Band-to-band Phase Transfer with ALMA: April-May 2013
ALMA Technical Note Number: 1
Status: FINAL
Prepared by:

Organization:

Date:

Kim Scott

NAASC

27 May 2013

Band-to-band Phase Transfer with ALMA: April-May
2013
Kim ScottMay 27 2013

1

Introduction

Finding strong calibrators within 10o of a science target at frequencies above ∼ 300 GHz
is challenging. Using a phase calibrator further away is undesirable, since both systematic
phase errors that arise from antenna position uncertainties and variable tropospheric delays
get worse. Quasars are much brighter at lower frequencies, and so we would like to be able toobserve a quasar within 10o of a science target at a lower frequency, and correct its phase tothat of the target frequency. In this report, I describe initial testing of band-to-band phasetransfer (BBPT). More information is given in the ALMA JIRA ticket CSV-2730.
This report is organized as follows: in Section 2, I describe the basic method of BBPT;in Section 3, I discuss the commissioning tests carried out in April and May 2013; I discuss
the data reduction steps to analyze these data in Section 4, and present the main resultsfrom this study in Section 5; I summarize this work in Section 6.

2

Band-to-band Phase Transfer: General Descriptionof the Method

The observed phase difference between interferometric observations at two different frequencies (ν1 , ν2 ) has two components. The first is an instrumental phase difference that is almost
constant in time (φi (ν1 ), φi (ν2 )), and the second is a highly variable delay component due
to tropospheric fluctuations (φt (ν1 , t), φt (ν2 , t)). The latter thus scales with frequency, suchthat
ν2× φt (ν1 , t).
(1)
ν1
We need a calibration sequence that allows us to solve for both types. The basic method
is to observe a bright quasar (BQ) that is > 10o from the science target (ST) at both
frequencies in order to measure the instrumental phase difference, and then observe a fainterφt (ν2 , t) =1

quasar (FQ) < 10o from the target at the lower frequency to track the delay component withtime. The scan sequence looks like this:
1. BQ(ν1 )2. BQ(ν2 )3. FQ(ν1 )4. ST(ν2 )5. Repeat steps 3 and 4 for time tcrit
6. FQ(ν1 )7. Repeat all steps to the end of the execution.
The BQ(ν1 ) – BQ(ν2 ) scan pairs are revisited every tcrit minutes (hours?) to track the(hopefully) small drifts in instrumental phase differences. Determining an optimal valueof tcrit is one of our goals. Another important scale is the time it takes to switch between
frequencies, tswitch . This must be short enough that tropospheric variations between adjacentscans at different frequencies are small, so that the phase difference between the BQ(ν1 ) –BQ(ν2 ) scan pairs is dominated by the constant instrumental phase difference.

3

Commissioning Tests, April-May 2013

We carried out a number of BBPT tests at ALMA during commissioning time in April andMay 2013. These include testing BBPT between Bands 3 (90 GHz) and 7 (340 GHz), andBands 6 (240 GHz) and 9 (690 GHz). For these initial tests, we observe a single quasar,and simply swtich between the two frequencies. These data thus are not able to inform on
the degradation of the phase transfer from one source to another, which we will test in the
future. All data were taken in TDM mode. Table 1 summarizes the BBPT tests carried out
during these observing sessions. Some of the executions were run back-to-back using similar
settings; for these, I concatenate the data for the analysis as noted in Table 1.
Since we only observed a single source per execution, I select a finite number of adjacent
low/high frequency scan pairs to treat as the “BQ” scans, which I use to solve for the
instrumental phase difference (see Section 4). I select scan pairs at the beginning, middle, andend of the executions to be approximately equally separated in time by tcrit ≈ 10 min. The
rest of the scans I treat as the “FQ” (low frequency) and “ST” (high frequency) observations,using the low frequency observations to derive a phase solution to apply to the high frequency
observations.
The BBPT script includes on option to use the scan-sequencing mode, which allows
the user to specify a list of scan-level observations to be queued in the correlator. This is
desirable for BBPT to reduce the time lag between observations at the two frequencies. An
2

