.11. VLBI OBSERVING MODE

127

VLBI Observing Mode Schedule Block and Execution
As with other modes, VOM observations are executed with a Scheduling Block which provides observationspecific details to an SSR observing script. In the case of the VOM, the script is called StandardVLBI.py,
although, as noted elsewhere, VLBI is a non-standard observing mode in Cycle 6.
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 Schedule 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 schedule block with VEX2VOM is done by the Friend of VLBI or the AoD prior to execution when all thenecessary details of the observing array are known.
Like the StandardInterferometry.py script, the StandardVLBI.py ensures that the necessary calibrations
as specified by the OT are performed with the desired repetition rate. 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 have provided gaps of various durations which are createdto allow the observing script to make these ALMA-specific calibration observations. Thus the script organizes
its work by first noting when the next VLBI scan will occur and then noting which calibrations might fit into thetime until the VLBI scan and finally executing those 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 something similar to:
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 some appointed times.
The VOM translates this request into a sequence of (ALMA) correlator scans which typically start prior to thespecified time in order to allow the phasing system to stabilize on a good solution. Each of these correlator scans
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 polarization in eachband of each antenna) relative to those of a designated “reference” antenna. These phases are calculated from“channel-averaged” data products calculated within the correlator. Presently there are eight channel averages
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 the antenna phases byexactly the computed values so as to bring all signals into phase with those of the reference antenna. Oncethese 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 the recording. The
phasing loop is closed in the sense that small errors in the phase adjustments may be corrected on subsequentscans. This is the so-called “slow” loop which is illustrated schematically in Figure 8.7.

128

CHAPTER 8. OBSERVING MODESVLBI 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 (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 the data to be dumped out for subsequent 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 6, the subscans are likely to be 16 s long with 4 s (channel
average) integrations; there are then about 30s of observations prior to the start of the recording. Note that
the ALMA correlator does its processing by subscans—each subscan must be dumped and processed by thecorrelator and ultimately archived—with a gap of several seconds between subscans. On the other hand, thesignals from the antennas flow continuously to the summation logic and recorders, so there are no comparable
gaps in the VLBI data.
In addition to the “slow” loop, there is also a “fast” loop that may be enabled and which uses the WVR
data from each antenna to correct the antenna phases in response to the wet component of the atmosphere.
These corrections are performed at a frequency of ⇠1 Hz (blue in Figure 8.7). This loop is open (corrections arecontinuously made, but feedback is only achieved through the “slow” loop). Note also that all WVR corrections
are made online in the ALMA correlator, but obviously after the WVR data was collected, so the phasingcorrections are at their best in stable atmospheres, and deteriorate with increasing atmospheric instability.
There is no limit to the duration on the operation of these loops (other than general ALMA ones 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 are controlled by the phasing system to form thecoherent sum signal which is used for the VLBI recordings. The previously mentioned reference antenna ismerely 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 available fordiagnosing 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 the VOM), so it8.11. VLBI OBSERVING MODE

129

is possible to have the ALMA correlator correlate the sum signal during online processing. This is done byco-opting some antenna that is not used by the VOM and placing the sum signals into the correlator as if it
had come from this “sum antenna”. The sum signal therefore appears as antenna “APP001” in any ASDM filecontaining ALMA data acquired with the VOM. There are a few things to note about the data and metadata
for this antenna:• it has no useful metadata, as it is not a physical antenna• it has no WVR data, for the same reason• it is highly correlated with other antennas in the phased array since the non-physical receiver noise ispresent in both.
The selections of antennas for the phased array and comparison array are made when the Scheduling Blockis created, although these may be adjusted if necessary during the observation. Normally, the antennas to bephased are all chosen to lie within a certain radius from the array center. 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 thecomparison antennas is chosen to be within the radius of the phased array. An additional detail is that becauseof 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 ina plot of visibility phase as a function of frequency on any baseline.) Unfortunately, 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 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 a relatively large numberof channel averages (at least 8) and the normal phase-solving procedure produces diﬀerent, independent phasesthat can be applied to the TFBs corresponding to each channel average. This does remove most of the delay,
but it does leave a small residual of phase-slope within each channel average. The only restriction is that thesource needs to be bright enough in each of the channels so that a usable phase solution can be found. The flux
limit of 500 mJy in Cycle 6 ensures that this is the case.
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 document17 . 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 the “sum” antenna whose properties in turn depend on the phasing performance, a
few details should be pointed out. The most significant point is that the eﬀective area of the “ALMA dish” isroughly proportional to the square root of the number of phased antennas. (In Cycle 6, only 12 m dishes areto be used, and they have similar eﬀective areas. If the 7-m dishes were to be included, the relation is more
complicated.) In practice, a number of eﬀects conspire to lower performance from this ideal relation18 to about
60% of what would be expected in a perfect system (see Matthews et al. 2018, PASP, in press for discussion).
Part of this eﬃciency loss stems from the fact that the sum antenna signal is decimated to two bits from theindividual antenna signals, which were in turn also decimated to two bits. Thus there is an additional reduction
17 A VLBI analysis handbook is in preparation.
18 ALMA-05.11.63.03-0001-A-REP.pdf

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CHAPTER 8. OBSERVING MODES

in sensitivity by 0.88 that must be taken into account in the VLBI analysis. In any case, the net eﬀective areaof the ALMA “sum” dish may be calculated from the ASDM on a per-scan basis.
The performance of the phasing system is captured in the metadata in ASDM CalAppPhase tables. Thereis 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”. In Cycle 6, there is one value per channel average per polarization per antenna.
Additionally, the CalAppPhase table reports lower-level details of the phasing system, including online perantenna assessments from TelCal of the antennas drawn from the quality of the phasing solution. This table
may be used in conjunction with the ALMA data for a particular scan to calculate the phasing eﬃciency andthus to make an appropriate correction for the absolute VLBI correlation amplitudes.
As indicated in Section 8.11.1, the correlation products are delivered to the PI for analysis. Traditionallyfor the GMVA this has been in the form of FITS-IDI files. A complication for work with ALMA data is thatthe polarization conversion is performed with a software tool (PolConvert) that requires input from the CASA
analysis of the ALMA data set. This conversion can be performed on the FITS-IDI file or at the correlator using
the raw correlator output if the the CASA analysis is available. Arrangements for doing this will be worked out
between the PI of each project and the supporting observatory collaborations (GMVA and EHT) following theobservation.

8.12

High 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 standard observing modes, arebeing progressively implemented in the ALMA observations for Cycles 6 and beyond, after some extensive
testing is carried out. It is expected that all of them will improve not only the quality of the final data products,
but also the overall observing eﬃciency at the ALMA highest frequencies. For reference, a brief description of
the nomenclature 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.
• Bandwidth Switching (BWSW): For high-frequency observations (Bands 8, 9, 10) with spectral setups including only narrow-band spectral windows, the PI will be asked to add an additional wide-band
spectral window. This approach increases the accuracy of the gain calibration, allowing a solution acrossthe combined spectral windows and/or transferring of the wide-window solutions to the narrow spectral
windows.When adding extra spectral windows is not possible (i.e., projects that have occupied all the
spectral windows with narrow-band set-ups), it is possible to use bandwidth switching, in which the phasecalibrator is observed with wider spectral windows for increased signal-to-noise. The wide-to-narrowspectral window 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, please read 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 on Receivers). Prior to Cycle
6 the only option available for interferometric observing in these bands has been to use orthogonal LO

8.12. HIGH FREQUENCY OBSERVING

131

frequency-switching sequences to suppress the contributions of one sideband to the visibilities. Since Cycle
6 a means 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 6, onlya single pair of spectral windows (LSB+USB) in each baseband is oﬀered, and either the TDM (2 GHz,
256/Npol channels) or widest bandwidth FDM (1.875 GHz, 7680/Npol channels) modes must be used(additionally for FDM, the spectral window 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.

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CHAPTER 8. OBSERVING MODES

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 are crucial.

9.1.1

Sky Temperature

The OT’s estimate of both the atmospheric zenith opacity, ⌧0 , 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 that
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.

133

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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.
the emission from the atmosphere can be approximated asTsky = Tatm (1e ⌧0 sec z ).

(9.1)

Inserting the ATM values of Tsky (z = 0) and ⌧0 into Equation 9.1 allows the mean physical temperature of theatmosphere, Tatm , to be measured i.e.
Tsky (z = 0)
Tatm =.
(9.2)(1 e ⌧0 )This can be reinserted into Equation 9.1 to calculate the sky temperature at any zenith angle asTsky (z) = Tsky (z = 0)

(1 e ⌧0 sec z )(1 e ⌧0 )(9.3)

Tsky (z) is then corrected for the fact that the required noise temperatures (Tn ) are defined assuming P⌫ = kT
and thus a correction for the Planck law is required, i.e.
Tn = T ⇥✓h⌫/kTeh⌫/kT

1

◆

(9.4)

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. 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.

9.1.3

Receiver Temperatures

For ALMA Bands 4 and 10, the calculator currently only uses the specifications for the receiver temperatures(required over 80% of the receiver bandwidth) and not the actual measured values. For ALMA Bands 3, 5, 6,
7, 8 and 9, however, typical values measured in the laboratory are used as these are usually significantly better
than the specifications. The measured values are somewhat conservative and so are in between what might be
expected at the middle and edges of the bands. 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.
Note that the calculator doesn’t concern itself with the so-called “zero-point fluctuations” as the requisite
half photon of noise (h⌫/2k) has already been included in the noise measurements provided by the various
receiver groups (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.

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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)
17
30
45
51
55
55
75
150
110
230

Table 9.2: Receiver temperatures assumed in the ASC as a function of ALMA band. In general, these adopted
values are conservative numbers towards the upper 10% of the actual measured Trx averaged over the wholeband and over all antennas. For many bands, these are considerably better than the original specifications inTable 4.1.

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 spectral window 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 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 thesource 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 spectral window 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 spectral windows andthe 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 spectral windows in the upper sideband if possible.
Therefore, to take a simple case, a single spectral window centred at 637 GHz will find its image equivalent
in the middle of the zero transmission feature at ⇠621 GHz. Where possible, this situation can be avoided bydefining dummy spectral windows such that 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⌘e↵ e ⌧0 sec z⇣

2 ⇥ Trx + ⌘e↵ (Tsky,s + Tsky,i ) + (1⌘e↵ ) ⇥ (Tamb,s + Tamb,i )

⌘

(9.5)

9.1. CALCULATING THE SYSTEM TEMPERATURE

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 spectral window can fall into an area of poor atmospherictransmission, leading to much higher Tsys than necessary. Placing a dummy spectral window at a higher
frequency can remedy the situation (bottom).

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• ⌘e↵ – 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 ⌧0 sec z – the fractional transmission of the atmosphere, where ⌧0 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).
The terms ⌘e↵ and e ⌧0 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:
Tsys,ndsb =

1
⌘e↵ e

⌧0 sec z⇣

Trx + ⌘e↵ Tsky,s + (1where the terms are all the same as in Equation 9.5.

⌘e↵ ) ⇥ Tamb,s

⌘

(9.6)

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CHAPTER 9. ALMA SENSITIVITY CALCULATOR

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 =
Trx + ⌘e↵ Tsky,s + (1 ⌘e↵ ) ⇥ Tamb,s .
(9.7)
⌧
sec
z
0
⌘e↵ e
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
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,
S =The various parameters are:⌘q ⌘c Ae↵ (1wr 2 k Tsyspfs ) N (N 1) np

S , is given by the standard equation:⌫ tint.

(9.8)• wr – robust weighting factor. Pipeline imaging and subsequent QA2 assessment is performed assumingthat the visibilities are weighted using robust weighting, specifically a Briggs robustness factor of 0.5.
Simulations have shown that this factor is equal to 1.1.
• Ae↵ – eﬀective area. This is equal to the geometrical area of the antenna multiplied by the apertureeﬃciency ⌘ap = R0 exp ( 16 ⇡ 2 2 / 2 ) where 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 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.
• ⌘q – 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.
• ⌘c – 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.
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.

9.3. USER INTERFACE

139

Band
3
4
5
6
7
8
9
10

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

⌘ap,12 m (%)
71
70
69
68
63
60
43
31

⌘ap,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, Ae↵ , is equal to ⌘ap multiplied by the physical area of the dish i.e. 113.1 m2 and 38.5 m2 for the
12 and 7 m antennas respectively.
• 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.
•⌫ – 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 spectral window being limited to1.875 GHz by the anti-aliasing filter through which the baseband signal passes. np ⌫ is often referred toas the eﬀective bandwidth.

• tint – total on-source integration time.
The associated surface brightness sensitivity (K) is related to the point-source sensitivity (Jy) by
T =

S

2

(9.9)

2k ⌦

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

⇡✓2
.
4 ln 2(9.10)

This assumes that the telescope beam is a circular Gaussian with a half power beamwidth of ✓.

9.2.2

Total Power Array

In the case of the TP Array, a diﬀerent equation is usedTP =2 k Tsysp⌘q ⌘c Ae↵ N np

This is similar to Equation 9.8, but there is only a factor oftake shadowing into account.

p⌫ tint.

(9.11)

N in the denominator and there is no need toParticularly 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.

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.

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 aﬀect
the 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 (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 and 3
from the TP Array.

9.4. TOTAL TIME ESTIMATES

141• 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.
The calculator reports the values of Trx , ⌧0 , 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.

