Event Horizon Telescope
Memo Series

EHT Memo 2023-L1-02

L1 Processing and Validation
Absolute Flux Density Calibration of the Greenland Telescope
Data for Event Horizon Telescope Observations
J. Y. Koay1 , K. Asada1 , S. Matsushita1 , C.-Y. Kuo2,1 , C.-W. L. Huang1 , C. Romero-Cañizales1 ,S. Koyama3,1 , J. Park4 , W.-P. Lo1 , G. Bower1 , M.-T. Chen1 , S.-H. Chang1 , C.-C. Chen1 , R. Chilson1 ,C. C. Han1 , P. T. P. Ho1 , Y.-D. Huang1 , M. Inoue1 , B. Jeter1 , H. Jiang1 , P. M. Koch1 , D. Kubo1 , C.-T. Li1 ,C.-T. Liu1 , K.-Y. Liu1 , P. Martin-Cocher1 , M. Nakamura5,1 , T. J. Norton6 , G. Nystrom1 , P. Oshiro1 ,N. Patel6 , U.-L. Pen1 , H.-Y Pu7,1 , P. A. Raffin1 , R. Rao6 , T. K. Sridharan6 , R. Srinivasan6 , T.-S Wei1
Oct 10, 2022 – Version 1.0
1

Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), No.1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan, R.O.C.
Physics Department, National Sun Yat-Sen University, No. 70, Lien-Hai Rd, Kaosiung City 80424, Taiwan, R.O.C
3
Niigata University, 8050 Ikarashi-nino-cho, Nishi-ku, Niigata 950-2181, Japan
4
Department of Astronomy and Space Science, Kyung Hee University, 1732, Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do
17104, Republic of Korea
5
National Institute of Technology, Hachinohe College, 16-1 Uwanotai, Tamonoki, Hachinohe, Aomori 039-1192, Japan
6
Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA
7
National Taiwan Normal University, Taiwan, R.O.C
2

Abstract
Starting from the observing campaign in April 2018, the Greenland Telescope (GLT) has been added
as a new station of the Event Horizon Telescope (EHT) array. Visibilities on baselines to GLT, particularlyin the North-South direction, potentially provide valuable new constraints for the modeling and imaging ofsources such as M87*. The GLT’s location at high Northern latitudes adds unique challenges to its calibration
strategies. Additionally, the performance of the GLT was not optimal during the 2018 observations due toit being only partially commissioned at the time. This document describes the steps taken to estimate thevarious parameters (and their uncertainties) required for the absolute flux calibration of the GLT data as partof the EHT. In particular, we consider the non-optimized status of the GLT in 2018, as well as its improved
performance during the 2021 EHT campaign.

Contents
1

Introduction
1.1 GLT-Specific Calibration Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 GLT Performance Issues During the 2018 EHT Observations . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 GLT Status During the 2021 EHT Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Scope of this Memo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2
3
3
4
5

2

Basic Concepts for (Sub-)mm VLBI and EHT Flux Calibration

5

3

Estimating Effective System Temperature∗
3.1 A More Generic Formulation for T sys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
∗3.2 T sys Errors When Not Using Generic Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 System Noise and Temperature Measurements at the GLT . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Re-scaling the Continuum Detector Outputs for the 2018 Observations . . . . . . . . . . . . . . . . . . . .

6
6
7
8
9

4

Aperture Efficiency and DPFU
4.1 GLT Aperture Efficiency and DPFU in 2018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 GLT Aperture Efficiency and DPFU in 2021 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12
13
13

5

Note on Elevation and Time-Dependent Gains

14

6

Pointing Uncertainties
6.1 Pointing Uncertainties During the 2018 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Pointing Uncertainties in 2021 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14
15
15

7

Summary

15

1

Introduction

The Greenland Telescope (GLT, Inoue et al., 2014; Chen et al., 2023) is a 12-m single-dish (sub-)mm telescope currently
located at the Thule Air Base in Greenland (LAT: +76◦ 320 06.00 6, LON: −68◦ 410 08.00 8). It is managed and operated by the
Academia Sinica Institute of Astronomy and Astrophysics (Taiwan) and the Smithsonian Astrophysical Observatory (USA).
The antenna was originally the North American ALMA prototype antenna (Mangum et al., 2006a,b), and has since been
retro-fitted to withstand the harsh Arctic conditions (Raffin et al., 2014, 2016). While its current altitude is close to sea
level (87.4 m), the eventual goal is to move the telescope to the Summit station in Greenland at an altitude of 3200 m,
where even THz observations are possible (Matsushita et al., 2017). Despite the low altitude at Thule, 230 GHz observations can still be conducted due to the dry conditions at the site, with a mean atmospheric opacity of τ = 0.17 at zenith
during the winter season (Matsushita et al., 2022).
The construction and re-assembly of the GLT was completed in July 2017 (Chen et al., 2018, 2023), after which the frontend and backend systems were installed (Kubo et al., 2018; Han et al., 2018), together with the computer and network
setup (Nishioka et al., 2018; Huang et al., 2020). Scientific commissioning began in December 2017 (Matsushita et al.,2018). The first ALMA-GLT fringes were detected for the quasar 3C279 as part of the EHT dress rehearsal in January
2018. The GLT was included in the EHT array for the April 2018 observing campaign, which represents the GLT’s firstscientific observations (Matsushita et al., 2018), despite it being only partially commissioned. Commissioning activities
continued through 2019 and 2020, during which the EHT observing campaigns were cancelled due to technical issues and2the global Covid-19 pandemic. Transitioning to remote operations during the pandemic allowed the GLT to participate in
the EHT observing campaign in April 2021.