additional option with this mode is pre-tuning of the LO settings. We ran several BBPT
tests with and without scan-sequencing, including one test data-set with pre-tuning. With
scan-sequencing and no pre-tuning of the LO’s, this reduced the time to switch between
frequencies from tswitch = 34 s to 29 s. With pre-tuning tswitch is reduced to 10 s. The values
for tswitch for all executions are shown in Table 1, with the ones that used scan-sequencing
and/or pre-tuning indicated.
At this time, the observations must be run in script mode (implementation of this observing mode into scheduling blocks is in progress). It is difficult to include Tsys measurements
in script mode unless they are done after every delay scan, which introduces an additionaltime lag of ∼ 20 s between adjacent observations at different frequencies. This can hinder
the ability to calibrate out the instrumental phase differences. We decided to remove theTsys measurements for the second half of the executions (see Table 1). The resulting timelag between adjacent scans ranges from tswitch = 10 s to 50 s, as listed in Table 1.
Without Tsys measurements, I am thus only testing phase calibration, and not amplitude
calibration (which we’ll want to do at some point). The observations include water vapor
radiometer (WVR) measurments, so I applied the WVR calibration to all data. Since weobserve a bright quasar, I use all scans to determine a bandpass solution.

4

Data Reduction

I reduce each observation using the same procedure. The main steps are listed below. All of
this analyis was done using CASA version 4.0.1.
1. Flag autocorrelations, and Tsys scans (if present).
2. wvrgcal, and smooth calibration to 2 s. Apply WVR calibration table to data andsplit out science spws (four in each band).
3. Flag shadowed antennas and edge channels. Inspect data with plotms and flag otherbad antennas, scans, etc.
4. Bandpass calibration:(a) gaincal with solint=‘int’ to determine phase solutions on integration time scales.
(b) bandpass with solint=‘inf’ and combine=‘scan’ to use all scans in determining
the bandpass for each spw, applying gain table above on-the-fly. This bandpass
calibration table is applied on-the-fly in all calls to gaincal below.
5. Gain calibration:(a) Run gaincal to derive the instrumental phase offset between the two bands using
selected adjacent scan pairs at the beginning, middle, and end of the observation,such that tcrit ∼ 10 min.

3

(b) Run gaincal to derive the phase solutions for all of the low frequency scans. Apply
the calibration table from the previous step on-the-fly to remove the instrumental
phase component before solving. Since this also removes offsets between the spws
and polarizations, I use combine=‘spw’ and gaintype=‘T’ in this step to increase
the signal-to-noise.
(c) Apply both calibration tables to the high frequency data. The first removes the
instrumental phase component. For the second, the phase table determined fromthe low frequency data is applied to the high frequency data via spwmap. Theinterp=‘linearPD‘ option in gaincal scales the low frequency solutions to the highfrequency data by the ratio of the frequencies (Equation 1).
Step 5 is demonstrated in Figures 1, 2, and 3. For this study, I examine both 1) applying the low frequency phase gain tables to the high frequency data without scaling by thefrequency ratio (interp=‘linear’) and 2) applying them with scaling (interp=‘linearPD’).

5

Results

5.1

Initial Checks

I did several important checks that I don’t describe in detail here, but I want to briefly
mention.
First, I tested whether the phases in the four spws (and two polarizations) within a given
band track each other well. That is, while they may be offset by a constant value, they
follow the same trend about this mean offset as a function of time. This is expected sincethese variations are due to tropopheric fluctuations which depend on frequency. I found thatthe spws within a given band do indeed trace each other well (this has also been studied byothers and reported in the previous JIRA ticket on BBPT (CSV-413).
In previous analyses (see CSV-413) it was reported that interp=‘linearPD’ was not scaling
the phases by the frequency ratio in some cases. I investigated this since we want to makesure that this option is working at the task level in CASA. I tested this by comparing thephase solutions from gaincal using interp=‘linearPD’, and using interp=‘linear’, where forthe latter, I scaled the solutions manually using the CASA table tools. These give the same
results, confirming that interp=‘linearPD’ scales by frequency as expected. The previous
reports that this was not working may have been due to errors in using spwmap to apply
solutions from one band to another.