142

CHAPTER 9. ALMA SENSITIVITY CALCULATOR

Chapter 10

Calibration and Calibration Strategies
10.1

Introduction

This chapter describes the methods used by ALMA in order to calibrate and edit data for imaging and forscientific analyses. First, a review of aperture synthesis, visibility functions and calibration assumptions is given.
Then, the organization and descriptions of all ALMA calibrations are separated into four parts: Section 10.2
for initial calibrations and improvement of antenna properties; Section 10.3 for antenna integration/calibrations
after an antenna move or major configuration changes; Section 10.4 for Execution Block (EB) Calibrations;
Section 10.5 for additional calibrations that the PI could consider, including self-calibration. Short sub-sections
10.5.8 and 10.5.9 contain information on where information about ALMA total power and solar calibrations
and imaging can be obtained.
Since about 2014 an increasing number of EB executions have been calibrated using the ALMA pipeline
and its processing steps1 are referenced in this chapter. For non-standard PI observations and many test
observations, a python script is run manually2 . The pipeline reduction methods evolved from the manual script
so they are similar.
Section 10.4 and Section 10.5 may be of most interest to PI’s to check their ALMA calibrated data and to
improve the calibrations. But, first we review the steps and assumptions as applied to ALMA data.

10.1.1

Complex Visibility Function

An ALMA observation is made in one of (currently) eight frequency bands, at specified frequency resolutions,with an array in a given configuration capable of producing images at diﬀerent resolutions, with up to fourpolarization states. ALMA contains 54 antennas of 12 m diameter and 12 antennas of 7 m diameter and theirgeneral properties and uses are described in Chapter 2.
The fundamental theory of aperture synthesis is given in Chapter 3 and the correlation of the signals between
any antenna-pair is described in Chapter 4, These correlation quantities are called the complex visibility function,
V(u, v), where (u, v) is the projected east-west and north-south separation of the two antennas as viewed fromthe source direction. Its name is often shortened to visibility.
It is assumed that the emission from celestial objects is random and incoherent; that is, there is no correlation
between the emission between two diﬀerent times or between two diﬀerent points in the sky. This lack ofcoherence permits the simple integration of the intensities (sky and visibility) with no interference terms thatwould be associated with coherent emission processes.
1 https://almascience.org/documents-and-tools/alma-science-pipeline-reference-manual-4-7.2
2 https://github.com/keflavich/SgrB2_ALMA_3mm_Mosaic/blob/master/script_7m \/uid___A002_X85b7b_Xb3.ms.scriptForCalibration.py

143

144

CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIESThe angular distribution of emission from the sky can be described in a coordinate system of directional
cosines I(l, m). The van Cittert-Zernike theorem (Section 3.4) shows that the emission distribution is related tothe complex visibility functions by a two-dimensional Fourier transform. If the visibility functions are sampled
in the (u, v) plane suﬃciently well, an estimate of the sky distribution can be reconstructed with a resolutionthat depends on the maximum length of (u, v). In practice, the visibility functions are sampled and averaged
over a short period of time (a few seconds), with each antenna pair sample corresponding to a (u, v) separation.
In this case, the approximate emission distribution is then given by the sum of these visibility functions overthe k measurements as,
X
A(l, m)I(l, m) =V(uk , vk )wk e 2J⇡⌫(uk l+vk m)(10.1)kp

where J = ( 1). The term wk is a visibility function weight that is related to the density of the samplingin the (u, v) plane. See Chapter 7 for interpretation and use of the visibility weighting.

10.1.2

ALMA Visibility Data Flow

All PI observations are made from a scheduling block (SB) that contains the observation schedule needed toobtain an image of the target (see Section 8.1). All relevant calibrations are included in the SB so the data canbe completely calibrated. An execution block (EB) is the use of an SB for one observation that rarely exceeds
two hours. During the EB execution an assessment of the data quality using electronic monitoring results andsome initial calibrations is made. This assessment is called QA0 and is described in Chapter 11.2. If the data
quality passes or provisionally passes, the data are stored in the ALMA archive.
Many PI projects need multiple EB executions of an SB at one configuration in order to meet the rms or
uv-coverage specifications of the experiment. These executions need not be observed consecutively. However,polarization experiments require an SB to be run two or more time in succession, and these linked EB’s arecalled a session.
The combination of data from several configurations including the 7-m Array and the TP array may beneeded to meet the science goals of a proposal, and the collection of these data may cover more than one year.
This chapter, however, concentrates on the calibration for a single EB, but the last section will discuss methods
and suggestions for combining many EB’s to make an image.

10.1.3

True and Measured Visibility Data

Before the measured set of visibility functions can be used to determine the intensity distribution in the sky,
the data set must be calibrated. This is a catch-all term that is used to correct for the changes of the radio
signals on their path from the radio source through the atmosphere to each antenna; the changes as they passthrough the complicated electronics and long signal paths of ALMA; then multiplied pair-wise in the correlator
where the visibility function from each antenna pair are formed and then stored in the archive.
The measured complex visibility for any single frequency stream at any time t and frequency ⌫, associated
i,jwith antennas i and j can be split into a visibility amplitude ai,jm (t, ⌫) and visibility phase, m (t, ⌫),
i,j
i,j
i,j
Vm
(⌫) = R(Vm(t, ⌫)) + JI(Vm(t, ⌫))i,jm (t, ⌫)
= ai,jm (t, ⌫) + Je

(10.2)

R and I signify the real and imaginary parts with J = sqrt( 1. The archive also contains information about
each antenna and other array parameters needed to interpret the set of visibility data. The true visibility
function in the same notation isi,jo (t, ⌫)
Voi,j (t, ⌫) = ai,j(10.3)o (t, ⌫) + Je
Notice that the dependence of the visibility on the (u, v) coordinate has been replaced by the antenna pair (i, j)
associated with the visibility data. The (u, v) coordinates can be determined from the time, frequency, andlocation of the antennas.

10.1. INTRODUCTION

10.1.4145

Calibration Simplification

The simplest conversion of the observed visibility function to the true visibility function is made with a complex
baseline calibration gain Gi,j (t, ⌫) . It is a function of antenna pair (i, j), time (t), and frequency, (⌫),
Voi,j (t, ⌫) = Vmi,j (t, ⌫) ⇤ Gi,j (t, ⌫).

(10.4)The time sampling depends on the averaging period of the visibility data and the time-scale for significant
changes in the calibration parameters.
Although this calibration approach is valid, the number of complex gain calibration terms is proportional
to number of the baselines which is about 1000 for a typical ALMA observation. However, there are threefactorizations of the complex baseline calibration gain that are valid and generally utilized:
Antenna-based: Nearly all of the changes that corrupt the visibility function (atmosphere, system noise,amplitude changes, etc) can be decomposed into the two complex antenna-based gain factors associatedwith a baseline. This reduces the number of gain correction terms for an N-element array from N (N 1)/2
to N with a considerable increase in signal to noise per antenna-based gain compared with the baselinebased gain. The antenna gain separation property is called closure3 .
Amplitude and Phase-based: The calibration of the antenna signals are nearly always associated withchanges that can be separated into an amplitude and a phase correction, rather than independent realand imaginary corrections.
Dispersive and non-Dispersive: Many antenna-based phase changes are associated with eﬀective pathlength variations along the antenna signal routes (including the troposphere) which produce antenna-based
phase changes that vary linearly with frequency. These changes are called non-dispersive. Their linear
phase-frequency relationship means that these corrections need to be measured at only one frequency.
Using the above simplifications concerning the calibration properties of the ALMA (and most interferometric)
system, the conversion of the measured visibility function into the true visibility function becomes:
Voi,j (t, ⌫) = Vmi,j (t, ⌫)Visibility diﬀerencejj⇤ A (t) ⇤ A (t)) ⇤ B (⌫) ⇤ B (⌫)

Antenna-based amplitude(⌫)])

Antenna-based phases+ ai,j (t, ⌫)exp[j2i⇡ i,j (t, ⌫)]Any residual non-closure.

ii+ exp(2i⇡[↵ (t)

j

i

i

↵ (t) + ( (⌫)

j(10.5)

where Ai (t) is the temporal amplitude variations of antenna i; B i (t) is the frequency amplitude variationsof antenna i; ↵i (⌫) is the temporal phase variations of antenna i; i (t) is the frequency phase variations ofantenna i. The non-closing part of the amplitude and phase is given in the last line and is negligible for mostastronomical applications.
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 changeof an amplifier and that from an atmosphere absorption change will combine appropriately in their summed
correction factor.

10.1.5

Reference Antenna

The observed visibility phase data for any baseline, frequency and time is corrected by applying the diﬀerence inthe antenna-based phase calibration of the two relevant antennas at the relevant frequency and time. It is clearthat adding an arbitrary temporal phase to all antenna-based phases will not change the corrected baseline
visibility phase. Hence, to bring specificity to the antenna-based phase corrections it is most convenient to
3 see e.g. Taylor et al. 1999 Synthesis Imaging in Radio Astronomy, ASP Conference Series, Vol. 180, 1999

146

CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIES

choose one antenna as the reference antenna which is defined to have zero phase at all times for all relevant
frequency, time and polarization. This then determines unambiguous antenna-based calibration phases over theEB.
Since the antenna phases are used for many types of reduction and analysis algorithms, choosing a reasonably
phase-stable reference antenna will make such analysis easier and more robust since the non-reference antennaphases will be more continuous. The pipeline task hif_refant picks a set of possible reference antennas byusing several criteria, such as the amount of data flagged, and distance from the array center. It is strongly
recommended that the same reference antenna is used for all data streams and calibration steps associated withan EB.

10.1.6

Calibrator Sources

Some antenna calibrations can be accurately predicted from algorithms associated with the environmental orelectronic metrics associated with ALMA. After these corrections are made, additional calibrations are necessary,and these can be estimated from short observations using test sources of emission with known and measured
radiative properties. Nearly all additional calibrations are made with interferometric observations, even if
parameters are needed only for one antenna, because the correlated signal between two antennas removes muchof the single antenna-based noise that interfere with many single antenna calibrations.
The absolute flux density scale for many experiments is derived from an observation of selected solar systemobjects that have accurate emission models and are not too large in angular size, Section 10.4.8. Every approximately 15 days, there are short ALMA observations of a solar system object with 40 brightest compact sources,
called grid sources to determine their variable flux densities at 100, 250 and 350 GHz, and the current list is
shown Table 10.1. Because these sources have a straight power-law spectra, the extrapolation of the measured
100 and 350 GHz flux densities to higher frequencies can be estimated to about 10% accuracy. They are used
for determining the bandpass amplitude and phase shape for all observations.
J0006 0623
J0237+2848 J0238+1636
J0319+4130
J0423 0120
J0510+1800 J0519 4546L J0522 3627L
J0635 7516L J0750+1231 J0854+2006
J0904 5735
J1058+0133
J1107 4449 J1127 1857
J1146+3958
J1229+0203L J1256 0547 J1331+3030R J1337 1257
J1517 2422
J1550+0527 J1617 5848
J1642+3948
J1751+0939
J1924 2914 J2008 1748
J2025+3343
J2148+0657
J2232+1143 J2253+1608
J2258 2758
L = Large scale emission: R = Resolved source

J0334
J0538
J1037
J1159
J1427
J1733
J2056
J2357

4008
4405
2934
2914
4206
1304
4714
5311

Table 10.1: Bright Quasars Used For Bandpass and Flux Density Calibrators
For phase referencing (see Section 10.4.9) calibrators, the ALMA catalog4 contains a list of about 5000
small-diameter sources (mostly quasars) with accurate positions obtained from VLBI catalogs5 . This large list
is needed to find a relatively close calibrator and check source to any ALMA target.

10.2

Initial Calibrations

These calibrations are made as soon as possible after incorporation of an antenna into the array or after major
overhauls. They are executed by the ALMA staﬀ.
4 https://almascience.eso.org/sc/

5 Petrov VLBI catalog: astrogeo.org/vlb/solutions/rfc_2017c10.2. INITIAL CALIBRATIONS

10.2.1

147

Antenna Surface Setting and Eﬃciencies

The surface accuracy of an antenna is obtained using interferometric holographic techniques by measuring therelative amplitude and phase of a bright quasar as the antenna pointings are oﬀset from the quasar position6 ,At higher ALMA frequencies, experiments are made at several elevations. After correcting the surface panel
deviations from the desired antenna parabolic shape, the nominal antenna eﬃciencies at frequencies less than
300 GHz are about 70%, and decrease at 690 GHz to about 43%, 52%, respectively for 12 m and 7 m antennas(see Table 9.3). The minimum loss of eﬃciency is 30%, and is caused by the aperture blocking of the feed andsubreflector and by small residual panel oﬀsets. At the higher frequencies, the rms surface accuracy of 20 µm
for the 12 m antennas and 15 µm for the 7 m antennas cause a further decrease in eﬃciency. These eﬃciencies
are only achieved during the night when thermal antenna deformations are a minimum.

10.2.2

Antenna Focus

The emission reflected from the main antenna surface is directed toward the feed for each band by 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 remain fixed for weeks. Additional information is given in Appendix A andelsewhere7 . However, daytime observations may contain a short focus-check observation of a bright source atthe beginning of the EB. The FocusModel.xml and Focus.xml files attached to the ASDM data set contain theparameters used for each scan.file.

10.2.3

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, ✓ (defined as the angular width between half-power sensitivity) inradians is inversely proportional to the number of wavelengths ( in the antenna diameter D.
✓ = 1.13 /D(10.6)

More details on the shape and characteristics of the primary beam are given in Baars(2003)8 , and in Chapter 3.
The beam pattern shape is important for constructing accurate mosaic images.

10.2.4

Antenna Pointing

The antenna pointing correction is the diﬀerence between the true sky location of the peak sensitivity of theantenna primary beam and the location shown on the azimuth and elevation encoders. After an antenna has
been assembled or had mechanical work performed, interferometric observations of about 40 quasars around thesky are made with this antenna, plus several others. The measured all-sky pointing oﬀsets are then fit to 19
parameters that describe the expected azimuth and elevation dependencies. These interferometric observations
are called all-sky pointing, and are usually made at nighttime. Each quasar scan of about 25 sec consists of fivesub-scans; at the nominal source location; and at the four nominal half power points. The TPOINT analysis
program9 is used, with details of the ALMA implementation are given by Mangum & Lucas(2007)10 . The
pointing fits have an accuracy of about 1.500 over the sky, and are generally made at 230 GHz.
The pointing diﬀerence between the ALMA bands are azimuth oﬀset and an elevation oﬀset above the generalfit, and these oﬀsets are accurate to about 1.500 . They are determined from a short pointing observation of astrong quasar at the relevant band. The pointing parameters are nearly constant over days and weeks as long
6 Mangum et al, PASP,118,1257,2006

7 https://arxiv.org/pdf/1210.1899.pdf

8 http://legacy.nrao.edu/alma/memos/html-memos/alma456/memo456.pdf, (ALMA Memo 456)
9 http://www.tpointsw.uk/index.htm)

10 https://safe.nrao.edu/wiki/pub/ALMA/CalExamples/PointingCalStepByStep.pdf

148

CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIES

as the antenna remains at the same pad. However, some small pointing updates may be needed for daytime
observations and these are discussed below.