1.1

GLT-Specific Calibration Challenges

The GLT’s location at high latitude and extreme weather conditions place unique challenges for GLT flux calibration.
These are:
1. Limited variations in elevation of available calibrator sources due to the telescope’s extreme Northern locationmeans that it is difficult to obtain gain curves by observing a source over a large range in source elevation.
2. Limited availability of bright sources with known brightness temperatures, namely planets, due again to thetelescope’s high latitude location. As the Sun does not rise above the horizon in winter, the availability of planets,
located along or close to the ecliptic, is very limited during winter.
3. Significant differences between the atmospheric temperature and the ambient temperature at the receiver,
due to the receiver cabin being heated to room temperatures (typically set to ∼ 16◦ C) for ideal performance of theelectronics. This may lead to large systematic errors in the estimation of the effective system temperatures of thetelescope based on the standard voltage measurements of hot load against that of the cold sky.

1.2

GLT Performance Issues During the 2018 EHT Observations

As mentioned, the performance of the GLT was not optimized during the 2018 observations. Remaining issues at the time
included:
1. Low antenna efficiency. Photogrammetry procedures conducted in the summer of 2018 found the dish to have apoor surface accuracy of ∼ 180 µm and a systematic saddle-shaped curvature (Figure 1, left). This was most likely
imprinted when the dish was lifted by crane to be mounted on the support cone, since the curvature matched thelocations at which the harnesses were attached (Koay et al., 2020; Chen et al., 2023).
2. Continuum detector instability and amplitude offset. Measurements of the system noise temperature, antenna
efficiency and the sky opacity (using sky-dipping) for the GLT during the April 2018 observations were made using
the continuum detector, whose output was later found to exhibit small fluctuations (2.8% peak-to-peak) resulting
from its sensitivity to receiver cabin ambient temperatures. Concurrent effective system noise temperature and skydipping atmospheric opacity measurements using both the continuum detector and the power-meter, conducted in
October 2018, reveal time-dependent amplitude offsets between both measurements due to the continuum output
variability. A rescaling/recalibration of the April 2018 continuum detector output is needed for the estimation of thesystem noise temperatures.
3. Large pointing errors at low elevation. The low sensitivity of the GLT at the time led to very low SNR observations of pointing sources at low elevations. The pointing model derived just before the EHT observations was foundto have pointing errors of 10 − 3000 at source elevations . 10◦ . This leads to additional amplitude losses for sources
observed at these low elevations.
Another challenge for the calibration of the 2018 GLT data is that continued commissioning activities were carried out
through the summer of 2018 and beyond. The performance and characteristics of the GLT have thus changed significantly
multiple times since the EHT 2018 observations. For example, the antenna efficiency, beam shape and gains have changed,
and their values in April 2018 can only be estimated using archival measurements close to those dates. If an issue is found3

Figure 1: Left: Antenna rms surface accuracy of ∼ 180 µm measured in summer 2018, likely to be the state of the dish during the EHT
observations. The saddle-shape is consistent with the location of the attached harnesses (shown as red ellipses) when the dish was lifted
onto the telescope mount. Right: Antenna rms surface accuracy of ∼ 25 µm measured after panel adjustments conducted between Augustand October 2018 (Koay et al., 2020).

in the measurements, there is no way of ‘re-setting’ the telescope conditions to those in April 2018 for further measurements and verification.

1.3

GLT Status During the 2021 EHT Observations

The issues pertaining to the 2018 GLT data have since been rectified:
1. The antenna efficiency has significantly improved from ∼ 22% in 2018 to ∼ 65% at 230 GHz, via photogrammetry
and subsequent panel adjustments. The surface accuracy of the GLT is now at ∼ 25 µm in summer and ∼ 40 µm in
winter (Figure 1, right; Koay et al. 2020).
2. The more stable outputs of the power-meter (no more than 0.5% peak-to-peak variations) are now used for measurements of the system temperatures and antenna efficiencies.
3. The pointing accuracy at low elevations has improved. With the improved antenna sensitivity, we were able to
track pointing sources down to very low elevations with high SNR detections, providing better constraints for the
pointing model at these elevations. The pointing uncertainties are now typically at ∼ 300 at elevations as low as 7◦ at
230 GHz.
On the other hand, due to the pandemic, regularly scheduled maintenance of the telescope frontends, backends and othersystems could not be carried out prior to the EHT 2021 observing campaign. Furthermore, the GLT observations as partof the EHT 2021 campaign were conducted via remote operations for the very first time. Some issues affecting the flux
calibration of the GLT data during the 2021 campaign include the following:∗
1. Due to a technical problem with the block down-converter, the T sys
measurements obtained on one of the observing

4∗
days, 13 April, were erroneous and cannot be used. This problem was fixed and T sys
could be measured properly forthe rest of the campaign.

2. The on-site 225 GHz tipping radiometer broke down in early March 2021 due to hardware problems, so there wasno opacity monitoring during the EHT 2021 observations. To make up for this, we performed sky dipping measurements with the GLT to determine the sky opacity before and after each observing track, and whenever possible, in
between scans separated by large gaps in time.
3. Due to poor weather conditions leading up to the observations, the antenna efficiency at 345 GHz was not measured
in 2021.

1.4

Scope of this Memo

All the issues outlined above for the GLT in general and those pertaining specifically to the 2018 and 2021 EHT observations require that additional steps and care be taken when preparing the meta-data for the absolute flux calibration of the
GLT data. This document describes these steps in detail. In the next section (Section 2), we provide a brief overview of thestandard telescope parameters necessary for the absolute flux calibration of (sub-)mm VLBI data. In Section 3, we describe
the measurement and derivations of the time-dependent effective system temperatures for the GLT, including the specificfixes needed for the 2018 measurements due to the continuum detector instability. We then discuss the estimation of theantenna efficiencies in Section 4 before and after the antenna surface adjustments; this is followed by a brief remark on theantenna gains (Section 5). Section 6 discusses the estimated pointing uncertainties and their effects on the flux calibration.
The performance of the GLT during the EHT 2018 and 2021 campaigns is summarized in Section 7.