5.2

Main Results

In Figure 3, I compare the corrected phases after applycal for one of the data-sets and asingle antenna, using Band 3 to calibrate Band 7, and using Band 7 to calibrate Band 7.
The latter is a self-cal and is used as a control case to evaluate the effects of calibrating thehigh frequency data with low frequency gain solutions. There are two main effects that will4

degrade the final image quality: 1) a mean non-zero phase offset will result in positional
errors, and 2) an increase in the corrected phase r.m.s. will spread out the signal in theimage plane. I therefore try to boil down these results from all data-sets and all baselines bylooking at the mean and standard deviation per antenna. I focus on baselines shorter than
400 m here since there are very few data points at longer baselines.
Figures 4 to 12 show the mean corrected phase for each antenna as a function of baseline
distance for the nine Band 3/Band 7 observations, using interp=‘linear’ (i.e. not scaling
the solutions by the frequency ratio). The error bars show the corrected phase r.m.s. The
results are summarized in Table 2. Each antenna shows a mean phase offset ranging (inabsolute value) from ∼ 2−20o which tends to be larger for the longer baselines (but notalways); however, the phase offset averaged over all antennas is < 5o . Table 2 also shows themean (and range of) phase r.m.s., which is displayed as a function of baseline distance forall observations in Figure 13. The phase r.m.s. ranges from ∼ 2 − 20o and tends to increase
with baseline distance. It is interesting to compare this with the phase r.m.s. for the control
case (self-calibrating the Band 7 data): the fractional increase in the r.m.s. over the self-cal
r.m.s. is also given in Table 2 and shown as a function of baseline distance in Figure 14.
There is a wide range of values in the fractional r.m.s. increase over all observations (25%
to 400%) with no obvious correlation with weather conditions (PWV), though these may
be dominated by a few outliers. The next step will be to continue with the imaging steps
and evaluate how much these effects degrade the image quality (positional errors, peak flux
attenuation, etc.).
The results for the Band 3/Band 7 observations using interp=‘linearPD’ – where thephase solutions in Band 3 are scaled by the frequency ratio and then applied to the Band
7 data – are shown in Figures 15 to 25 and summarized in Table 3. I find that the phaser.m.s. is similar (slightly higher) to that seen without frequency scaling; however, the mean
corrected phases are generally higher (i.e. worse). It is not clear why this is the case andthis needs to be investigated further. With frequency scaling (νB7 /νB3 = 3.9 in this case),
any error in measuring the instrumental phase offset between the two bands will propagate.
It’s possible that the results we are seeing imply that values of tswitch = 10-50 s are not fastenough to remove the effects of tropospheric fluctuations. It is interesting to note that forthe one data-set where scan sequencing and pre-tuning of the LO was used (X3a+X6b) –where tswitch is only 10 s – the phase transfer was not improved. I also tried calibrating out
the phase offset using an average over the whole execution for Xc87, with the idea that this
could help average out atmospheric fluctuations, but this did not improve the observed phasescatter.
The results for the Band 6/Band 9 observations using interp=‘linear’ are shown in Figures 26 to 30 and summarized in Table 4; the results using interp=‘linearPD’ are shown in
Figures 31 to 35 and summarized in Table 5. For interp=‘linear’, we see mean phase offsets
similar to those observed for the Band 3/Band 7 data (absolute values up to ∼ 20o ), but themean over all antennas is . 1o . Again, there is a large range in the fractional increase in
the phase r.m.s., particularly for the X33+X66 observation. We see the same effect as with
the Band 3/Band 7 data-sets, where using interp=‘linearPD’ results in slightly higher phase5

r.m.s. and larger mean offsets.

5.3

Other Tests

I did a few additional tests that I won’t present in detail, but will mention here.
I used one of the data-sets (Band 3 to Band 7) to verify that applying the WVR corrections improves BBPT. I find that the phase r.m.s. in the Band 7 data after applying theBand 3 gain table is indeed lower when the WVR corrections are applied to both bands.
There are some scans for which the WVR corrections make the phases considerably worse.
These seem to occur at random times. I flag such scans in my analysis above.
I did some moderate testing of changing the value of tcrit for Xc87, varying between∼ 5-25 min, to see if the mean corrected phases and r.m.s decrease with smaller values. The
value of tcrit did not make any difference.
Finally, mathematically speaking, Steps 5a and 5b can be reversed – that is, one can first
derive the low frequency phase solutions, then use adjacent scan pairs in both frequencies
to derive the phase offset. I tested both methods and find that they give similar results.
However, the method described in Section 4 allows us to combine spectral windows andpolarizations and increase the signal to noise, so I chose this one.