10.3

Antenna Integration Calibrations

There are presently 10 ALMA configurations of the 12 m antennas with maximum baselines from 160 m to 16.2
km. At least 43 antennas are needed for PI observation in any configuration. There is a configuration change
every 6 weeks for which about 15 antennas are moved over a period of about 10 days. Sometimes the hybrid
arrays can be used for PI science projects. After an antenna is moved, calibrations are needed to beintegrated
into the array, and these major calibrations are listed below.

10.3.1

Improved Antenna Pointing

Additional pointing observations are needed after an antenna has been moved to a new pad. Five of the 19
pointing parameters are expected to change: the azimuth and elevation oﬀset, two antenna tilt terms and one
overall rotation term. This relevant observation is part of the antenna integration process and uses a shortall-sky-pointing observation, described in Section 10.2.4. This short observation will provide a nominal pointing
accuracy over the sky of about 200 .

10.3.2

Antenna Delay

The signal paths from an antenna to the correlator will diﬀer considerably among antennas. If these path length
diﬀerences are not removed, then the correlated visibility between the relevant baselines will show large phaseslopes. For example, at an observing frequency of 100 GHz, if the residual baseline path length oﬀset is 10 m,
then the resultant phase slope will be (10 m)/(3 mm) = 300 rad. Thus, in a 2 GHz spectral window, there
will be a phase slope of (2 GHz)/(100 GHz) * 300 rad = 6 rad or about one revolution. To remove these large
and smaller residual delay oﬀsets, an observation of a strong source can measure a phase slope over 2 GHz toa 40 accuracy, corresponding to a residual delay oﬀset 1.5 cm will lead to a phase slope of 40 over a 2-GHz
bandwidth. An even more accurate phase slope is determined when the bandpass shape observation associatedwith each EB (See Section 10.4.7).

10.3.3

Antenna Positions

In order to make high quality images, the relative antenna locations should be known to 0.2 mm accuracy inorder to limit systematic phase errors between the calibrator and the target that will produce distortions in thetarget image. However, the estimated antenna position after placed on a new pad may be in error by up to 5mm, so its position must be more accurately determined. Unlike antenna pointing and focus oﬀsets that not
only decrease the eﬀective antenna sensitivity but distort the derived image, an antenna position oﬀset aﬀects
only the visibility phase which can be corrected by the oﬄine calibration with no deleterious eﬀect on the image
quality. Hence, the accurate determination of antenna positions for a configuration need not be determined
before the initial PI observation are made for a configuration, as long as the improved antenna positions aremeasured before the oﬄine reductions are made.
The accurate antenna positions are determined from a sequence of many short observations of bright quasars
that are observed over the sky. Using a script called all-sky-delay, each quasar is observed for 20 sec and about
40 sec are needed to move to the next quasar that is usually be more than 40 away in order to sample theentire visible sky in about 20 min. The observations are made at Band 3 where the quasars are strongest, in
TDM mode with a total bandwidth of 8 GHz in the four spectral windows. Often, the entire ALMA array isused to improve the SNR of the solutions, even though only 10 to 20 antenna positions need be improved. Fora typical observing time of about 45 min, the accurate antenna-based delay for about 50 scans are obtainedfor each antenna and scan at the < 0.001 psec accuracy. If the assumed antenna position is accurate, then the10.4. EXECUTION BLOCK CALIBRATIONS

149

residual delay for all scans will be constant, independent of quasar elevation and azimuth. An analysis script in
the reduction tool TelCal, called tc_antpos is used to fit the set of the residual delays to obtain the estimatedposition oﬀset and error estimate for each antenna. An example of the fit for one antenna of the scan delays
before and after the correction of the fitted residual antenna oﬀsets are shown in Figure 10.1.

Figure 10.1: Antenna Position Determination: The antenna position fit for DA46, at 3.5 km from thereference antenna, from a 50-min all-sky-delay observation on Dec 25, 2017. Each of the 45 points show thedelay solution from one scan, separated by about 1 min. The observations were made at Band 3 where a delaychange 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 considerablyless.
As part of the antenna integration procedure, a shorter all-sky-delay run of a small number of antennas is
now made in order to obtain the antenna position to an accuracy of 1 to 2 mm. This does not replace the full
all-sky-delay run, but decreases the position errors so that test data reductions and PI reductions will not besignificantly impaired by errors larger than 2 mm.
After the all-sky delay run, the updated antenna positions be placed in the on-line data base (TCMBD)
that is used by the delay server. The updated antenna positions are also currently placed in a file which canbe accessed by the pipeline and other oﬄine reduction systems from the Analysis Utilities depository of useful
ALMA oﬄine scripts. The antenna position uncertainties depend on the distance from the array center (thereference antenna is usually chosen near the array center), because the atmospheric phase variations, caused bylarge-scale turbulence, generally increase with baseline length. The typical antenna position errors are about
0.05 mm per km of baseline length. Hence, at the longest baselines, a typical antenna position could be as largeas 1 mm.

10.4

Execution Block Calibrations

This section describes how each ALMA PI execution block are calibrated. A pipeline calibration system is used
for standard ALMA executions11 . For non-standard observations (currently solar, polarization, astrometry,
11 https://almascience.eso.org/documents=and-tools/documents-and-tools

150

CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIES

band-to-band and bandwidth switching) a similar but flexible reduction methods, called scriptForClibration.py,
is used manually. This was the early ALMA reduction script that evolved into the ALMA Pipeline.

10.4.1

Making the Measurement Set

The archived data from the array are stored only at the ALMA site and at JAO, Joint ALMA Operation
Center in Santiago, Chile. These data are transformed into an ASDM (ALMA Science Data Model) data
structure12 data structure using asdmExport.. This format is then converted into a measurement set (ns) using
the CASA task importasdm. These steps will not be needed by most PI’s, but could be useful for special tests
and calibrations before oﬃcial reductions are made. The pipeline task hifa_importdata makes this ASDM to
ms conversion.

10.4.2

Flagging Data Based on Calibrations

A significant part of the flagging of data is determined from derived calibration values that are faulty in someway. This discrimination is made relatively simple for ALMA data since most calibration values should be
similar among more than forty antennas that are used for most PI observations. There are several methods
used in the pipeline to determine reasonable flags, such as ; hifa_flagdata (which includes antenna shadow
flagging), hifa_fluxcalflag and hif_rawflagchans. See the pipeline manual for implementation details.

10.4.3

Water Vapor Measurements

Variations from water vapor (PWV) in the antenna line-of-sight cause significant delay variations, up to 0.5mm/sec, corresponding to 50 of phase/sec at 90 GHz. The changes are driven by wind turbulence and cloud
structure, and cover a large range of spatial scales from 5 m to many km. All 12 m ALMA antennas are equippedwith a Water Vapor Radiometer (Dicke-type) that measures the emission from atmospheric water vapor every
1.1 sec at four frequencies near 183 GHz, in nearly the same direction as the ALMA pointing. The radiometers
were developed by B. Nikolic13 and information about their design and use is given in Section A.6.
These WVR corrections are made by the online calibration software system in TelCal14 . An oﬄine script
using the CASA task wvrgcal also coverts the water vapor emission to a predicted antenna delay, and thealgorithms of the two corrections are similar. In the near future only the uncorrected visibility data will be
stored in the archive and the oﬄine WVR correction will be applied as part of the calibration process. This
enables small edits or scaling of the WVR emission to delay to be made if needed15 . The on-line corrected data,
however, will be available for use of the QA0 (Chapter 11) analysis of each experiment, but not stored in thearchive.
The use of the WVR correction reduces by more than 50% the water vapor-induced phase fluctuations ontime scales of 2 sec to many minutes, enabling more experiments to meet the minimum success level, and to
produce significantly higher quality images. An example of the antenna-based phases at Band 9 for an antenna
before and after WVR correction is shown in Figure 10.2. The PWV was about 0.45mm for this example, and
it is the typical improvement for relatively low WVR content. The generation of the WVR delay correction is
given in the reduction script mystep = 4. The pipeline tasks hifa_wvrgcal and hifa_wvrgcalflag determine theWVR correction and associated flags from WVRgcal value that are out of range or noisy.

10.4.4

System Temperature Measurements

Another important supporting calibration of ALMA determines the antenna receiver sensitivity and the radiative
sky temperature. These are obtained from a 15-sec scan where a hot load and ambient load are placed in front
12 http://adsbit.harvard.edu/full/2006ASPC..351..627V
13 2013, A&A, 552, 104

14 http://adsabs.harvard.edu/abs/2011ASPC..442..277B
15 L. Maud, https://arxiv.org/abs/1707.03506

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Figure 10.2: WVR correction: The improved temporal phase by using the WVR correction is shown in thefour panels for four diﬀerent antennas at Band 9. The red lines show the temporal phase before correction;
the green lines after correction. The rms phase fluctuations before and after correction are (in rms phase indegrees): DV16-40 to 26 deg; DV60-51 to 38 deg; DA56-36 to 26 deg; DV12-31 to 23 deg. The oﬀsets from zero
phase are arbitrary.
of the feed. Both 12 m and 7 m antennas are equipped with these Amplitude Calibration Devices (ACD), andtheir description and use are given in Section A.5.1.
At frequencies below about 400 GHz, where the system temperatures are relatively constant over an hourof time or 10 in the sky, a ADC scan is made every ten to twenty minutes. However, at higher frequencies allscans should have an associated ADC 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 show possible
measurement problems immediately for QA0 assessment. An example of the Tsys measurements from a Band
9 observation is shown in Fig. 10.3. The two antennas show the typical range of the Tsys measurements at thishigh frequency. Notice that the Tsys in each spectral window contains narrow lines that are associated withtropospheric emission. For example, the additional line emission of 20% in the first spw near channel 60 is theemission from the Hydrogen recombination 673.91 GHz line.
The Tsys measurements are applied to the correlated data in the reduction script mystep=4. The pipelinetask hifa_tsyscal determines the Tsys correction and hifa_tsysflag produces flagged antenna data when Tsysvalues are out of range. Most of the atmospheric line emission will be removed in the Tsys corrected spectrum,
but there will be increased noise level at these line locations.

10.4.5

Antenna Pointing Tweaking

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

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Figure 10.3: 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 axis is the channel number in each spw. The averagefrequency for each spw is 673.9, 675.9, 677.9, 679.9 GHz, and the channel separation is 1.56 MHz. The twopolarization Tsys diﬀers significantly for DV05. The finite width of each Tsys curve is caused by the small time
variation over the 50-min EB.
solution. Hence, a pointing observation with the bandpass/flux density calibrator scan (see Section 10.4.7) andwith the phase calibrator may be included. Also, for observations that demand the highest pointing accuracy,
say < 0.500 , a pointing every 10 min on a source near the phase calibration or target can be done (pointing
referencing).

10.4.6

Antenna Position Tweaking

The determination of the most accurate antenna positions after a configuration change is described in Section 10.2.4. Because a PI observation may be executed before the most accurate antenna position are measured,
the visibility phases should be corrected for the most recently measured antenna position oﬀset. The corrections
are determined from the comparison of the on-line antenna positions in the data base to the updated positionin an oﬄine file16 . The reduction script mystep = 6 reads the new antenna positions, compares them withthat used during the observations and determines the phase oﬀset to be applied. The pipeline task hifa_antpos
calculates the corrections.

10.4.7

Bandpass/Frequency Calibration

The goal of the bandpass calibration is the determination of the relative amplitude and phase of the frequency
channels in each data stream. As discussed in Section 10.1.4, because of the excellent stability of the ALMA
bandpass (Kameno 2015)17 , the relative frequency dependence is constant to within a few percent and one
degree over an hour-long EB; hence, a bandpass calibrator is observed once at the beginning of an EB, with a
16 /AIV/science/PadData/almaAntPos.txt

17 https://almascience.nrao.edu/documents-and-tools/documents-and-tools/alma-technical-notes/ALMATechnicalNotes15_FINAL.pdf

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Figure 10.4: BP Phaseup: The phase variation for a Band 9 bandpass calibrator. (Top) Xpol and Ypol phaseand 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 and spws, andthese phase oﬀsets are virtually constant over an EB

2-min to 30-min scan, depending on the requested bandpass accuracy. In some cases, the phase calibrator (seebelow) that is observed many times over the entire EB can be used, if necessary, as the bandpass calibrator.
A bright quasar is generally chosen from the list of grid sources (see Table 10.1) that is closest to the target,and it is called the bandpass calibrator. The choice of quasar will also depends on the observing band, channel
frequency width and the bandpass accuracy that is needed for the science goal. The nominal accuracy goal is2% per relevant antenna channel-width.
There are two steps in obtaining the bandpass calibration. First, the temporal phase variations over the
bandpass scan are determined. An example of the phase changes over the bandpass scan is shown in Fig. 10.4.
These time-dependent phase fluctuations are contaminated by tropospheric delay changes that are polarization
independent and scale with the small frequency diﬀerence between spectral windows. This similarity can beused to combined frequency channels for subsequent temporal phase calibrations, described in Section 10.4.9.
After removal of the bandpass scan phase changes, the second step determines the bandpass amplitude andphase dependence for all channels in each spw/polarization. The bandpass solutions are usually normalized toaverage amplitude 1.0 and phase 0.0 for each spw to produce a relative bandpass across each spw. The pipelinetask hifa_bandpass and manual script determine the bandpass. The bandpass solution for four antennas at Band
9 for four spw is shown in Fig. 10.5 and Fig. 10.6. The accuracy of each channel solutions is < 1% and < 1 .
The bandpass response is flat over a 2-MHz width and up to this frequency width can be averaged to improve
the S/N of the bandpass. The 200 MHz ripples in the figure are real and may have several causes related to theantenna structure reflections and very small reflections in some of the antenna paths in the system. Finally, near
one of both edges of many spectral windows, there may be significant deviations from the nominal bandpass

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behavior. This part of the spectrum tend to have a much larger noise component and be variable over time, sothey are generally flagged. The pipeline task for bandpass determination and flagging is hifa_bandpassflag. In
this case channels 0-9 and 123-127 should be removed for all antennas/spw.