2

Basic Concepts for (Sub-)mm VLBI and EHT Flux Calibration

Detailed elucidations of the basic terms and concepts for a-priori flux calibration of (sub-)mm VLBI and EHT data areprovided in the EHT memos by Issaoun et al. (2017) and Janssen et al. (2019). In this section, we provide a brief summaryof these terms, mainly those that are referred to in this memo.
To convert VLBI visibility amplitudes from correlation coefficients to units of flux density, taking into account the inhomogeneity of telescopes in the array, the system equivalent flux densities (SEFD) of each telescope need to be determined. Fora single dish telescope, the SEFD is given by (e.g., Event Horizon Telescope Collaboration et al., 2019):
SEFD =∗T sys

DPFU × gE,(1)

where the degrees per flux density unit (DPFU) is a conversion factor from units of temperature (K) to units of flux density(Jy), and gE is the elevation-dependent gain curve of the telescope. The DPFU can be estimated as:
DPFU =

ηA Ageom,2k(2)where ηA is the aperture efficiency, Ageom is the geometrical area of the antenna dish, and k = 1.38 × 103 is the Boltzmann
constant in units of Jy m2 /K.
∗
T sys
is the effective system noise temperature (Issaoun et al., 2017; Janssen et al., 2019), corrected for atmospheric attenuation. This needs to be differentiated from the regular T sys value used in cm-wavelength VLBI which does not account for∗
the atmospheric attenuation. T sys
is thus given by:
∗
T sys
=

eτ
T sys ,
ηl5(3)

where τ is the atmospheric opacity, and ηl is the forward efficiency (i.e., the coupling of the receiver to the sky, accounting∗
for ohmic losses and rearward spillover and scattering losses). Single dish (sub-)mm telescopes typically measure T sys
directly by placing a hot load of known temperature in the signal path. This is done regularly during or in between target∗
scans to account for the time and elevation (airmass) dependence of T sys
as the telescope points to different targets.
∗
The above parameters, i.e., T sys, DPFU and ηel , need to be measured for the GLT to enable the absolute flux calibration of
the visibility data on GLT baselines. These parameters are typically stored in a standard format calibration table (ANTAB),
which is then used by data reduction software to calculate the SEFDs and apply the calibrations.

3

Estimating Effective System Temperature∗
To calibrate the visibility amplitude for the EHT data, it is necessary to measure the T sys
as a function of time/elevationfor each station in the array during the observing track. It is typically assumed that the ambient, the atmospheric, and the∗
hot load temperatures are similar enough such that the process to derive T sys
values can be simplified. However, such an∗assumption may lead to significant systematic errors in the estimates of the GLT T sys, for which the effective atmospherictemperature T atm is much lower than the ambient temperature T amb at the receiver and hot load, compared to many of
the other EHT sites. This is because the receiver cabin is heated to room temperatures for the proper functioning of theelectronics systems. Therefore, a more generic equation which allows T amb and T atm to be different is needed to estimate
∗
∗
T sys
for the GLT and reduce the systematic uncertainties. In this section, we present the more generic formulation of T sys,∗
and provide an estimate of the systematic error in T sys that arises if we ignore the differences between T amb and T atm for the
GLT.

3.1

∗
A More Generic Formulation for T sys

The system noise temperature, T sys , describes the noise contribution from the receiver and the sky to the flux density measurement of a radio source. For the case where the effective atmospheric temperature (T atm ) is comparable to the ambient(or room) temperature of the receiver cabin (T amb ), T sys is expressed following the nomenclature used in Issaoun et al.
(2017) as:
T sys = T rx + T sky = T rx + T atm (1 − ηl e−τ ) ,(4)
where T rx refers to the receiver noise temperature, and T sky = T atm (1 − e−τ ) is the sky brightness temperature. Again, ηl is theforward efficiency and τ is the line-of-sight atmospheric opacity. If T atm signficantly differs from T amb , for a station such as
the GLT, then the system temperature is expressed more generally as (Ulich & Haas, 1976; Rohlfs & Wilson, 2006):

T sys = T rx + ηl T sky + (1 − ηl )T amb= T rx + ηl T atm (1 − ηl e−τ ) + (1 − ηl )T amb .

(5)

To further account for the signal attenuation caused by the atmosphere and the rearward efficiency loss, it is convenient to∗define the effective system noise temperature, T sys(Section 2), which explicitly indicates that the system sensitivity drops
exponentially as line-of-sight opacity increases:
∗
T sys
=

eτ
eτ
T sys = [T rx + ηl T sky + (1 − ηl )T amb ] .
ηl
ηl

(6)

∗
To determine T sys, the receiver output voltage Camb is first measured when the hot load with an ambient temperature, T amb ,is placed in the signal path of the receiver, and this load blocks everything except for the receiver noise. This step is fol-6

lowed by the measurement of the receiver voltage Csky when the hot load is removed and the feed horn is directly pointing
towards the cold sky with a temperature of T sky at a certain elevation. For the hot load measurement, one can relate thereceiver output and the ambient/receiver temperature as:
Camb = G(T amb + T rx ) ,(7)

where G is the voltage gain. For the cold sky measurement, the receiver responds to empty sky noise (T sky ) and noise fromthe receiver cabin (corresponding to T amb ). In this case, the relationship between the receiver output and the sky/groundnoise can be expressed as (see Equation 7.26 in Rohlfs & Wilson (2006)):hiCsky = G ηl T sky + (1 − ηl )T amb + T rx .
(8)Taking the difference between Camb and Csky , we obtain:∆Ccal ≡ Camb − Csky = Gηl (T amb − T sky ) .

(9)Since T sky = T atm (1 − e−τ ), ∆Ccal can be expressed as:∆Ccal = Gηl (T amb − T atm + T atm e−τ ) .