6

Conclusions and Future Tests

The main results from these test data are:
1. The observed phases in the four spws and two polarizations track each other very well,and can thus be combined after running gaincal on a subset of the scans to increase
the signal-to-noise. This is good, since in principle we will be able to choose relatively
weak phase calibrators (even in Band 3) that are spatially close to the target of interest
for BBPT.
2. Using interp=‘linearPD’ in applycal scales the phase gains by the ratio of the frequencies in the two bands, as expected. This is in contrast to (some) previous tests, whichwere likely using spwmap to transfer the phases at one spw to another incorrectly.
3. For both Band 3/Band 7 and Band 6/Band 9 BBPT tests, we see mean corrected
phases from ∼ 2-20%, with phase r.m.s. that increases with baseline distance. The
next step is to image the high frequency data to determine the overall effect on theimage quality.
4. Using interp=‘linearPD’ to scale the low frequency phase solutions to high frequency
in general gives worse results, which is opposite from what we expect. This could meanthat switching times between the two frequencies of < 10 s are needed. However, wehave only a single data-set with tswitch . 30 s, which was executed after a major power
disruption at the site, and the system had been brought back up without full testing6

of the antennas, correlator, etc. It may be worth doing a few more executions withscan sequencing and pre-tuning of the LO to get more data with short tswitch .
Very few of the observations had baselines > 400 m, so I have focused on the phasetransfer on smaller baselines. The few data-sets with longer baselines show that they follow
the general trend of increasing residual phase r.m.s. with baseline distance. BBPT on longer
baselines may be challenging, and we will need more data to test this.

7Table 1: Band-to-band Phase Transfer Data: April-May 2013
Date
17-Apr-2013
21-Apr-2013
21-Apr-2013
21-Apr-2013
21-Apr-2013
22-Apr-2013
08-May-2013
08-May-2013
10-May-2013
08-May-2013
08-May-2013
08-May-2013
09-May-2013

ASDM Name
uid A002 X61068c Xc87
uid A002 X617ed5 X12
uid A002 X617ed5 X4a5
uid A002 X616da1 X530
uid A002 X616da1 X717
uid A002 X618902 X129
uid A002 X62932c X358
uid A002 X62932c X2f6
uid A002 X62932c X327b
uid A002 X62cc28 X3a
uid A002 X62cc28 X6bb
uid A002 X62932c X1c5
uid A002 X62932c X202b
uid A002 X62932c X6e
uid A002 X62932c Xabb
uid A002 X62932c X188a
uid A002 X62a5df X33
uid A002 X62a5df X66b

Bands
3/7
3/7
3/7
3/7
3/7
3/7
3/7
3/7

Source
Nant
3c279
26
3c279
32
1924-292 30
3c279
29
3c279
29
3c279
30
1924-292 20
1924-292 20

PWV (mm)
1.1
1.2
1.2
1.1
1.1
1.2
0.45
0.42

tswitch (s)
51
52
51
53
53
40
34
29

scanSeq?
no
no
no
no
no
no
no
yes

pre-tune LO?
no
no
no
no
no
no
no
no

3/7

3c279

16

1.05

10

yes

yes

6/9

1924-292

26

0.45

34

no

no

6/9

1924-292

27

0.49

29

yes

no

6/9
6/9

1924-292
3c279

26
33

0.47
0.36

29
29

yes
yes

no
no

Notes: a This observation had low S/N in both bands and did not give good solutions. I needto look more carefully at these data to figure out why (possibly bad WVR); for now, I do
not include this data-set in the analysis. b This execution was run immediately after theprevious one using the same settings, so I concatenate these data for all analyses in thisreport.