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 (Fig. 10.3), has been significantly reduced
after multiplication of the raw visibility amplitude by the Tsys factor.

10.4.8Absolute Flux Density Scale

The application of the system temperature correction, Section 10.4.4, converts the visibility amplitudes fromcorrelator units to Kelvin (K). The conversion factor from K to Jy (SEFD: Source Equivalent Flux Density)
can then be found by using an astronomical object with a known flux density model. For ALMA, the SEFD
is stable with time and pointing direction, so the value found from the flux calibrator source is valid to a few
percent (see last part of this section) and the flux density of other calibrators can be derived.
After the bandpass calibration is applied and the phase variations are removed for all calibrator sources inthe EB, the following calibration steps are made using the pipeline to obtain the flux density of all calibrator
sources.
Solar System Object: If the primary flux scale object is one of the six solar system objects that are usednormally (Mars, Uranus, Neptune, Ceres, Pallas, Juno), the source model is obtained from CASA task
setjy and the task gaincal will determine the SEFD ratio for each antenna and spectral window. For larger
ALMA configurations and high frequencies, only the antennas near the array center, where the source
model does not drop to less than 50% of maximum, should be used.
Transfer SEFD: The next step made in the task fluxscale that transfers the above measured SEFD to10.4. EXECUTION BLOCK CALIBRATIONS

155

Figure 10.6: Bandpass Phases: The bandpass phase at Band 9 for four antennas, Xpol blue dots and Ypol
green dots.
other calibrators, most important is the (grid) bandpass calibrator. Sometimes the transfer to the phasecalibrator and check source to obtain their flux density has a noise bias value if they are weak.
Grid Source: If an appropriate solar system object is not available, then one of 40 (variable!) grid bandpass
sources can be substituted as the amplitude calibrator. Their flux density and spectral index between 100
and 350 GHz are measured every 15 days (Section 10.1.6) so that their flux density can be estimated at
any observing frequency between Bands 3 to Band 10. This SEFD is then transferred to phase calibrator,
check source and target.
Narrow Bandwidth with Low Signal-to-Noise: If some of the spectral windows are too narrow to derive
an accurate SEFD, then the SEFD derived from one wide band spectral window can be transferred to
the frequencies of the narrow bands using the known spectral index of the solar system object or gridcalibrator.
Flux Density Scale Accuracy: There are many variables in the determination of the flux density scale
for any observation, with most eﬀects becoming more severe with higher frequencies. The approximate
absolute flux scale limits are 5% at Band 3, rising to 10% at Band 7, and then to 20% at Band 9 and 10..
The SEFD distributions derived from many PI, grid and test observations, now being compile, confirm thatthe expected SEFD stability for nearly all antennas and frequencies is stable to a few percent. The spread of
SEFD for more than half of the antennas have an rms distribution (1-sigma) about 2% at Band 3 to 5% at Band
9 around an average value that is stable. Those antennas with SEFD out of the range generally have alreadyknown problems. These results suggest that the accurate flux density scale of an ALMA observations may be
determined apriori from the SEFD value clustering for half of the array, especially below 400 GHz. At higher
frequencies, the elevation dependence of the antenna gains and other eﬀects must be incorporated, regardlessof the method for determining the flux density scale of an observation.

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10.4.9Phase Referencing Calibration

A critical calibration for obtaining good quality images from an EB is called the phase referencing calibration.
The calibration goal is the removal of temporal changes of the amplitude and phase in the target visibility
measurements over the EB. The phase referencing ’technique’ alternates quickly between the target and thephase calibrator that are separated by less than a few degrees in the sky. The CASA task gaincal is then used todetermine the amplitude factor needed to transfer the measured (or corrected so far) visibility amplitude to the
known calibrator flux density, and the visibility phase oﬀset needed to transfer the measured (or corrected soare) visibility phase to zero — for each antenna and spw and polarization. This antenna amplitude and phaseis then applied using a simple interpolation between phase calibrator scans, to the target.
The properties of a good quality phase calibrator are:
Calibrator-target Separation: The closer the calibrator is to the target, the more likely that the calibrator
measurements will apply accurately to the target. This includes short-term phase variations of timescale of 10 sec and systematic phase diﬀerences of many minutes that are associated with large-scaleatmospheric structure and antenna position oﬀsets.
Calibrator Detection: The calibrator antenna-based solution from each scan and antenna and spw must
be determined with suﬃcient sensitivity. For example, an S/N = 10 for an antenna solutions produces a
10% amplitude error and 5 phase error. The SNR can be increased by a factor of 2.8 by summing thefour spws and two polarizations (after obtaining their phase oﬀsets derived from the bandpass observation(Section 10.4).
Calibration Cycle Time: The cycle time is defined as the time between subsequent calibrator scans. For
successful phase referencing, the calibrator phase diﬀerence between adjacent cycles should be less thanabout 60 . The cycle times as a function of frequency and configuration are currently fixed to nominal
values, so cannot be adjusted to the phase conditions at the time of observations.
For configurations longer than 5 km, the current cycle time is 80 sec, with the phase calibrator scan lengthof 18 sec. For smaller configurations, the cycle times increase to 240 sec with the phase calibrator scan length
about 30 sec. These cycle times may be updated in the future. At frequencies above 400 GHz, the cycle times
can be made longer in order to have suﬃcient SNR on the phase calibrator. For ALMA configurations lessthan 2km and frequencies below 400 GHz, the best calibrator (closest to the target and above a detection
limit of 15 per antenna solution) is chosen automatically from the ALMA catalog. For longer baselines andhigher frequency observations, a candidate list of calibrators is observed in short observation sessions called acone-search that (1) determines if the calibrator flux density at the high frequency is above the detection limitand (2) determines if the calibrator not extended. Cone-searches are also used for selection of the check source.
For any EB with maximum spacing greater than 5 km, and/or at frequencies greater than 400 GHz, checksource observations are included in an EB. The criteria for choosing a check source from the ALMA catalog are:(1) about the same distance from the phase calibration as the phase calibrator is from the target and (2) strong
enough to produce an image SN R > 15. This flux limit is about a factor of three less than that for a phasecalibrator. Most of the catalog sources are unresolved even at the longest ALMA baselines, but exceptions do
occur. Although there are no firm rules yet, a check source is observed every fourth cycle with a length thesame as the phase calibrator. At least two or possibly three check source scans should be included in each EB
unless it is shorter than about 30 min.
The CASA task gaincal determines the antenna-based amplitude and phases from the phase calibrator for
an EB. The pipeline task hifa_timegaincal is used. An example for two antennas from a Band 9 observations fora 1-km configuration is shown Fig. 10.7. The X- and Y-polarized phases follow each other since the variations
are mostly 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. It should be relatively flat withvariations that are consistent with the expected noise. From the amplitude and phase solutions, periods of
unstable gain and phase conditions can be easily recognized with the appropriate data flagging made.
Data should be flagged based on the temporal calibration anomalies. The cause of the bad data and its
duration should be investigated but often requires a long investigation that is not possible. A conservative

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157

Figure 10.7: Calibrator Phases: The calibrator temporal phase at Band 9 for two antennas p(top) 1.0 km
from the reference antenna and (bottom) 0.3 km from the reference antenna. Over the 4000-sec EB, 10 phasecalibrator scans were made, each of length 60-sec with three 20-sec points connected to show the internal scan
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 min the diﬀerence is about 50 and is alittle larger for the longer baseline. The X-Y phase diﬀerence (green (points/line) shows the approximate SNRof each solution, and is much less than the atmospheric variations. The oﬀset is arbitrary for clarity.
scheme is to flag all data for the oﬀending antenna between the time of the preceding good calibrator value tothe time of the next good calibrator value. Please report to the ARC any serious flagging conditions that were
missed by the ALMA reductions.
The antenna-based calibration amplitude (based on the estimate of the phase calibrator flux density discussed
in Section 10.4.8 and phases) are then interpolated to all of the other scans using the task applycal. Since theamplitude variations are generally much smaller and smoother in time than that of the phase, the interpolations
are often made independently for amplitude and phase. For the phase a simple two point (from calibrator scan tocalibrator scan) linear interpolation is generally used, although more complicated interpolation and smoothingtimes are available. For the amplitude correction, a solution over many calibrator scans are often made (after
applying the phase corrections), because the amplitude stability of ALMA over tens of minutes is often a few
percent or less.
Finally, an image of the phase calibrator is provieded as part of the calibration package. See hif_makeimlist
and hifa_makeimages. It should be a good quality point source with a peak intensity and integrated flux densitythat agree to 2% of the flux density assumed in the calibrations. The residual sidelobes or rms noise should be< 1% of its peak intensity. If the phase calibrator image does not meet these expectations, then the calibrationand editing process is suspect.

10.4.10Check Source

The analysis of the check source image defects and position oﬀsets are a good indication of what to expected
for the target image, even though the integration time on the check source is considerably less. The scaling of
the check source problems will depend mainly on the separation ratio of the check source to phase calibrator
compared with that of the target to the phase calibrator. For example, if the target is half the distance fromthe calibrator as that of the check source, then to first order the decoherence of the target and its position oﬀset
should be about half found from the check source.
Check source images are not routinely included in the pipeline or script PI packages. Thus, it is recommended
to make a check source image with the same parameters as that made for the phase calibrator and target inorder to derive information about the EB quality from the check source.

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Since the check sources are point sources of known position (about 5% of the them may have some extended
structure), their cleaned image is a good indication of the quality expected for target image quality. If the PI
data package does not already contain a check source image, it should be made using the imaging parameters
as that for the phase calibrator and target. The characteristics of the check source image to be noted are:
What is the ratio of the peak flux density to the integrated flux density, am approximate measure of the EB
de-coherence? A rough guideline is: above 0.9 is good, below 0.5 is not good.
What is the position oﬀset of the check source from its assumed position? This is an indication of the positional
uncertainty of the phase referencing. An oﬀset up to 0.2 times the resolution is normal, but an oﬀset larger
than > 0.5 resolution is suspect. Such an oﬀset could be caused by an inaccurately known check source
position or structure, or caused by a low elevation (< 45 ) observation.
Is the Check Source Image Distorted? If the check source image is more than symmetrically broadened, withclear substructure, then the phase referencing quality of the experiment is suspect.
Can the Check source be used as a secondary Calibrator? Sometimes the check source is nearly as strongas the phase calibrator and can be used as a secondary phase calibrator. The target image made fromonly the check source as the calibrator will provide information on the quality of the phase referencing.
For astrometric observations, the check source should be observed as often as the phase calibrator. See
Section 10.5.2

10.4.11

Polarization Calibration

The feed at the focus of each ALMA band receives two orthogonal linear polarization streams, called X (n/sdirection) and Y (e/w direction) polarizations. The four resultant correlation pairs are designated as XX, XY,
YX, YY. The initial calibration procedures are the same as that for the normal calibration of the XX,YY
polarizations described above. However, the additional calibrations using all four of the polarization streams
to obtain the total, linear and circular polarization emission of the target require more reduction steps that are
discussed in Section 8.7. These data must be reduced with the manual reduction script.

10.5

Additional Calibrations

This section contains suggestions for additional analyses and calibrations beyond that normally done withstandard ALMA reductions. Depending on the science goals, the observing conditions, and the complexity ofthe target image, further processing by the PI may improve the image quality. Several common techniques aredescribed, but additional information and support can be obtained from your local ARC.