(10)

For many of the EHT stations, it is reasonable to assume that T amb = T atm , such that ∆Ccal = Gηl T amb e−τ . As mentioned,
the difference between T amb and T atm is non-negligible for the GLT; in this case, one can express the ambient temperature
as T amb = T atm + ∆T , where ∆T is the difference between the ambient and the effective atmospheric temperature, andEquation 10 can be re-written as:∆Ccal = Gηl (∆T + T atm e−τ ) .
(11)∗
Now, in order to relate T sys
to the measured receiver outputs (i.e., Csky and Camb ), we evaluate the ratio, rcal , of Csky to∆Ccal , obtaining:
Csky
G[ηl T sky + (1 − ηl )T amb + T rx ]rcal ≡
=
,
(12)
∆Ccal
Gηl (∆T + T atm e−τ )which can be rearranged as:
ηl T sky + (1 − ηl )T amb + T rx
ηl T atm e−τ [1 + ∆T/(T atm e−τ )]
∗
T sys
=
.
T atm [1 + (∆T/T atm )eτ ]rcal =

Finally, one obtains:∗
T sys= rcal T atm [1 + (∆T/T atm )eτ ] .

(13)

(14)

In summary, the determination of the effective system temperature of a submillimeter radio telescope involves the measure∗ments of the voltage outputs from the receiver which can be used to derive T sys
via equation 14. This equation explicitly∗
accounts for the difference between T atm and T amb , and thus should be applied for GLT T sys
measurements.

3.2

∗
T sys
Errors When Not Using Generic Equation∗
For telescopes at which ∆T = 0 is a reasonable assumption, the ratio rcal is simply the effective system temperature T sys
divided by T amb , since from Equation 12:
!
∗
T sys
eτ ηl T sky + (1 − ηl )T amb + T rx.
(15)rcal,∆T=0 =
=
ηl
T atm
T amb

7

∗
In this case, one can easily evaluate T sys. To emphasize that this expression is valid only when ∆T = 0, we define the∗effective system temperature when ∆T = 0 as T sys0:∗
T sys0≡ rcal,∆T=0 T amb .

(16)

Substituting T atm = T amb − ∆T into Equation 14, we have:∗T sys= rcal (T amb − ∆T )(1 + ∆T eτ /(T amb − ∆T )) ,(17)

which, to first order, can be approximated as:
"
#
∆T τν
∗
T sys
≈ rcal T amb 1 +(e − 1)
T amb
#
"
∆T τν
∗
(e − 1) .
= T sys0
1+
T amb

(18)

The terms in the square parenthesis in the above equation represent the correction factor that needs to be multiplied to the∗
T sysvalues evaluated assuming T amb = T atm . Considering typical receiver cabin temperatures of 15◦ C, and typical winteratmospheric temperatures of −25 to −35◦ C, ∆T can be as large as 50◦ K. Assuming T amb = 290◦ K and τ = 0.2, then this∗∗correction factor represents a 4% error relative to T sys0
, if only T amb is used to calculate T sys. If T atm is used instead to∗∗∗
calculate T sys0 , i.e. if one had assumed T sys0 ≡ rcal,∆T=0 T atm , the error in T sys would be as large as 25%, based on the term inparenthesis in Equation 14.
∗
Therefore, for typical conditions at the GLT, T amb should used instead of T atm in the calculation of T sys, when using the∗standard equation. In such a case, the T sys systematic uncertainties introduced would be no more than 4%. However, to∗reduce these systematic uncertainties further, we use Equation 14 to estimate the GLT T sys
values.

3.3

System Noise and Temperature Measurements at the GLT∗In order to measure T sys, a continuum detector was installed on the GLT. A 4 GHz bandwidth intermediate frequency (IF)signal (at 3.85 - 7.85 GHz) is divided with a coupler in the GLT IF assembly system, and the continuum detector measures
the power of this signal. It was later discovered that the continuum detector output was sensitive to the receiver cabinambient temperature, which was unstable during the 2018 EHT campaign due to insufficient optimization of the HVAC
receiver cabin temperature control (see Sect. 3.4). After the 2018 EHT observations, we have permanently switched to∗using the power-meter for the T sys
measurements, since it provides more stable outputs that are less dependent on theambient temperature.

For the EHT observations, the GLT measures the system temperatures before and after each scan, using the continuum de∗tector in 2018, and the power-meter from 2021. During a T sys
measurement, the system noise of the hot load (Camb ) is firstmeasured by the continuum detector for a duration of 10 s, followed by that of the sky (Csky ) for 10 s. For the 2018 observations, the receiver cabin temperature (T amb ) is automatically recorded by 5 separate sensors located at different positionsin the cabin, and their mean values are assumed to be equivalent to the hot load temperature. A new sensor has since been
installed on the hot load, so for the 2021 observations onwards, T amb is directly read from this hot load temperature sensor.
Comparing the hot load temperature readings with the mean temperatures from the five cabin sensors show differences of
no more than a few degrees K (< 1%). Therefore the 2018 T amb measurements are expected to be representative of the hotload temperatures.
The atmospheric opacity is measured with the GLT using the sky-dipping technique, as well as with an on-site 225 GHz
tipping radiometer (Matsushita et al., 2017, 2022), which as noted, was not functioning during the 2021 EHT observing
campaign. The effective atmospheric temperature, T atm , is also monitored continuously by an on-site weather station.
8

Figure 2: Estimated calibration curves for the GLT continuum detector; these were measured by comparing the input power level of thenoise source measured with a power-meter and output of the continuum detector, as a function of frequency. While calibration curves
are expected to have first and second order terms, the frequency range we were using was mainly dominated by the zeroth order terms.
Therefore, the relationship between the power-meter and continuum detector measurements is expected to vary linearly in frequency, andto require only a constant offset in the observed output power.