Table 2: Band 7 Calibrated by Band 3: interp=‘linear’
ASDM(s)Phase r.m.s. (deg)Self-cal
Xc87
10.4 (7.6 - 12.8)X12
4.1 (2.8 - 6.1)
X4a5
4.5 (3.0 - 6.1)
X530
6.4 (4.0 - 9.9)
X717
6.0 (4.0 - 8.2)
X129
6.1 (4.2 - 19.1)
X358
1.9 (1.3 - 2.7)
X2f6+X327
2.9 (1.8 - 14.7)
X3a+X6b3.9 (3.2 - 4.8)

Phase r.m.s. (deg) Fractional Increaselow-ν calin r.m.s.
13.1 (8.6 - 17.3)
0.25 (0.04 - 0.51)
8.9 (3.7 - 16.4)
1.15 (0.22 - 2.27)
8.6 (4.5 - 13.1)
0.89 (0.33 - 1.60)
14.4 (9.5 - 22.5)
1.25 (0.46 - 2.29)
9.5 (5.9 - 14.5)
0.60 (0.12 - 1.63)
9.1 (5.6 - 20.1)
0.54 (0.05 - 1.45)
5.5 (2.2 - 10.2)
1.71 (0.38 - 3.16)
11.0 (3.4 - 22.7)
4.01 (0.42 - 11.65)
13.5 (6.9 - 21.5)
2.39 (1.10 - 4.16)

Mean Phase (deg)low-ν cal
2.7 (-4.3 - 11.3)
1.3 (-2.3 - 9.4)
1.3 (-2.9 - 8.1)
1.0 (-6.6 - 5.2)
-1.6 (-6.1 - 2.7)
3.8 (-4.3 - 18.0)
0.3 (-3.1 - 5.0)
4.6 (-3.1 - 15.6)
1.4 (-11.1 - 13.4)

Notes: For each column, the first value is the mean from all antennas, and the range listed
in parentheses shows the minimum and maximum values. Column four shows the fractional
increase in the corrected phase r.m.s. when using the low-frequency gain solutions tocalibrate the high frequency data.

8

Table 3: Band 7 Calibrated by Band 3: interp=‘linearPD’
ASDM(s)
Xc87
X12
X4a5
X530
X717
X129
X358
X2f6+X327
X3a+X6bPhase r.m.s. (deg) Phase r.m.s. (deg)Self-callow-ν cal10.4 (7.6 - 12.8)
15.1 (8.8 - 22.6)
4.1 (2.8 - 6.1)
9.5 (4.3 - 16.3)
4.5 (3.0 - 6.1)
9.3 (4.8 - 14.0)
6.4 (4.0 - 9.9)
16.6 (9.3 - 23.5)
6.0 (4.0 - 8.2)
10.7 (6.8 - 16.0)
6.1 (4.2 - 19.1)
10.3 (6.0 - 22.4)
1.9 (1.3 - 2.7)
6.1 (2.0 - 10.2)
2.9 (1.8 - 14.7)
8.7 (3.5 - 20.0)
3.9 (3.2 - 4.8)
15.1 (10.6 - 22.6)

Fractional Increase Mean Phase (deg)in r.m.s.
low-ν cal
0.44 (0.05 - 1.06)
8.0 (-4.5 - 25.9)
1.28 (0.41 - 2.25)
1.4 (-3.8 - 7.9)
1.05 (0.27 - 1.78)
0.2 (-4.4 - 8.1)
1.59 (0.51 - 2.58)-0.2 (-11.9 - 12.3)
0.80 (0.22 - 1.75)-3.5 (-9.0 - 1.3)
0.76 (0.15 - 1.77)
6.9 (-3.0 - 32.2)
2.01 (0.42 - 5.11)
0.7 (-5.3 - 5.2)
2.77 (0.37 - 4.77)-0.3 (-4.5 - 5.1)
2.85 (1.82 - 4.66) -14.2 (-22.6 - -6.5)

Notes: For each column, the first value is the mean from all antennas, and the range listed
in parentheses shows the minimum and maximum values. Column four shows the fractional
increase in the corrected phase r.m.s. when using the low-frequency gain solutions tocalibrate the high frequency data.
Table 4: Band 9 Calibrated by Band 6: interp=‘linear’
ASDM(s)Phase r.m.s. (deg)Self-cal
X1c5+X202 19.0 (15.0 - 27.0)
X6e+Xab24.1 (19.5 - 37.2)
X33+X66
9.2 (3.0 - 19.2)