10.5.1

Self-Calibration

For each EB, the pipeline or manual script produce an image of the target. For about 25% of the targets,
especially at configurations larger than about 2 km, the self-calibration algorithm may 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 theimage, and also increase the reliability of fainter image features. Hence, this is the first extra-calibration stepthat is recommended and described. This method is more robust than with other high frequency arrays becauseof the more than 40 antennas used for ALMA observations.
The self-calibration algorithm uses the CASA task gaincal much like that for the phase referencing of thetarget, Section 10.4.9. In this case, the phase calibrator model is known: usually a point source of measured
flux density at a known position. Using gaincal, the antenna-based amplitude and phase corrections that areneeded to make the phase calibrator visibility data more consistent with the model are determined. Whenthese calibration corrections are applied, the resultant calibrator image is much high quality, and additional
calibrator structure down to the few percent level that was not included in the original calibrator

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159

model, will appear in the new image. This demonstrates that the antenna-based calibration procedure to
improve the image is not very sensitive to the input source model. This is because any additional calibrator
structure, which changes the closure properties of the visibility data (see Section 10.1.4) will largely average out
when using 43 antennas, and thus have little eﬀect on the antenna-based corrections that produce an improved
image. This structure versus antenna calibration isolation depends on the ratio of the number of baselines tothe number of antennas, and is about 20 for an ALMA observation of 43 antennas. If the source structure isvery complicated and extended, then this isolation is less strong even if the target is relatively strong.
The starting input image for the target self-calibration is usually the target image determined from thenormal calibration and editing. Whether to use the continuum image or a spectral line image18 is related
to which image has a larger peak/rms ratio. The success of the target self-calibration will also depend on thequality of the initial phase-referenced image, especially if the target is extended. Finally, the quality of the checksource image, if available, is also a guide to whether self-calibration of the target will be useful. For example,
if the check source image is almost point like with little loss of coherence, then the target image quality shouldbe even better and self-calibration may not improve the image.
A recommendation is to try self-calibration on a target when the normally calibrated image shows emission
with a peak of at least 20 times the rms noise.19 Use the CASA task gaincal with the target.model as input,
and for this initial attempt use solint = ’inf ’ to obtain one antenna solution for each target scan. This timescale of several minutes will not remove the image degradation from faster changing phase variations from thetroposphere, but will remove longer term systematic phase errors that also decrease image fidelity. Use the samereference antenna as that used for the normal calibrations. For continuum self-calibration, use calmode=’p’,gaintype=’G’. Combining spectral windows for this first self-calibration try is recommended combine=’spw’ all
spws have virtually the same phase deviations.
From this attempt, the likelihood that self-calibration can improve the image quality can be assessed. The
antenna-based phase solutions (using task plotcal) should show continuity between scans. Also, a measure of theeach solution noise error is obtained with the plot of the (X-Y solution) (poln = ’/’) since all true atmosphericphase variations will be the same at either polarization. For sources with significant extended emission, theself-calibration noise phase scatter will increase with the longer spacings because of the decrease of the target
correlated flux density. But, even with an rms scatter of the X-Y phases of 15 per scan/antenna solution, theatmospheric phase variations are often larger, and this additional random phase component will not significantly
reduce the self-calibration image quality.
If the results from this initial attempt suggests that self-calibration may be successful, then the continued
reduction path will vary depending on many properties of the data and source. A few suggestions for the caseof a moderately strong and not too extended a target follow:
Initial Phase-only self-calibration: It will be clear from the above first execution if the solution interval
can be shortened to (considerably) less than one target scan. If the scan solution interval produces noisy
solutions, then self-calibration may not be useful.
Next phase-only self-calibration: Assuming good results from the above step, put in the improved target
model, and phase self-calibration again, with a shorter solution interval if possible. After this phase selfcalibration, deep cleaning, especially of an extended source, is recommended. Even cleaning a large region
down to only 1.5-sigma will still leave a significant amount of residual flux density in the image. This
will leave symmetric image feature in the residual image that are not real. If in doubt, keep cleaning the
known emission regions
Later amp and phase self-calibration: If you reach a 100:1 peak to residual image quality, another selfcalibration iteration that includes amplitude can be useful. Put in the model image from the previous
phase self-calibration, and then use a relatively long solint (about 5 to 10 min) since ALMA generally has
excellent short-term amplitude stability. Use the option calmode=’ap’ rather than calmode=’a’ because
this option gives better stability amplitude solutions even though the phase corrections are minimal.
18 from a small number of channels, suitably averaged over velocity using the CASA task mstransform

19 For the initial image model to use, the natural weighting option will give better image SNR and less resolution which may
produce a more accurate self-calibration first iteration.

160

CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIESIn summary, the self-calibration of moderately strong sources that are not too extended is robust with ALMA
data and should be attempted by the PI. The above suggestions are meant as a guideline to get started, but
may require advice from your local ARC or from the JAO, especially if image peak/rms levels over 1000 are
possible to achieve. In a few years, the ALMA reduction systems may include self-calibration techniques toimprove image quality.

10.5.2Astrometric Observations/Calibrations

The main goals of astrometric observations are to determine the accurate position, proper motion, and/or
parallax of relatively compact objects. The (u, v) coverage is not critical, but the most stable phase conditions
and long baselines (as long as the object is not too resolved) are needed. The two major astrometric limits are1) the SNR of the peak of the relatively compact object; 2) the systematic position error associated with normal
phase referencing results. Obtaining higher precision involves using more than one calibrator. A discussion of
ALMA astrometric results can be found in20 and are summarized below.
The astrometric limit precision of an object on an image of often limit by the SNR of the object. This limits,p, in mas is approximately,p = 60mas ⇤ (100GHz/F REQ) ⇤ (10km/BslM ax)/SN R(10.7)

where SN R is the intensity ratio of the peak to rms of the image, F REQ is the observing frequency in GHz and
BslM ax is the maximum baseline in km of the configuration. If two objects are in the same image, then theaccuracy of their relative separation is given by the above thermal noise limitation if they are both within the⇠ 70% primary beam power sensitivity. If they are further apart, then their separation accuracy will decrease,and this will depend on the phase calibration stability. In order to eliminate image gridding errors, the image
pixel size should be no larger than about 10% of the image resolution. If the field field contains one or a few
compact objects that dominate the total emission in the field, then (u, v) model fitting (CASA task uvmodelfit)
may provide an accurate determination of the astrometric parameters.
The absolute ALMA astrometric limit is the precision of an object in an ALMA image with respect to the
ICRF fundamental reference frame that is used for ALMA observations and all calibrators. The phase stability
during the EB and the proximity of the phase calibrator to the target field are the major influences of theabsolute image astrometric accuracy. Of course, the SNR limit of astrometric precision is also relevant. Witha stable atmosphere and a calibrator-target separation less than a few degrees, an absolute astrometric limit ofabout 2% of the synthesized beam is possible, but this also requires an SNR=50 for the object. To reach thisastrometric accuracy under less ideal conditions, cycling among several phase calibrator surrounding the target
will improve the accuracy. These techniques is described in the above reference.
The year-to-year ALMA configuration cycling is not conducive for parallax determinations that require
periodic observations over the year period. Proper motion accuracy are not critically sensitivity to specificconfigurations, so can be scheduled with some flexibility to obtain the relevant time coverage needed.

10.5.3

Calibrator Structure

Some calibrators (and check sources) are not perfect point sources and there use may eﬀect the image quality.
However, for those calibrators where > 80% of the emission in contained in an unresolved component, the eﬀects
on the antenna-based phase solutions are minimal, generally less than a few degrees. If these calibrators areused to improve amplitude calibration of the target, errors up to 5% and be made, and it is recommended torely on the SEFD values obtained from the bandpass calibrator. An analysis of the imaging errors obtained
from non-point sources will be available21 . In the cases when a significantly resolved phase calibrator has beenused (egs. a solar system object), the visibility data should be recalibrated using the a priori model or thatobtained from the phase calibrator data in the experiment.
20 http://alma-intweb.mtk.nao.ac.jp/ diono/meetings/longBL2017/fomalont_astronometry_1.pdf
21 Image Errors from Calibrators with Structure, H. Messias, in preparation

10.5. ADDITIONAL CALIBRATIONS

10.5.4

161

Band-to-Band Phase Calibration

For phase referencing at frequencies above 400 GHz, finding a suitably strong calibrator closer than 10 to atarget is not common, As noted in Section 10.4.9, the closer a calibrator is to the target, the more likely that
1) the short-term (< 1 min) phase fluctuations will be similar between the phase calibrator and target, and 2)
the longer term (2 to 60 min) phase diﬀerences between them will be decreased.
The goal of band-to-band phase transfer is to calibrator a target observation at high frequency by using
phase referencing with a phase calibrator at a much lower frequency where there is a greater chance of findinga detectable calibrator nearer to the target. The success of this calibration requires that; 1) all phase changes
among all of the spectral windows (high frequency and low frequency) are non-dispersive (delay-like) and scalewith frequency, regardless of their time-scale and origin; 2) there is a constant instrumental phase oﬀset for all of
the spws that varies less than a few degrees over the EB period. These constraints are illustrated in Equ.(10.8)
h (t) =

l (t) ⇤ (⌫h /⌫l ) +(10.8)The instrumental phase diﬀerence is determined by alternating observations of a bright source at the low
and high frequencies, and is called the DifGainCal observation (DGC). Tests are in progress to determine theoptimal frequency switching time in order to remove the short-term atmospheric phase changes between thetwo frequencies, to determine guidelines for the length of DGC observation to measure the for each spw toan accuracy of a few degrees, to confirm that this spw-phase oﬀset is constant with time up to two hours, andto confirm that the instrumental phase is independent of sky position. There are also tests to determine atwhat distance ratio between the nominal high frequency calibrator from the target compared with a closer low
frequency calibrator to the target will produce significantly higher quality B2B target images.

10.5.5Band-Width Switching

When observing a target within narrow spw bandwidths (typically < 250 MHz), a suitable phase calibrator,
especially at the highest frequencies, may not be detectable within a one to two minute calibrator scan. Two
methods of calibrating these narrow bandwidths are available:
One wide spw: If the aggregate bandwidth in the combined spws in the experiment has a bandwidth > 1
GHz (usually because one of the spws is wide band), then there will be suﬃcient sensitivity to determine
the antenna-based gains.
Band-Width-Switching: If all of the spws are narrow 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 phase calibrator with wide-band spectral windows and the target in the desired narrow bandwidths byswitching the spectral 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 todetermine their phase diﬀerence among the spws that should be constant with time. There will be aslight delay change among the diﬀerent spws, but they will be much closer in frequency than that forband-to-band observations.
Tests are now in progress to determine the stability of the wide-to-narrow bandwidth phase diﬀerence.

10.5.6

Multiple EB Combination

Many PI projects require several EB’s from one configuration in order to obtain suﬃcient SNR or (u, v) coverage
to meet the scientific goals. The guidelines are evolving, but usually the pipeline processing does not begin until
all of the EB executions from one configuration have been completed. All EB’s are then individually calibrated,then concatenated into one measurement set, imaged, and then sent to the PI, and the calibrated data sent to162

CHAPTER 10. CALIBRATION AND CALIBRATION STRATEGIES

the archive. For weak targets (where the peak/rms intensity per EB is less than 10), the concatenation of theEB’s are needed to obtain an image with reasonable SNR.
For those targets in which the SNR is greater than about 20 from each EB from an SB, it is useful todetermine the eﬀective quality associated of each EB before combining them to produce the target image. The
easiest check of the EB to EB consistency and quality is to make an image of the target separately for each
EB. Even with slight diﬀerences in their resolution and integration time, the images should be similar. The
diﬀerences that might arise among the images are:
Registration among the Images: This is determined by comparing the position of the peak emission oneach of the images, as described in Section 10.4.10. Oﬀsets at the level of 0.2 times the resolution are
typical because of diﬀerence of the phase conditions among the EB’s. Significantly larger oﬀsets are usuallyassociated with relatively poor phase stability or low elevation associated with the relevant EB.
Quality among the Images: Unless the images are dynamic range limited (usually when peak/rms intensity> 100), the rms noise in each EB should be similar, whereas the peak intensity can vary considerably
depending on the average atmospheric phase variations over the EB. As a rough guide, for EB’s in which
the peak flux density is less than 70% of the nominal peak value from the other EB’s, it is likely that thephase stability during the EB was poor and this EB should be down-weighted.
The default image presently made from a concatenated data set containing several EB’s uses the relative
weight in each EB based on the average Tsys and on-target integration time. This weighting does not include
the phase stability that aﬀects the image quality, but probably should. Guidelines for this additional weighting
among EB’s are being discussed, and the PI should consider down-weighting some EB’s (or even ignoring them)that are of poor quality.

10.5.7

Combining Configurations

For targets that contain a wide range of angular structure, two diﬀerent 12 m configurations and the possible
addition of the 7 m configuration will be observed. A description of how the data are combined and weighted22
is based on the rms noise of the data points. The concatenation of all of the interferometric data, up to two
12 m configurations and the 7 m configuration into one measurement set, can be made using the CASA task
concat and is the responsibility of the PI for subsequent imaging. The entire interferometric data set is thencleaned and examples are given described in Chapter (7.9). With data that cover a large range of angular size,
it is likely that images at a variety of resolutions will be useful to display the relevant information for a complex
source.

10.5.8

Total Power Observations

Total power (TP) observations are made using up to four of the ALMA 12 m PM antennas for determining thestructure of sources that are larger in extent than the 7 m antenna primary beam size. These data are usuallyassociated with mosaic interferometric images. The reference for the calibration of these data can be found in23 ,and the observing modes are discussed in Chapter 8 and the imaging in Chapter 7.
Good quality TP images require two important calibrations: First, an oﬀ position is needed to define the zero
sky temperature in the vicinity of the target. Second, using a fast TP raster to map the target area, the systemtemperature diﬀerence between all the target raster points and the oﬀ-position is gives the target temperature
distribution. Third, the conversion from Kelvin to Jansky can be made from the relatively accurately known
SEFD of each of the PM antennas used for the TP, or by observing a solar system object with a known thermal
temperature.
The TP image is combined with the cleaned image made from all of the interferometric data using afeathering method, CASA task feather. In most cases, these images are mosaics that have been obtained
22 https://casaguides.nrao.edu/index.php/DataWeightsAndCombination

23 https://casaguides.nrao.edu/index.php/M100_Band3_SingleDish_4.5

10.5. ADDITIONAL CALIBRATIONS

163

from many interferometric pointings and a corresponding TP image area. The feather method uses a Fourier
technique in which each image distribution is converted to the (u, v) domain, and then combined. The twocontrols are a scaling factor between the TP and interferometric (FFT) image, and a low pass filter as needed(See Chapter 7). This total Fourier data is then transformed back into the image plane to produce the combined
image.
A second combination method is based on a software program called tp2vis, and is being developed for future
ALMA use24 . This method converts a total power image into appropriate (u, v) data which is then concatenatedto the much higher resolution interferometric data. This entire data set can then be cleaned to obtain an image
that contains all angular scales. This combination approach gives more flexibility with the total power data
and the interferometric data combination and weighting. Another advantage is that the interferometric data
are cleaned after the TP image has been included. This avoids some of the large-scale sidelobes that are often
associated with interferometric data that do not include the large-scale structure.

10.5.9Solar Observations

ALMA provides a unique facility for research of the solar chromosphere and the structure and dynamics ofthe many small-scale solar phenomena. The document25 provides the most up-to-date information on thepresent aspects of ALMA solar observations. These experiments are significantly diﬀerent from other ALMA
experiments, so contact your local solar-expert at the appropriate ALMA ARC for information about proposal
submission, observations and support for calibration and imaging of the data. At the present time only Bands
3 and 6 are supported, and both the 12-m and 7-m Arrays are observed simultaneously, usually with total
power using the PM antennas. Configuration 3 (maximum baseline of 0.5 km) is the largest configuration
allowed at present. It is also the preferred configuration since the 7-m Array is well-displaced from the centerof Configurations 1 and 2 that give non-circular (u, v) coverage.