∗
The method described in this section was used to determine the GLT T sys
for each scan during the 2021 observations, andwill be used for all subsequent EHT observations. For the 2018 EHT observations, Camb and Csky were also measured using∗
the method described above, but the T sys
estimates derived are unreliable due to the 2.8% fluctuations of the continuum∗
detector as a function of time and cabin temperature. We used a workaround method to derive the T sys
values for 2018,
which we describe in the next subsection.

3.4

Re-scaling the Continuum Detector Outputs for the 2018 Observations

We discovered that the continuum detector output showed 2.8% fluctuations that were consistent with the receiver cabintemperature variations linked to the HVAC cycles. The continuum detector output is read out as a function of frequency.
This output is then converted into units of power using the apriori obtained calibration curve. Figure 2 shows the calibration curves obtained at two different days before the EHT observations in 2018, which are different for each measurement,
presumably because of the temperature fluctuations. We thus expect the continuum detector measurements to have large
uncertainties.
∗
Therefore, to estimate the GLT T sys
values for 2018, we (1) estimate the nominal receiver temperature, then (2) estimate theatmospheric temperatures and zenith opacities measured by the 225 GHz tipping radiometer, and (3) estimate the effective
system temperature by considering the elevation towards the target source. We now describe each of these steps in detail.

3.4.1

Estimation of the nominal receiver temperature

We estimate the receiver temperature (T rx ) using sky dipping observations. The output power from the continuum detector
can be expressed as:Pout = G T rx + T sky = G T rx + T atm 1 − e−τ .
(19)Assuming a plane-parallel atmosphere, the opacity, τ, can be expressed as τ0 sec(Z), where τ0 is the opacity towards thezenith and Z is the elevation angle, giving:Pout = G T rx + T atm 1 − e−τ0 sec(Z) .
(20)

9Figure 3: Tipping measurements for the GLT during the 2018 EHT campaign, with each colored line representing one of the 20 recorded
measurements.

Normalizing Equation 20 by the output measured towards the hot load, we obtain:
T rx + T atm 1 − e−τ0 sec(Z)Pnor =.
T rx + T amb(21)

There were twenty sky dipping observations at 230 GHz after the continuum detector was last calibrated on 2018 March
27. In Figure 3, we show all of the sky dipping measurements. The horizontal axis corresponds to the path length (air mass)and the vertical axis corresponds to the output power normalized by the output power measured towards the hot load, Pnor .
In the tipping curve, the slope corresponds to the increase of the sky temperature at different air masses, which should
be different between measurements due to the varying opacity and atmospheric temperature. The receiver temperature is
expected to correspond to the normalized power at the cross section with the vertical axis, when sec(Z) = 0, such that:
Pnor,sec(Z)=0 =T rx.
T rx + T amb(22)

We expect this cross-section to be a constant value that is dependent only on T rx and T amb , both of which should not varysignificantly. However, we clearly see that the cross sections also show large fluctuations presumably due to the fluctuations of the output of the continuum detector. In Figure 4, we show the histogram of the estimated receiver temperature
based on each sky dipping observation. These receiver temperatures are estimated from the measured normalized output power using Equation 22. Most of the measurements are clustered in the range between 40 to 80 K. While individual
estimated numbers are not reliable due to the continuum detector output fluctuations, we used the median of those measurements as the nominal value for the GLT receiver temperature in the 2018 experiments, which is 57.9 ± 9.2 K. The estimateduncertainty excludes the outlier value at about 115 K.

10Figure 4: Histogram of the estimated receiver temperature based on sky dipping observations.

3.4.2

Estimation of the sky opacity

During the EHT 2018 observations, tipping measurements are conducted every 10 min with the 225 GHz radiometer. For
each tipping, we measure the brightness temperature of the atmosphere at 5 different elevation angles, tilting in both theNorthern and Southern directions. Elevation angles are 90, 42, 30, 24.6 and 19.2 degrees, corresponding to zenith air
masses of 1, 1.5, 2, 2.5 and 3, respectively. We note that the opacity data will be used when both the opacities toward
Northern and Southern directions are the same within errors. We also measure a built-in absorber brightness and monitor
the atmospheric temperature in order to do a gain calibration at the time of tipping. By utilizing those measurements, weestimated the opacity towards the zenith τ0 every 10 min (Matsushita et al., in prep.).

3.4.3

Estimation of the effective system temperature

Based on the estimates of τ0 and T rx , and measurements of T atm and T atm , we calculated the effective system temperaturefor each scan. Since the opacities and temperatures were measured every 10 min and there are missing data in some cases,
we just used the values closest in time to each particular scan. We obtained τ values towards the source by considering theelevation of the telescope during that scan, which was extracted from the observing schedule file (VEX file) used to control∗
the telescope. Based on the T rx uncertainties and using nominal values for τ0 and T atm , we estimate T sys
uncertainties of11∼ 15% for the GLT in 2018. This assumes that the continuum detector instabilities are the dominant sources of error in the∗
T sysestimate.

4

Aperture Efficiency and DPFU

By observing a source with known temperature and size, namely a planet, it is possible to derive the main-beam efficiency
as follows (Mangum, 1993):
! −1θplanet 2 1 − exp − ln 2
,
ηmb =
×




J(T planet ) − J(T CMB ) θmb
1 ∗2 T A,planet(23)

where:∗• T A,planetis the single-sideband antenna temperature of a planethν/k• J(T ) is the Planck function at frequency ν and brightness temperature, given by: namely J(T B ) = exp(hν/kTB )−1• T planet is the brightness temperatures of the planet• T CMB is the brightness temperature of the cosmic microwave background• θplanet is the diameter of the planet in arcsec• θmb is the telescope main-beam Full Width at Half Maximum (FWHM) in arcsec
In the typical case where the size of the observed planet is smaller or comparable to the FWHM of the telescope mainbeam, this equation gives the main-beam efficiency (in the case where a planet is smaller than the main-beam, one needs
to consider the filling factor within the main-beam). However, when the Moon instead of a planet is used for this measurement, since the size of the Moon is significantly larger than the main-beam and covers most of the side-lobes, theexpression above actually gives the forward spillover efficiency, ηfss (Mangum, 1993).
The main-beam efficiency can also be expressed as follows:
2
θmb
Aeff
,
λ2

ηmb =

(24)

where Aeff is the effective aperture area of the antenna. From this equation, Aeff can be expressed as:
Aeff =

λ2 ηmb
.
2
θmb

(25)

ηA =

Aeff
,
Ageom

(26)

The aperture efficiency, ηA is expressed aswhere Ageom is the geometrical area of the antenna dish. Using Eqs.(23) and (25), ηA can therefore be expressed as:! −1θplanet 2 ηA = 2×
1 − exp − ln 2
.