Phase r.m.s. (deg) Fractional Increaselow-ν calin r.m.s.
16.1 (10.3 - 26.4) -0.13 (-0.36 - 0.23)
25.7 (15.0 - 52.2)
0.07 (-0.23 - 1.36)
25.9 (10.2 - 54.1)
2.90 (-0.14 - 8.95)

Mean Phase (deg)low-ν cal
0.1 (-5.4 - 4.8)
-1.1 (-21.5 - 18.2)-0.9 (-17.7 - 17.9)

Notes: For each column, the first value is the mean from all antennas, and the range listed
in parentheses shows the minimum and maximum values. Column four shows the fractional
increase in the corrected phase r.m.s. when using the low-frequency gain solutions tocalibrate the high frequency data.
Table 5: Band 9 Calibrated by Band 6: interp=‘linearPD’
ASDM(s)Phase r.m.s. (deg)Self-cal
X1c5+X202 19.0 (15.0 - 27.0)
X6e+Xab24.1 (19.5 - 37.2)
X33+X66
9.2 (3.0 - 19.2)

Phase r.m.s. (deg) Fractional Increaselow-ν calin r.m.s.
20.0 (10.9 - 31.2)
0.08 (-0.32 - 0.99)
28.4 (16.0 - 55.6)
0.18 (-0.18 - 1.51)
27.1 (11.2 - 53.8)
3.09 (-0.34 - 8.88)

Mean Phase (deg)low-ν cal
-1.8 (-7.4 - 5.4)
-1.9 (-25.9 - 15.9)-6.3 (-30.9 - 11.7)

Notes: For each column, the first value is the mean from all antennas, and the range listed
in parentheses shows the minimum and maximum values. Column four shows the fractional
increase in the corrected phase r.m.s. when using the low-frequency gain solutions tocalibrate the high frequency data.
9

Figure 1: Demonstrates Step 5a of the BBPT data processing described in Section 4, where
the instrumental phase difference between the low and high frequency bands are determined.
This is from a single observation (X3a+X6b), switching between Band 3 (blue) and Band
7 (red) on 3c279, and shows only two spws and the XX polarization for one antenna. The
small circles show the results from running gaincal on all scans; the resulting table is not
used for futher calibration, but is shown only to demonstrate the phase variations over thecourse of the observation and the scan sequence. The large squares show the beginning andend scan pairs used to derive the instrumental phase difference between the two bands. The
gain table derived from these scan pairs is applied to the Band 3 and Band 7 data in Steps
5b and 5c.

10Figure 2: Demonstrates Step 5b of the BBPT data processing described in Section 4, where
the phase solution is determined from the low frequency data after applying the instrumental
phase offset determined in Step 5a (note that the scans used to derive this offset are now at
0o as expected). This gain table is applied to the Band 7 data in Step 5c. See caption to
Figure 1 for details of this observation.

11

Figure 3: Demonstrates Step 5c of the BBPT data processing described in Section 4, where
the phase solution from the low frequency data is applied to the high frequency data. The
red squares show the corrected Band 7 phases calibrated by Band 3 (per integration, averaged over all channels), and the red curve traces the per-scan average. In this case I usedinterp=‘linear’ (does not scale the phases by the frequency ratio). The black squares show
the results using Band 7 to calibrate Band 7 for comparison. See caption to Figure 1 fordetails of this observation.

12

Figure 4: Mean corrected phase for each antenna as a function of baseline distance for theobservation Xc87. The Band 7 data were calibrated using the Band 3 gain solutions withinterp=‘linear’ (no scaling of the solutions by the frequency ratio). The blue circles show
the mean phase offset averaged over all scans, and the blue error bars show the standard
deviation. The black error bars centered on zero show the standard deviation of the corrected
phases using Band 7 gain solutions (self-cal). Figures 5 to 12 show the same thing for theother Band 3/Band 7 observations.

13

Figure 5: Mean corrected phase for each antenna as a function of baseline distance for theobservation X12. See the caption to Figure 4 for a full description.

14

Figure 6: Mean corrected phase for each antenna as a function of baseline distance for theobservation X4a5. See the caption to Figure 4 for a full description.