24 https://github.com/tp2vis/distribute25 Shimono et al. 2017, Solar Physics, 292, 87S

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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 a reliable final data product is delivered to the PI,
that is, the product has reached the desired control parameters outlined in the science goals (or is as close tothem as possible), it is calibrated to the desired accuracy, and calibration and imaging artifacts are mitigatedas much as possible. The QA analysis will be based on a calibration plan that specifies which observations mustbe acquired and at which intervals to monitor system performance and environmental factors as they evolvewith time. Furthermore, it will also be used in assessing the merging of data within each science goal takenwith diﬀerent configurations, the inclusion of 7-m Array and TP Array data, and 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 or inadequate
uv plane coverage) are outside the scope of the ALMA QA, unless the error occurred due to faulty informationor 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: Monitoring of calibrations and overall performance during and just after observations
QA0+: A simplified fast pipeline imaging QA. This typically is completed 30-90 minutes after the observations
are taken, and is mainly used when the results from QA0 are unclear or marginal
QA2: Full Calibration and generation of science products
QA3: Issues found with the data by the PI or the ALMA contact scientist after data delivery
The QA0, QA0+ and QA2 stages will be handled by the Program Management Group (PMG) and the DataManagement Group (DMG) (with contributions from ARC personnel) using the ALMA Quality Assurance(AQUA) Tool (see Section 11.7). Responsibility for data quality assurance rests with the Data Manager and his
Deputy, within the Department of Science Operations, drawing upon the resources of the Program Management
Group and the Data Management Group. The final output of the ALMA QA0-QA2 process 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, the final imaging. This report is included in the data package delivered to the
PI. The QA3 stage will be handled separately, by the ARCs, via internal tickets created by the ARC personnel(see below). 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, will only be done
sporadically during Cycle 6. It is expected that group processing will be implemented as a regular data reduction strategy in later
ALMA cycles.

165

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11.1

CHAPTER 11. QUALITY ASSURANCE

Cycle 6 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 6 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, system performance atthe time of the observations, etc. 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).
Observers may need to invest their own time and expertise to ensure that the data products are of theappropriate quality and to re-reduce the raw data if the quality is not satisfactory. This may include the needto visit the relevant ARC or ARC node to get help and to assist with quality assurance and potential data
reduction.

11.2

QA0

The first stage of quality assurance, known as QA0, is a near-real-time verification of data quality for eachSB 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, andQuickLook, based on semi-real time output from the calibration scans obtained by the real-time TelCal ALMA
software. This information is complemented with reports derived using Monitor and Control display tools tomonitor 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 goes through thecalibration data, looking for outliers or out-of-spec results, and other problems. Together with additional checks
in AQUA itself, these are combined to provide a QA0 assessment for each EB. These parameters can be grouped
into the following general categories2 :Atmospheric Eﬀects: Weather Parameters, Sky Opacity, System Temperature, Phase Fluctuations, WVR
Outputs.
Antenna Issues: Antenna Gains, Antenna/pad delays, Relative/Oﬀset Pointing, Geometric Shadowing, Antenna/Pad positions.
Front-End Issues: Bandpass, 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.
Correlator Issues: Bandpass, Delay Measurements.
Observation Issues: Calibrator fluxes, Incomplete datasets or incomplete mapping, mismatch between desired
and actual synthesised beam shape.
Tolerances for individual parameters in the above list (for example the maximum range of Trx ) are definedin aoscheck. These are combined to assess the QA of individual sub-units of the EB, such as antennas, spws,
2 Some additional hardware problems can occur which are automatically flagged out by the system and are not seen in thedata or at QA0 unless this hardware flagging has failed. Examples of these are LO lock problems, antenna not on-source, or thecalibration device not in position.

11.2. QA0

167

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 have been adopted by ALMA for this Cycle
are listed in Section 11.2.1. Apart from these, checks are made in AQUA on other observatory calibration data,
including a recent measurement of the flux of the amplitude calibrator, and a relevant measurement of theantenna/pad position.
Based on these results, each SB execution is classified into three main categories:• QA0_PASS are datasets that comply with all the QA0 criteria and that will be used for the final imaging• QA0_SEMIPASS 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 and reduce them if they wish.
• QA0_FAIL datasets are those that are not included in the other two categories. Since they represent
unusable/uncalibratable data, they are not visible to the PIs in the Project Tracker or 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+ 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 (normally also thebandpass calibrator) has no recent flux measurement (within the last 7 days). Once a flux measurement
is available in the archive, this will automatically be set to a 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 database (Telecope Monitor
and Control Database, or TMCDB) have not yet been updated after an antenna move. Once the positions
are measured and updated, this will be set to a Pass.

11.2.1QA0 criteria

QA0 pass/semipass/fail criteria that have been adopted by ALMA during Cycle 6 are the following:- Antennas: Situations that will be considered to render an antenna as not available include issues withthe antenna itself, such as Tsys values > a factor of 2 higher than the others in all spws, or Tsys > 2000 K
in Band 3-6, delays > 0.5 ns, relative amplitude on the calibrators <10% of the median of other antennas,
or if the gain calibrator amplitude or phase fluctuations are significantly higher (factor of > 3) than otherantennas at the same distance from the array centre. This detects outliers because of antenna problems,
which are diﬀerent from high phase noise from poor weather conditions, noted below.
- Weather: If the atmospheric fluctuations are such that the antenna-based phase noise3 is larger than
1 radian, then this is regarded as too high for this antenna to be safely usable. The number of high phasenoise antennas in the dataset is determined. For the EB to be a PASS, the minimum number of usable
antennas (ie with low phase noise) is then the same as above; so if fewer than 20 antennas in the 12-m
array have phase noise < 1 radian, the EB will normally be a Semipass. In practice, such datasets will
initially be set by the AoD to Pending Other, meaning that the data quality is marginal. Further checks
on the image quality are then carried out using QA0+ or oﬄine before deciding whether the EB should
be a Pass or Semipass (see Section 11.3).
3 The antenna-based phase noise is determined in the following way: data from spws and the two polarisations are phased up
and combined to get a single phase solution per antenna per phase cal scan. The phase noise for that antenna is then the medianvalue of the phase diﬀerence between adjacent scans.

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CHAPTER 11. QUALITY ASSURANCE- Bandpass: QA0_SEMIPASS if the bandpass calibrator signal is too weak. The limit on signal/noise
ratio is that a suﬃciently high SNR (>30) is available per channel only if the data is spectrally averaged
down to 2 channels.
- Gain/phase: QA0_SEMIPASS if the gain/phase calibrator signal is too weak, with an SNR <5 after
averaging all spws or a detected flux < 10% of the predicted value.
- Execution: QA0_SEMIPASS All datasets whose execution failed at some point and contain less than
20% of the expected time on the science target for a given SB execution, or where the Execution Fraction(see 11.2.2) is less than 0.2 .
- Calibrations: QA0_FAIL Datasets missing critical calibrations that render them uncalibratable. Execution Blocks only containing usable calibrator data shall be labelled QA0_SEMIPASS.
- Storage: QA0_FAIL Data that could not be read from the Archive- Time-Critical Observations: QA0_SEMIPASS if observations have not been carried out at the requested dates and times.

11.2.2

Execution Fraction

For operational and scheduling purposes, individual SB executions during Cycle 6 will eﬀectively be weighted
by measuring their data quality. This weighting is quantified by an Execution Fraction (EF), where 1.0 is thepredicted value, 0.0 means that the data is not usable, and > 1.0 means that the EB is better than predicted.
The EF is a single number representing the normalized fraction of the theoretical sensitivity (based on theradiometer equation) that a given execution should have reached, combined with a measure of the expected
image quality (see below). It is calculated using the number of unflagged antennas compared with the numberthat should be in an array in Cycle 6 (i.e., forty-three 12 m antennas on the main array, ten 7 m antennas on
the Morita Array, and three TP 12 m antennas), the actual time on-source compared with expected, the mean
Tsys at the representative frequency compared with that assumed by the OT, and the fraction of antennas withphase noise below a set limit (of 1 radian)3 . Executions with lower data quality than the reference will havefractional 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 a fractional execution value
above 1.0. For Cycle 6, the EF of an EB will be capped at 2. The scheduler then sums the EFs of executions
to determine how many more are required.

11.3

QA0+ and imaging quality

QA0+ is a second stage of QA0, which runs a mini-pipeline reduction of the channel-averaged data, producing
continuum-only images of the science target, phase calibrator, 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 is unclear for any reason), the QA0+ images can be used as a second level of data
quality assessment. The EB can then potentially be set to ’Pass’ if the images meet the QA specifications.
Typically the QA0+ pipeline takes 20-90 minutes to complete. To speed up reduction, it does not run bandpass
or Tsys calibration, and uses the online-corrected WVR datastream. It uses flags from the QA0 process andcombines both polarisations and all spws with bandwidth >400 MHz. For imaging it will run a single iterationof CASA clean with a centred simple clean box on the first science target and, for targets with SNR >20, andit will try self-calibration on a scan-based time interval and will produce a self-calibrated image.
For EBs requiring QA0+, checks of image quality are performed where possible: the metric used is the peak
to integrated flux ratio for a point source (either a check source or the science target if this is compact). Also
the peak to residual ratio after a single CLEAN 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 or large-scale atmospheric11.4. OBSERVATORY CALIBRATION AND QA

169

phase changes over the array will distort the image in a semi-coherent way. These can be more egregious duringlong-baseline or high-frequency observing, and their eﬀect can be monitored by observing a check-source as partof the observations4 ; QA0+ is then used to assess the image quality. A perfect image has a peak/integrated
value of 1.0, ’good’ image quality is peak/integrated > 0.8, and datasets with values less than 0.5 are regarded
as marginal for a QA0 pass. The QA0+ criterion is that datasets with a peak/integrated flux ratio on the checksource of >0.5 are set to Pass. For those without a check source, in some cases the science target is brightenough that the images can be compared with previous executions of the same EB; those judged 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 areunclear cases, and require a further stage of checking, usually oﬄine by the full CASA pipeline, before setting
to either Pass or Semipass.

11.3.1

Relationship between image quality and phase noise criteria

The quality of images is strongly aﬀected by the phase stability of the atmosphere5 , and so measuring the phasenoise does provide a good proxy for the final image quality. However, there is a ’grey area’, where imaging
is required. ALMA uses nearby phase calibrators to measure and correct for residual sky phase fluctuations(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 structure6 . The spatially-dependent
diﬀerences between target and phase calibrator are linked to the time-dependent phase fluctuations throughthe turbulent structure of the atmosphere, so monitoring just the time-dependent fluctuations should still givea reasonably good measure of the overall data quality, even without checking the images. Figure 11.1 confirmsthat image quality (measured by the ratio of peak-to-integrated flux on a point source, taken from QA0+ resultson the check source during the 2017 long-baseline campaign) is correlated with the phase fluctuations (measured
by the median phase diﬀerence between antennas3 ). The phase is measured in degrees, therefore just depends
on the on the changing pathlength compared with the wavelength, independent of the actual observing band.
A perfect image has a peak/integrated value of 1.0, ’good’ image quality is peak/integrated> 0.8, and datasetswith values less than 0.5 are regarded as marginal. It shows that datasets with phase fluctuations less than
1rad almost always give good image quality and so can be set to QA0 Pass immediately. The QA0+ imaging
stage is for the marginal cases; some are then set to Pass as the images are deemed acceptable, but a significant
number give very poor imaging.
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).

11.4

Observatory calibration and QA

As well as data taken during the SB execution, the observatory tracks array and antenna performance parameterswhich vary slowly (typically on timescales longer than a week) and which can aﬀect data quality. They aremeasured by AoDs and System Astronomers at predefined periods as “Observatory Tasks”, and after majorinterventions such as antenna moves, Front-End swaps, subreflector fixes, etc, or if significant deterioration of
performance is detected during operations. Typically after such interventions, antennas are set to non-integrated
state and not used for regular science observing. Antenna integration into the array then requires measurement
4 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
5 Although many of these eﬀects can be removed using self-calibration, when the target is bright enough to allow this - see
Chapter 10.5.1
6 The baseline errors only become significant on the longest baseline observations.

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CHAPTER 11. QUALITY ASSURANCE

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, redcrosses are QA0 semipass. Encircled symbols indicate that the phase calibrator is more than 3 deg separationfrom the check source. The highest image quality (peak/integrated >0.8) generally occurs for phase fluctuations< 40 deg and for the closest calibrators. The cutoﬀ for an immediate QA0 Pass from AosCheck is < 57 deg (1rad); higher phase noise datasets are passed on to QA0+ for assessment of image quality.

and ingestion of these parameters. Observations and reduction of such data is done jointly by the AoDs, theDSOANT group, and System Astronomers within the DMG. The product is a set of parameters that are ingested
into observatory databases, in particular the TMCDB (Telescope and Monitor Control DataBase) which records
the hardware status and history. The TMCDB gives the up-to-date view of hardware parameters, so that they
can be used by the system during observations. Problems that would significantly downgrade the quality of thedata are solved by dropping the oﬀending antenna from the active array, fixing, re-measuring and updating the
problematic parameters. Particular parameters which form these observatory calibrations are:Array Calibrations: Baseline and antenna position measurements, 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 frontends),
Source Calibrations: Monitoring of solar-system flux standards, and secondary quasar flux standards

11.5. QA2

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

11.5

QA2

QA2 deals with QA at the level of data reduction and imaging using the Science Pipeline or performed manuallywith the Script Generator by the ALMA Data Reducers Team. It is only at the stage of data reduction thatthe science goals set by the PI can be compared with the actual value in the data products (i.e., RMS, angularresolution, SNR, dynamic range, etc). The oﬃcial software for ALMA data reduction is CASA.
During Cycle 6, it is expected that, for the ALMA standard observing modes, the automated Pipeline(see the ALMA Science Pipeline Reference Manual on the Science Portal7 ) will be used for the calibrationof the data and imaging. The Pipeline provides a Weblog page with detailed information on the quality of
the calibration, which will provide the basis for Pipeline QA2. This information will also be made available
to SnooPI during Cycle 6, and the weblogs will also be included in the data packages sent to the PIs. 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. (Note: Some datasets can be calibrated by the pipeline, butneed 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 in Section 11.8.
A summary list of QA2 parameters/issues checked during data reduction (calibration of individual Execution
Blocks and joint imaging) are:
Calibration Issues:
7 https://almascience.org/documents-and-tools/alma-science-pipeline-reference-manual-4-7.2.