θmb
2θ Ageom [J(T planet ) − J(T CMB )] ∗
λ2 T A,planet

mb

12

(27)

We used the latest flux density models for planets in the ALMA Common Astronomy Software Application (CASA; McMullin et al., 2007) package (Butler, 2012). These are found in CASA versions 4.0 or later. The brightness temperaturesof planets for the frequency range between 30 GHz and 1000 GHz are in the data files located at [CASA home directory]/data/alma/SolarSystemModels/. So far, we have only used Venus and Mars as the target planets for the GLT aperture
efficiency measurements. The brightness temperature of Venus depends only on frequency, but that of Mars also depends
on time.
In the case of Moon observations, the brightness temperature depends on the Moon’s phase. The brightness temperature of
the Moon, T B,Moon , toward the center of the lunar disk is described as follows:
T B,Moon (λ) = T 0 (λ) + √0.77T 0 (λ)
1 + 0.48λ + 0.11λ2cos[χ − ξ(λ)],

(28)

where

!
Days since new Moon
× 360 − 180,
Period of Moon!
0.24λ
ξ(λ) ≡ tan−1,
1 + 0.24λλ is the observing wavelength, and the period of the Moon is 29.530589 days (Mangum, 1993; Krotikov & Troitskiı̆, 1964;
Linsky, 1966, 1973). Values for T 0 (λ) are 227.7±8.9 K at 3 mm (100 GHz), 219.1±6.3 K at 1 mm (300 GHz), and 217.6±8.1
K at 300 µm (1000 GHz) (Linsky, 1973).
χ≡

4.1

GLT Aperture Efficiency and DPFU in 2018

The ηfss at 230 GHz was observed around 1 AM on Mar.30, 2018 (UT), when it was 12.62 days after the new Moon. The
results were 92.1% for the Right-Hand Circular (RHC) polarization, and 92.2% for the Left-Hand Circular (LHC) polarization.
The ηA for 230 GHz was observed on Mar.17, 2018 toward Venus at an elevation of 17◦ , where there are no large pointing
errors (see Section 6.1). Due to the instability in the RCP data output, with large gain jumps during the scans of Venus, we
could only use the LCP data. We obtained three separate measurements, and the results gave ηA of 21.6 ± 0.9% (±1.4%
after adding the 5% uncertainties of the Venus flux density model (Butler, 2012)), which was much lower than the expectedvalue for a dish surface accuracy of 40 µm rms after panel adjustments but before the dish was transported to the site andmounted on the support cone. We later found that the low aperture efficiency was due to the surface deformation (saddlelike structure with the surface accuracy of 180 µm, as shown in Figure 1) when the dish was lifted using a crane (Koay etal., 2020). This led to significant astigmatism of the GLT antenna. These values of the antenna efficiency are thus zerothorder estimates, and their uncertainties are likely much larger due to the systematics introduced by the dish astigmatism.
Additionally, the efficiency is derived based only on azimuthal scans of Venus. Altitudinal scans could not be performed
due to the low elevation of the source, since there would be large variations in airmass throughout the scan.
Based on the aperture efficiency value of 21.6 ± 0.9% at 230 GHz, we estimate the DPFU using Equation 2 to be 0.0088 ±
0.0004 K/Jy. Considering the quoted 5% uncertainties of the Venus flux density model (Butler, 2012), and adding that inquadrature to the measurement uncertainties gives us 0.0088 ± 0.0006 K/Jy. We use this DPFU value and uncertainty for bothright and left hand circular polarizations.

4.2

GLT Aperture Efficiency and DPFU in 2021

The ηA for 230 GHz was measured on March 6, 2020 toward Venus at elevations of 26◦ − 27◦ , just before the pandemic
started world-wide. Both RCP and LCP receivers were working nominally at the time, and we took 13 individual measure13

ments. The calculated aperture efficiencies are 67.1 ± 1.3% and 64.7 ± 2.0% for RCP and LCP, respectively. These values
are consistent with the antenna surface accuracy of 40 µm rms, assuming the geometrical antenna efficiency of 75%. As
mentioned above, regular maintenance of the various GLT systems, including the cryostat, could not be carried out during
the pandemic, leading to a slight degradation of the performance of the SIS detector, which needs to be cooled to ∼ 4 K at
230 GHz. When we attempted to measure the efficiency again after the EHT 2021 observations, the sensitivity had deteriorated further, and we did not obtain any useful efficiency data at 230 GHz. We therefore only have the antenna efficiencies
measured a year before in 2020 as reference.
On the other hand, since the 86 GHz receiver is a MMIC amplifier that does not require 4 K temperatures, its sensitivity is
not expected to be affected by the cryostat issues. We obtained 7 measurements of ηA at 86 GHz on Nov.10, 2020 toward
Mars between elevations of 10◦ − 18◦ , obtaining ηA values of 75.3 ± 0.9% and 74.8 ± 1.7% for RCP and LCP, respectively. As
with the measurements at 230 GHz, these values are consistent with the antenna surface accuracy of 40 µm rms, assuming
the geometrical antenna efficiency of 75%. This suggests that the surface accuracy did not change significantly over thesummer between March 2020 and November 2020. We argue that it is reasonable to assume that the 230 GHz antenna
efficiency measurements from March 2020 can be applied to the 2021 EHT observations.
The DPFU for the GLT for the EHT 2021 observations is thus estimated to be 0.0275 ± 0.0015 K/Jy for RCP and 0.0265 ±0.0015 K/Jy for LCP. The uncertainties include the 5% uncertainties of the flux density model for Venus added in quadrature.