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CHAPTER 11. QUALITY ASSURANCE• Bandpass quality: is the spectral profile flat, well behaved and devoid of spectral lines?
• Flux scale calibration: is the absolute flux scale accurate enough?
• Phase transfer and astrometry: Cycle time and sky separation between phase reference and target;
typical and extreme (unflagged) phase diﬀerences between phase reference scans.
Final Data Characterization:• Longest baseline, visibility coverage and time on target (after flagging).
• Synthesised beam (spatial resolution) for specified weighting scheme; specific imaging requirements(if stated by the PI). See Section 11.8 for tolerances.
• Spectral resolution and channel ranges used to make sample images.
• RMS noise in target images: Values are compared with those predicted from data after flagging andwith those requested. See Section 11.8 for tolerances. (Note: For Solar Observations, this criteria
does not apply as there is no blank sky in most of the images.)• Residual imaging artefacts: Sidelobe Levels, eﬀects of “missing spacings” and possible dynamic range
limitations.
• Combinations of array configurations and/or total power, e.g. amplitude scale consistency.
• Mosaicing and/or contamination by bright sources outside FOV or aliasing in clean.
• Polarization purity: minimum fractional polarization detectable, and polarization angle accuracy (ifrelevant).
The data reduction scripts sent to the PI will include any modifications to the standard scripts which were
found to be essential during QA2.
There are three possible QA2 states a reduced dataset can be placed into. QA2_PASS implies that thescientific goals, as defined by measurable parameters such as noise RMS, LAS and angular resolution, have beenachieved at the representative spw within the specifications listed in Section 11.8. QA2_SEMIPASS 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 the PIs goals by a significant margin (see Section 11.8 ofthis Handbook) and needs to be scheduled for additional observations. Although the Observatory will try totake 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 data fail to obtain enough additional observations to pass QA2 by the end of an observing season andthey are not grade A proposals, their QA2 state is changed to QA2_SEMIPASS and they are delivered to the
PI.

11.6

QA3

QA3 is post-reduction evaluation of the data products delivered to the PIs. It is advisable that PIs check the data
products themselves and report any problems that they find to their Contact Scientist via the ALMA Helpdesk(https://help.almascience.org/). The QA3 process will be triggered by the PI, the contact scientist or other
ARC personnel. They will open an ALMA Helpdesk ticket reporting a problem with the data products which
may reflect an underlying problem with the data, observing procedure or calibration. The ARC receiving theHelpdesk ticket will retrieve the data from the archive and evaluate the nature of the problem. The evaluation by
the ARC should include an assessment on whether the problem is present only in a particular dataset or whether
others taken under similar set-ups and conditions also show it. If the problem is deemed to reflect a problem
with the performance of the array, the calibration or data reduction processes, or the QA process, the ARC will

11.7. THE QUALITY ASSURANCE REPORT

173

communicate their findings to the observatory, which will work on 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 with QA3 issues will be granted based on the policies in the Cycle 6 User Policies
document.

11.7

The Quality Assurance Report

During Cycle 6 the Quality Assurance Reports of QA0 and QA2 will be accessible to the PIs 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 non-standard observing modes that require
manual data reduction, script-generated QA2 reports will be delivered instead.
The basic unit of a Report is the ObsUnitSet, which represents part of the scientific goal stated by the PI
during Phase 1 (project creation and review). An ObsUnitSet will typically contain several executions of an SB.
For each execution, a QA0 report is generated by the AoDs using the information available at the time of theobservations, which includes TelCal outputs and other monitoring data (weather, total power levels, Corr GUI
outputs, etc). A given execution is only cleared for reduction if it has passed QA0. There will be only one QA2report for the whole ObsUnitSet8 generated by the JAO/ARCs at the end of the data reduction process; thisalso has to be approved before the data products are delivered to the PI. It is expected that sometime during
Cycle 6, a complete interface between the Pipeline and AQUA will be made available. From that point onwards,
complete QA Reports will be generated using the AQUA software and delivered as part of the data products
package (including the Weblog information). The final report per ObsUnitSet delivered to the PI would in thatcase be a concatenation of all the relevant QA0 reports per execution with the QA2 report. Comments on eachstage of the QA process (with supporting images, if required) would be added to the Report.
The standard policies for QA0 failures are that the observations of those Execution Blocks that failed haveto be repeated. Failures to pass QA2 may trigger additional observations if the achieved RMS or imaging
parameters do not fullfil 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

Overall QA Criteria

For an execution to be considered QA0_PASS it must have a phase RMS (post-calibration) of 1 rad in
most antennas, enough calibrator data to be able to calculate necessary calibration terms (bandpass/amplitude,
complex gain, and, if relevant, polarization), and enough science data to be useful (see above). Furthermore, theexecution has to be "significant" in terms of the fractional execution (i.e., more than 0.2). If it does not meetthese criteria, but has some useful data (calibrator or source), it is classified as QA0 SemiPass. Such data are
available through the ALMA archive, but they will not be used in the generation of the imaging data products.
If neither of these hold, the execution is deemed to have no useful data and declared QA0_FAIL.
For any other situation, the data will be accepted, although it may require some additional flagging for
mis-behaving antennas, baselines, etc.
For QA2 at the Member OUS, MOUS, level, the main criteria are:
• The achievement of the requested noise RMS in the images (it must be within 10%, 15% and 20% of thegoal for Bands 3/4/5/6, 7/8, and 9/10, in flux units per beam, respectively)• Achievement of the synthesized beam shape (In order to satisfy the QA2 criteria, the angular lengths ofthe major and minor axes of the synthesised beam must be within the angular resolution range requested
8 As stated above, processing of group ObsUnitSets will not be regularly done during Cycle 6. PIs should assume that allstatements here apply to member ObsUnitSets.

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by the PI, taking into account the modifications applied by OT to ensure schedulability of the SB (See
Proposer’s guide). This angular resolution range can be viewed at SB level in the OT in Phase 2 (Min.
and Max. Angular Resolutions).)• Reaching the required calibration quality (phase RMS of 5 degrees after calibration, and absolute flux
scales within the ALMA specifications9 ).
Observations that do not satisfy the QA2 criteria will be released as QA2 semipass if there is no realistic
chance of further observations improving the data quality to the level of a QA2 pass, or if further observations
are timed out. For the individual MOUS that must be combined at the GOUS level, the RMS values quoted
above should be scaled by the relative sensitivities of the configurations, using the most compact 12-m Arrayconfiguration as reference.

9 Absolute Calibration accuracy is regularly checked as an observatory task.

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.
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 http://dashboard.alma.cl/, Pietriga et al. 2014, SPIE, 9152, 1B.

175

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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.
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
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 representation of
the SB content. The observing scripts, which reside in the Science Software Requirements (SSR) module of thesoftware, use the SB content to determine the necessary execution sequence. The observing script commands theControl 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 from the observing scriptlevel. 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 and end on 48 ms (Timing Event)
3 For a description of the observing preparation processes, see the Observer’s Guide12.2. THE ALMA SCIENCE DATA MODEL

177

boundaries which are accurately synchronised among the whole system. The subscans result in raw data files
and metadata rows being sent to the archive subsystem and made available to the online Telescope Calibration(TelCal4 ) subsystem. TelCal publishes results from calibration scans it reduces, which are sent to the archive
as calibration tables, displayed by GUIs to allow Operator and AoD evaluation of the observation progress, andreceived by the observing script to apply online corrections e.g. for antenna pointing and focus. For details
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 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 thestorage side (see e.g., 2006 ADASS contribution by Hafok, Caillat and McMullin). It receives many inputs
from the Control, Correlator and TelCal subsystems for each subscan and scan, which it compiles together into
the ASDM tables. The Control software itself is also compiling values from many hardware devices into theinformation it provides to Data Capture. At the end of each scan the current table contents pertaining to thescan (an ASDM "slice") are passed to TelCal to allow it to produce any necessary calibration results (combinedwith binary data received directly from the Bulk Data streams), and when TelCal finishes it passes back resultsfor 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 last scan 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 thedata is fully archived or if there was an error.
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.

12.2

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 is
4 http://adsabs.harvard.edu/abs/2011ASPC..442..277B

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

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CHAPTER 12. DATA FLOW AND LOGICAL DATA STRUCTURE

Figure 12.2: Data flow components.
unrelated 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) 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 filesizes 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 at the center of the ALMA data flow (Fig. 13.1). It is a combined database andbinary data storage system that is accessed by the diﬀerent software subsystems through the same software
layer. The ALMA Archive stores all metadata and data of ALMA including the user accounts, proposals, antenna configurations, monitoring, raw, and reduced science data. The science data and metadata aremade available to PIs and archival researchers for query and download following ALMA’s data access policy(http://almascience.org/documents-and-tools/latest/alma-user-policies).
The ALMA Archive is divided into two parts. The ALMA Frontend Archive (AFA) and the ALMA Science
Archive (ASA). The AFA provides the core persistence functionality. The ASA holds a small subset of metadataof the AFA in a relational database and provides access to external interfaces like the Archive Query interface
and in the future Virtual Observatory (VO) tools. The storage architecture is based on the Next Generation
Archive System (NGAS) with Oracle technology for replicating the metadata.
Each of the three ALMA Regional Centers (ARCs) in North America, Europe and East Asia holds a copyof the entire ALMA Archive for backup, user support and data distribution to the ALMA PIs and archival
researchers. The ARCs provide a completely identical user experience to their communities and a user can
download data from any ARC.
An ALMA Science Archive Manual is available from the ALMA Science Portal.1 .

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 Chapter 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. Metadata harvested include all the information
1 http://almascience.org/documents-and-tools/latest/science-archive-manual

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needed 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
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.

Figure 13.1: The ALMA Archive is in the center of the ALMA data flow.
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
Proposer’s Guide. These data will be transferred to JAO from where they will be ingested into the ASA.

13.3

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 andsupporting 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 User’s
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.

13.4. ARCHIVE QUERY

181

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. CoIs. 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.

13.4

Archive QueryAt http://almascience.org/alma-data/archive users can query the holdings of the ASA (Figure 13.2). 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 13.2: The ALMA Science Archive Query Form
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 (Fig. 13.2) will present users with the metadata of the observations,although they can choose to also see the metadata per project or per publication. On the results page (Fig.
13.3), users can sort and subfilter the results and add or remove columns from the result table to narrow theirsearch. The sky coverage of the observations is visible in a graphical window.
The results page also oﬀers to download the results in VOTable, TSV (Tab-separated values) or CSV(Comma-separated values) format for further processing in tools like topcat2 . The URL used for the exporting
2 http://www.star.bris.ac.uk/~mbt/topcat/

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CHAPTER 13. DATA ARCHIVING

Figure 13.3: The ALMA Science Archive Results Pageof the query results can also be modified to access the ALMA Archive queries programmatically. Astroquery3
can be used to encapsulate and simplify programmatic access to the ASA. Neither Topcat nor Astroquery arepart of the oﬃcal ALMA software, and support of users of these tools will be limited to best eﬀorts.

13.5

Request Handler

Once data of interest are defined, they can be selected via checkboxes on the results page 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.
Four 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.
3 https://astroquery.readthedocs.org/en/latest/alma/alma.html

13.5. REQUEST HANDLER

183• Finally, 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".
The Request Handler also allows selecting individual files for download. Only the data deliveries that users havepermission to download can be selected. If they are not authorised to access 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.

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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.

185

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APPENDIX A. ANTENNAS

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.
Lifetime: a minimum of 30 years.
Antennas used during ALMA Cycle 5 have both 12 meter and 7 meter diameters, with the receivers mounted
at the secondary (Cassegrain) focus. The 12 m dishes 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 dishes have a focal length, to the primary focus, of 2.572 meters. Given aneﬀective 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).

A.2. ANTENNA FOUNDATIONS

Vertex
Melco 12 m
Melco 7 m
AEM

187

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.
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.
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.
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

188

APPENDIX A. ANTENNAS

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

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

A.3

189

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 .

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.
1 http://www.almaobservatory.org/en/technology/transporters

190

APPENDIX A. ANTENNAS

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.

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

A.4. CRYOSTAT

191

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

192

A.5

APPENDIX A. ANTENNAS

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.

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

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 for
diﬀerences 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 ↵ 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 = ↵VL1 + (1

(A.1)

↵)VL2

where ↵ 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:

↵

=

TCal

=

⌘JM + (1 ⌘)JSP JL2
JL1 JL2(JMs JBGs ) + g⌘ e⌧s ⌧i (JMi

(A.2)
JBGi )(A.3)

where ⌘ is the forward eﬃciency of the antenna, g the sideband ratio, ⌧ 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 = TCal

VL

VSky
VSky

(A.4)

194

APPENDIX A. ANTENNASFor 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 that can be achieved for Cycle 5.

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
WVRs 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”

A.6. WATER VAPOR RADIOMETERS

195

Figure A.10: Oﬀset optics used to collect the sky emission along the optical axis of the antenna into the WVR.
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):⇣
Lcorr  1 +w ⌘10µm + 0.02 Lraw .
1mm

(A.5)

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(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

196

APPENDIX A. ANTENNAS

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

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.
1 http://almascience.org/documents-and-tools/

197

198

APPENDIX B. THE LO AND IF SYSTEM

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 . Section 6 shows how to setup the system to observe spectral lines (particularly multiple spectral lines)
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 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 or
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

B.3. FREQUENCY GENERATION AND DISTRIBUTION IN ALMA

199

lower 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
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 rangeof 2-4 GHz, via a set of filters and tunable second LOs (LO2) (see IFS/IFP in Section B.3.5). LO2 isused to oﬀset 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 bya course synthesiser which can be set only in steps of 125.0 MHz, plus 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 spectral windows 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 tooﬀset the frequencies in conjunction with LO1 to suppress interference and select the sideband. Finallythe correlator 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.
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

200

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 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

B.3.1

201

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(CRG) 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 isused 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 in the observatory. The modulated 1532 nm signal is sent to an optical distributor (with 80 outputs), theLow Frequency Reference Distributor (LFRD), that feeds it into the Sub Array Switch (SAS) modules, where
it is merged 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 reference signals that are fed into the six Laser Synthesisers (LS) fed into the six Central Variable Reference modules, which the LSs use to control the frequencyof the the Slave Lasers producing a frequency oﬀset of the SL signal of 27-121.7 GHz with respect to the202

APPENDIX B. THE LO AND IF SYSTEM

ML signal. The SL signals are added to the ML signal. The oﬀsets between the ML and SL signals
provides the beat note which is used to generate the LO1 frequency in the photomixers in the Warm
Cartridge Assemblies (WCAs) in the front 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.
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 Az and El fiber wraps. All are fed through Line Length Correctors (LLCs), which areused 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 piezodriven fiber stretcher assembly and the fiber to the antenna. At the antenna end there is a 3-dB coupler, so that
half of the light goes to the turnaround assembly and half to the photomixer in each WCA. The turnaroundassembly consists of a fiber frequency shifter (located at 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 ofthe signal traveling back to the AOS technical building receives thus twice a frequency shift of 25 MHz, thus itcomes back oﬀset by 50 MHz from the original. The Faraday rotator reflects the signal but turns its polarization
5 This figure needs an update. The Slave Laser (variable) wavelengh is ⇠1557 nm.

B.3. FREQUENCY GENERATION AND DISTRIBUTION IN ALMA

203

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.
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
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.

204

B.3.5

APPENDIX B. THE LO AND IF SYSTEM

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 polarisation 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 polarisations. 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
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.

B.4. OTHER FUNCTIONS OF THE LO/IF

205

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).

Figure B.7: Block diagram of one polarisation channel of the IF Processor. This has two IF inputs (at left),and feeds 4 baseband (BB) outputs to the digitisers (to the right of the diagram).
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.3.6

Digitization and Signal Transmission

The outputs of the IF Processor units are fed into the Data Transmission System Transmitter (DTX), that
include digitizers and formatters to convert the signals to optical wavelengths for transmission via optical fibers.
There are four DTX units per antenna, each one handling data for a given baseband pair (i.e., the same 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.

206

APPENDIX B. THE LO AND IF SYSTEM

Figure B.8: The Data Transmission System Transmitter (DTX) module, as used in each antenna.

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
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
6 Although they have mixers to allow both sidebands to be observed separately and simultaneouslyB.4. OTHER FUNCTIONS OF THE LO/IF

207

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 Walshpattern 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.

208

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

209

210

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
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
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

211

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 Oﬃce
Single Dish212

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 Filterbanks
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) coverage, 90(u, v) plane, 22, 144(u, v) taper, 97
12-m Array, 9, 12
64-input Correlator, 9, 12, 59, 60
7-m Array, 9, 11, 13

design and properties, 185
foundations, 11, 187
pads, 187
panels, 186
performance specifications, 12, 185
PM, 12
power response, 19
ACA Correlator, 9, 62
response, 16
Airy function, 19
specifications, 185
Alcatel Alenia Space European Industrial Engineering
surface, 185
MT Aerospace (AEM), 185transportation, 189
Aliasing, 28transporters, 11All-sky pointing, 147
types, 186
ALMA
antenna-pointing, 147
Archive, 144, 179
AOS Technical Building, 199
Common Software (ACS), 175
Aperture, 17
Frontend Archive (AFA), 179
synthesis, 19
location, 11
Aperture blocking, 147
Science Archive (ASA), 179
Application Specific Integrated Circuit, 64
Science Data Model (ASDM), 177
Archive, 144
ALMA catalog, 146
Array
ALMA Common Software (ACS), 11
performance, 172
ALMA Project Data Model (APDM), 109
Array Operations Site (AOS), 11
ALMA Regional Center (ARC), 179
Astrometry, 160
ALMA Science Data Model (ASDM), 147
Astronomer on Duty, 109, 166
ALMA subsystem, 175
Atacama Compact Array, 9, 11
Control, 175
Atacama Large Millimeter/Submillimeter Array, 9
Executive, 175
Atmosphere, 144
Telescope Calibration, 175, 177
opacity, 133
Amplitude, 15, 22Atmospheric calibration (ATM), 193
Amplitude Calibration Device, 33
Atmospheric transmission, 31
Amplitude Calibration Device (ACD), 151, 192
Auto-correlation, 20
Angular resolution, 90
Antennaband-to-band, 161delay oﬀset, 148
Band-width-switching, 161
focus, 147
Bandpass
integration, 143, 148calibration, 152
pointing, 148, 151
calibrator, 153
position, 148, 152
Barlett weighting, 67
positions, 148
Baseband(s), 12, 13, 59, 75
power response, 19
desired center, 77
primary beam, 147
Baseline, 20
surface, 147
Baseline calibration, 145
Antenna(s)Baseline Correlator, 59
beam size, 17
Beam shape, 90
CM, 12Bessel function, 19

213

214

Binary Data File (BDF), 177
Binary Data Format, 68
Brightness, 15
temperature, 28
Brightness temperature, 28
Calibration, 143
amplitude, 115
astrometry, 160
atmospheric, 115
bandpass, 113, 152
flux, 113
phase, 113
polarization, 158
sources, 146
system-defined, 112
user-defined, 112
Calibration observation, 111
Calibrator
resolved, 160
Cartridge assembly, 31
Cassegrain focus, 186
Chajnantor, 11
Chajnantor Plateau, 10
Cittert-Zernike theorem, 22
Clock rate, 62Complex visibility, 22
distribution, 22
Complex visibility function, 143
Cone searches, 156
Configurations, 88
combining, 162
Contact scientist, 172
Correlator
64-input, 12
ACA, 12, 59
capabilities, 66
FX, 13, 62
XF, 12
Correlator and Integration Processor, 64
Correlator Data Processor, 62, 63
Correlator mode
FDM, 199
Cosmic Microwave Background, 134
Cross-correlation, 20
Cryostat, 189
Cycle 0, 9
Datadelegation, 181delivery, 181
download, 182
replication, 180
Data and Control Flow, 175
Data Capture module, 177

INDEX

Data Management Group, 165
Data rate, 12
average, 179
peak, 179
Data receivers, 65
Data Reducers Team, 171
Deconvolution techniques, 24
Delay
artificial, 20
geometrical, 20
Digital Transmission System Receiver, 64
Digital Transmitter, 64
Digitizers, 64
Director’s Discretionary Time, 180
Dirty
beam, 24
image, 24
Dirty beam, 87
Doppler shift, 197
Doppler tracking, 84
DTS and FFT processor, 64
Dump rates, 13
Early Science
Operations, 9Earth rotation, 23
EB calibrations, 149
Electromagnetic power, 15
Ephemeris file, 84, 119
Execution Block (EB), 111
Feathering, 105
Field of view, 23, 100
Field programmable gate array, 61
Flagging, 150
Flux density, 15, 28
Flux-scale, 154
Fourier transform, 15
Fraunhofer approximation, 19
Frequency
center oﬀset, 77
definitions, 77
generation, 199
rest, 77sky, 77
synthesizer, 76
Frequency and phase standard, 201
Frequency Division Mode (FDM), 60
Frequency Profile Synthesis, 63
Fringe, 22
rotation, 197
spacing, 22
tracking, 199
Frontend, 31, 189
Full Width Between Nulls, 18

INDEX

Full Width Between the Nulls, 18
FXF, 60
Gain, 145
Gibbs phenomenon, 97
Grid source, 114
Grid sources, 146
Group Observing Unit Set (GOUS), 111
Half Power Beam Width, 17Hanning function, 67
Helpdesk, 172
Holographic techniques, 147
Hot load, 150
Image fidelity, 24
Imagingsimultaneous, 77
Incoherence, 143
Integration time, 103
Interferometer
resolution, 26
two-antenna, 20Interferometry
single field, 113
Intermediate frequency, 33, 75
Jansky, 16
Joint ALMA Observatory (JAO), 11
JPL Horizon format, 119
Koh-ichiro Morita, 14
Lasers, 201
LO and IF systems, 197
operations, 198
Local Oscillator, 33, 59, 75
oﬀsetting, 82
Local Oscillator (LO), 12
Long Term Accumulator, 62
Lower sideband, 75
Maximum recoverable scale, 13, 26, 99, 101
Measurement set, 150
Member Observing Unit Set (MOUS), 111
Metadata, 177
Metrology, 187
Mitsubishi Electric Corporation (MELCO), 185
Morita Array, 9Mosaicing, 23, 100, 114
Multiple EB’s, 161
Multiple pointings, 114
Multiple Region Modes, 119
NED, 181
Next Generation Archive System, 179

215

non-dispersive, 145
Observations
non-standard, 143
on-the-Fly Mapping, 115
total power, 114
Observingproject, 109
proposal, 109
script, 109, 112
session, 111
Observing mode(s), 9
Observing session, 175
Observing Unit Set, 173
Observing Unit Set (OUS), 111
On-the-fly scan (OTF), 13
Operation Support Facility (OSF), 11
Ortho mode transducer, 35
Output radiance, 133
Pampa la Bola, 11
Parallactic angle, 118
Phase, 15, 22zero, 146
Phase calibrator
image, 157
Phase 1, 75, 109
Phase 2, 75, 109
Phase calibration, 80
Phase center, 21
Phase referencing, 156
Phase slope, 148
Phase switching, 84
phase-frequency relationship, 145
Phase-referencing, 156
Pipeline, 143
Plateau de Bure, 16
Pointing referencing, 152
Polarization, 16, 82, 115
instrumental, 116
oﬀ-axis, 116
Position switching, 13
Precipitable water vapor, 65
octiles, 133
Precipitable water vapour
octiles, 134
Primary beam, 100
Primary beam, 17, 147
correction, 23
Primary focus, 186
Program Management Group, 165
Proposer’s Guide, 9, 111
Proprietary period, 180
PWV, 150

216

QA0, 144
Quality Assurance, 165
categories, 167
classification, 165
report, 173
Quantization, 59
eﬃciency, 71
Radiometer
Dicky-switching, 195
Random, 143
Rayleigh resolution, 18
Rayleigh-Jeans limit, 28
Receiver(s)2 sideband, 136
double sideband, 136
heterodyne, 136
Rectangular field, 114
Reference Antenna, 159
Reflector
secondary, 18
Robustness, 93
San Pedro de Atacama, 11
Scan, 111, 176
Scheduling Block, 166
Scheduling Block (SB), 109
Sciencegoal, 109, 114
parameter(s), 109
Science Pipeline, 171
Science Software Requirements, 111
SEFD, 154
Self-calibration, 158
Sensitivity, 78, 133
point-source, 138
surface brightness, 139
Shadowing, 26, 90
Shutter, 187
Sidebanddouble, 32, 82
double (DSB), 12
dual, 12, 32
single, 32
Sidelobes, 17, 24, 87, 97
Simbad, 181
Sky brightness distribution, 15, 22
Sky frequency, 75
Snapshot, 97
Solar observations, 121
Solar system objects, 119
solar-obs, 163
Spatialfiltering, 24, 99
frequency, 15, 21

INDEX

Spatial coherence function, 114
Specific intensity, 15, 28
Spectral setup, 75, 77
Spectral window (spw), 60
Spectral window (spws), 75
Standard observing modes, 171
Stokes parameters, 115
Sub-arrays, 12
Submillimeter Array (SMA), 16
Subreflector, 147, 186
Subscan, 176
Subsystems
QuickLook, 112
Control, 112
Scheduler, 111
Telescope Calibration, 112
Surface accuracy, 147
Synthesized beam, 24
Technical Handbook, 9
TelCal, 149
Telescope
filled-aperture, 20
Telescope operator, 175
Temperaturesky, 133
system, 133
Tiltmeters, 187
Time Division Mode (TDM), 60
Tools
AosCheck, 166
AQUA, 166, 173
Monitor and Control, 166
Project Tracker, 167
QuickLook, 166
TelCal, 166
Total Power Array (TP Array), 11
Total Power Array (TP Array), 9, 13, 14
TP-obs, 162
TPOINT, 147
Transporter, 189
Tunable Filter Bank (TFB), 12, 60, 61, 198
Tuning range, 81
Upper sideband, 75User Policies, 173
van Cittert-Zernike theorem, 144
Van Vleck relationship, 72
Velocity definition
Optical, 85Radio, 85
Relativistic, 85
Velocity reference, 84
Barycentric, 84

INDEX

LSRK, 84
Topocentric, 84
VertexRS, 185
Virtual Observatory, 181
Visibility, 15, 143
amplitude, 144phase, 144
Visibility function
weighted, 87
Visibility function
measured, 144
true, 144
Vizier, 181
Voltage response, 19
VOTables, 181
Walsh-switching, 59, 84
Water Vapour Radiometer (WVR), 12, 65, 194
Weblog page, 171
Weighting
Briggs, 94
natural, 93
uniform, 93
visibility, 144
WVR Correction, 65
WVR correction, 59
Zero phase, 146
Zero spacing, 114
Zero-point fluctuations, 135
Zero-spacing problem, 13, 26

217