5Note on Elevation and Time-Dependent Gains

To date, variations of the GLT antenna efficiencies as a function of elevation have not yet been determined to model thegain curves. However, due to the high latitude location of the GLT, astronomical sources do not significantly change in elevation as they move across the sky. Therefore, the elevation-dependent gains can be assumed to be insignificant, comparedto the other uncertainties in the antenna efficiency measurements. Although there is a lack of sources that the GLT can trackover a large range of elevations to measure the gains, we are working to measure the antenna efficiencies of the GLT as afunction of time of day, ambient temperature, and elevation (where possible) to better characterize the telescope gains for
future EHT campaigns.

6

Pointing Uncertainties

Radio pointing models for the GLT are determined from observations of bright spectral line (SiO J = 2 − 1 masers at
86 GHz, CO J = 2 − 1 at 230 GHz, and CO J = 3 − 2 at 345 GHz) sources, mostly evolved stars with rather compact andsymmetrical emitting regions. To determine pointing offsets, the integrated intensity of a source spectral line is measured
at 5 different points: at the expected source center, and at ±X 00 in azimuth and elevation, where X is typically selected
to be the half-width at half maximum (HWHM) of the primary beam, i.e. 1500 at 230 GHz, or larger if the source size ismore extended than the beam HWHM. We then fit a Gaussian function to the line intensities in elevation and in azimuth toestimate the pointing offsets at these two axes. After obtaining a large sample of offset measurements for a large range ofantenna elevations and azimuths, we fit the pointing model to the measured offsets as a function of telescope elevation andazimuth, from which we derive the pointing model coefficients (see Koay et al., 2020; Chen et al., 2023, for details on the
pointing model).

14

6.1

Pointing Uncertainties During the 2018 Observations

Prior to the 2018 April EHT campaign, pointing measurements were carried out at the GLT between March 16 and 22.
Due to the low antenna efficiency at that time (see Sect. 4.1), we were limited to very bright sources as pointing sources,
which were IRC+10216, CIT 6, NGC 7027, CRL 2688, CRL 618, and R Cas. Using about 70 pointing measurements at
different azimuths and elevations, we updated the pointing model, then carried out more observations to verify the newmodel, finding an rms pointing accuracy of . 400 in both azimuth and elevation, for elevations above 10◦ . The low antennasensitivity meant that pointing sources were observed at very low SNR at elevations below 10◦ , thereby increasing theuncertainties of the pointing offsets.
Just before the EHT 2018 observations, we found pointing elevation offsets of 1000 at elevations of 10◦ , increasing to 4000
offsets at elevations of 6◦ . By then we did not have time to conduct more pointing observations to correct the pointing
model. This significantly impacts observations of 3C 279, as it was observed between an elevation of 6◦ to 8◦ at the GLT,
but should not affect observations of M87* (observed between 18◦ to 26◦ in elevation).
The 230 GHz FWHM beam sizes were measured to be 25.00 5 in the horizontal (azimuth) direction, and 36.00 7 in the vertical(elevation) direction, based on vertical and horizontal scans of the Moon. The beam elongation in the vertical direction
relative to the horizontal direction is likely caused by the saddle shape of the antenna surface. Assuming a Gaussian-shaped
beam, the rms pointing errors thus translate to amplitude uncertainties of . 7% for sources observed at elevations above
10◦ . At low elevations, the pointing errors can cause the amplitudes to drop by 18% at 10◦ elevation, up to as much as 96%
at 6◦ .

6.2

Pointing Uncertainties in 2021

With the improved sensitivities of the antenna, we have been able to better characterize the pointing model of the GLTdown to an rms accuracy of ∼ 200 at elevations as low as 7◦ at 230 GHz. Between 8 and 18 March 2021, just before theEHT campaign, we obtained 100 pointing measurements over a large range of azimuths and elevations. In addition to thebright pointing sources already used for 2018, we have added new (weaker) evolved star sources, such as χ Cyg, GL 3068,
TX Cam, LP And, V384 Per, IRAS 21282+5050, GX Mon, V Cyg, RX Boo, and HD 235858 to our catalogue of pointing
sources.
Using the updated beam sizes after the panel adjustments of 27.00 0, in both the horizontal and vertical axes, this translates toamplitude losses of . 2% for all azimuths and elevations down to 7◦ for the 2021 EHT observations. We expect to be able
to achieve this pointing accuracy for subsequent campaigns.

7

Summary

In Table 1, we summarize the GLT performance parameters during the 2018 and 2021 EHT observing campaigns, as described in this memo.

Acknowledgement
The authors would like to thank Claus Gonnsen, Ane-Louise Ivik, Chen-Yu Yu, Lupin C. Lin, Zheng Meyer-Zhao, Alex
Alladi, Aaron Faber, and Nicolas Pradel for their expertise and assistance to the development of the GLT project. The GLT15

Table 1: Summary and comparisons of the GLT performance between 2018 and 2021.

2018

2021

∗
T sys

∗
Due to continuum detector instabilities, T sys
values derived based on the nominal receivertemperature, plus measured atmospheric temperatures and line-of-sight opacities for each
scan.

∗
T sys
values measured via the standard methodof cold sky and hot load voltages, using themore stable outputs of the power-meter.

ηA a21.6 ± 0.9% for RCP and LCP

67.1 ± 1.3% for RCP
64.7 ± 2.0% for LCP

DPFUb

0.0088 ± 0.0006 K/Jy for both RCP and LCP

0.0275 ± 0.0015 K/Jy for RCP
0.0265 ± 0.0015 K/Jy for LCP

Pointing losses. 7% amplitude losses for elevations > 10◦ ;18% to 96% amplitude losses between elevations of 10 to 6◦. 2% amplitude losses for elevations > 7◦a

The ηA uncertainties quoted here comprise only the measurement errors.
b The DPFU uncertainties quoted here include the measurement uncertainties and the 5% uncertainty of the Venus flux density model.

is supported by the Academia Sinica (Taiwan), the National Science and Technology Council (formerly the Ministry of
Science and Technology) of Taiwan (grants 99-2119-M-001-002-MY4, 103-2119-M-001-010-MY2, 105-2112-M-001025-MY3, 105-2119-M-001-042, 106-2112-M-001-011, 106-2119-M-001-013, 106-2119-M-001-027, 106-2923-M-001005, 107-2119-M-001-017, 107-2119-M-001-020, 107-2119-M-001-041, 107-2119-M-110-005, 107-2923-M-001-009,
108-2112-M-001-048, 108-2112-M-001-051, 108-2923-M-001-002, 109-2112-M-001-025, 109-2124-M-001-005, 1092923-M-001-001, 110-2112-M-003-007-MY2, 110-2112-M-001-033, 110-2124-M-001-007, 110-2923-M-001-001, 1112124-M-001-005 and 112-2124-M-001-014) and the Smithsonian Institution. Support for the Hydrogen Maser frequency
standard used for VLBI at the Greenland Telescope was provided through an award to SAO from the Gordon and Betty
Moore Foundation (GBMF-5278). The GLT project members thank the National Chun-Shan Institute of Science andTechnology (Taiwan) for their strong support, the National Astronomical Observatory of Japan for their support in receiver
instrumentation, the United States National Science Foundation Office of Polar Programs for effective support in logistics,
and the United States Air Force, 821st Air Base Group, Pituffik Air Base, Greenland for use of the site and access to thebase and logistics chain. The GLT project members appreciate the development work done by Vertex AntennentechnikGmbH and ADS international, and also thank Atunas, an outdoor wear company in Taiwan, for sponsoring the Arctic
wear used by staff. NRAO and the Massachusetts Institute of Technology Haystack Observatory supported the acquisitionof the ALMA–North America prototype antenna and its re-purposing for deployment in Greenland. The GLT project
acknowledges the privilege of operating on the lands of Greenland and strives to work with the local government and thepeople of Greenland to realize the scientific and educational potential of this project.

References
Butler, B. 2012, ALMA Memo 594
Chen, M.-T., Raffin, P., Ho, P. T. P., et al. 2018, Proc. SPIE, 10700, 107000H
Chen, M.-T., Asada, K., Matsushita, S., et al. 2023, PASP, (accepted)
Event Horizon Telescope Collaboration, et al., 2019, ApJL 875, L3
16

Han, C.-C., Chen, M.-T., Huang, Y.-D., et al. 2018, Proc. SPIE, 10708, 1070835
Huang, C.-W. L., Matsushita, S., Patel, N. A., et al. 2020, Proc. SPIE, 11452, 114521S
Inoue, M., Algaba-Marcos, J. C., Asada, K., et al. 2006, Radio Science, 49, 564
Issaoun S., Folkers, T. W., Blackburn, L., Marrone, D. P., Krichbaum, T., Janssen, M., Martí-Vidal I., and Falcke, H. 2017,
EHT memo series, 2017-CE-02
Janssen, M., Blackburn, L., Issaoun, S., Krichbaum, T. P., Wielgus, M. 2019, EHT memo series, 2019-CE-01
Koay, J. Y., Matsushita, S., Asada, K., et al. 2020, Proc. SPIE, 11445, 114450Q
Kubo, D., Han, C.-C., Nishioka, H., et al. 2018, Proc. SPIE, 10708, 1070816
Krotikov, V. D. and Troitskiı̆, V. S. 1964, Soviet Physics Uspekhi, 6, 841
Linsky, J. L. 1966, Icarus, 5, 606
Linsky, J. L. 1973, ApJS, 25, 163
Mangum, J. G. 1993, PASP, 105, 117
Mangum, J. G., Baars, J. W. M., Greve, A., Lucas, R., Snel, R., and Wallace, P. 2006, ASPC, 356, 253
Mangum, J. G., Baars, J. W. M., Greve, A., Lucas, R., Snel, R., Wallace, P., and Holdaway, M. 2006, PASP, 118, 1257
Matsushita, S., Asada, K., Martin-Cocher, P. L., Chen, M.-T., Ho, P. T. P., Inoue, M., Koch, P. M., Paine, S. N., and Turner,
D. D. 2017, PASP, 129, 025001
Matsushita, S., Asada, K., Inoue, M., et al. 2018, Proc. SPIE, 10700, 1070029
Matsushita, S., Martin-Cocher, P. L., Paine, S., et al. 2022, PASP, 134, id.125002
McMullin, J. P., Waters, B., Schiebel, D., Young, W., and Golap, K. 2007, in Shaw R. A., Hill F., Bell, D. J. eds, ASP
Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI. p. 127
Nishioka, H., Huang, C.-W. L., Patel, N. A., et al. 2018, Proc. SPIE, 10700, 107005N
Raffin, P., Algaba-Marcosa, J. C., Asada, K., et al. 2014, Proc. SPIE, 9145, 91450G
Raffin, P., Ho, P. T. P., Asada, K., et al. 2016, Proc. SPIE, 9906, 99060U
Rohlfs, K. & Wilson, T. L. 2006, Tools of Radio Astronomy, Fourth Revised and Enlarged Edition, Corrected Second
Printing, Springer
Ulich, B. L. & Haas, R. W. 1976, ApJS, 30, 247

17