15

Figure 7: Mean corrected phase for each antenna as a function of baseline distance for theobservation X530. See the caption to Figure 4 for a full description.

16

Figure 8: Mean corrected phase for each antenna as a function of baseline distance for theobservation X717. See the caption to Figure 4 for a full description.

17

Figure 9: Mean corrected phase for each antenna as a function of baseline distance for theobservation X129. See the caption to Figure 4 for a full description.

18

Figure 10: Mean corrected phase for each antenna as a function of baseline distance for theobservation X358. See the caption to Figure 4 for a full description.

19

Figure 11: Mean corrected phase for each antenna as a function of baseline distance for theobservation X2f6+X327. See the caption to Figure 4 for a full description.

20

Figure 12: Mean corrected phase for each antenna as a function of baseline distance for theobservation X3a+X6b. See the caption to Figure 4 for a full description.

21

Figure 13: Corrected phase r.m.s. for each antenna as a function of baseline distance for all
Band 3/Band 7 observations as labeled, using interp=‘linear’ (no scaling of the solutions by
the frequency ratio).

22

Figure 14: Fractional increase in the corrected phase r.m.s. for each antenna as a functionof baseline distance for all Band 3/Band 7 observations as labeled, using interp=‘linear’ (noscaling of the solutions by the frequency ratio).

23

Figure 15: Mean corrected phase for each antenna as a function of baseline distance for theobservation Xc87. The Band 7 data were calibrated using the Band 3 gain solutions withinterp=‘linearPD’ (scaling of the solutions by the frequency ratio). The blue circles show
the mean phase offset averaged over all scans, and the blue error bars show the standard
deviation. The black error bars centered on zero show the standard deviation of the corrected
phases using Band 7 gain solutions (self-cal). Figures 16 to 23 show the same thing for theother Band 3/Band 7 observations.

24

Figure 16: Mean corrected phase for each antenna as a function of baseline distance for theobservation X12. See the caption to Figure 15 for a full description.

25

Figure 17: Mean corrected phase for each antenna as a function of baseline distance for theobservation X4a5. See the caption to Figure 15 for a full description.

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Figure 18: Mean corrected phase for each antenna as a function of baseline distance for theobservation X530. See the caption to Figure 15 for a full description.

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Figure 19: Mean corrected phase for each antenna as a function of baseline distance for theobservation X717. See the caption to Figure 15 for a full description.

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Figure 20: Mean corrected phase for each antenna as a function of baseline distance for theobservation X129. See the caption to Figure 15 for a full description.

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Figure 21: Mean corrected phase for each antenna as a function of baseline distance for theobservation X358. See the caption to Figure 15 for a full description.

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Figure 22: Mean corrected phase for each antenna as a function of baseline distance for theobservation X2f6+327. See the caption to Figure 15 for a full description.

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Figure 23: Mean corrected phase for each antenna as a function of baseline distance for theobservation X3a+X6b. See the caption to Figure 15 for a full description.

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Figure 24: Corrected phase r.m.s. for each antenna as a function of baseline distance for all
Band 3/Band 7 observations as labeled, using interp=‘linearPD’ (scaling of the solutions by
the frequency ratio).

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Figure 25: Fractional increase in the corrected phase r.m.s. for each antenna as a functionof baseline distance for all Band 3/Band 7 observations as labeled, using interp=‘linearPD’(scaling of the solutions by the frequency ratio).

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Figure 26: Mean corrected phase for each antenna as a function of baseline distance for theobservation X1c5+X202. The Band 9 data were calibrated using the Band 6 gain solutions
with interp=‘linear’ (no scaling of the solutions by the frequency ratio). The blue circles
show the mean phase offset averaged over all scans, and the blue error bars show the standard
deviation. The black error bars centered on zero show the standard deviation of the corrected
phases using Band 9 gain solutions (self-cal). Figures 27 to 28 show the same thing for theother Band 6/Band 9 observations.

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Figure 27: Mean corrected phase for each antenna as a function of baseline distance for theobservation X6e+Xab. See the caption to Figure 26 for a full description.

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Figure 28: Mean corrected phase for each antenna as a function of baseline distance for theobservation X33+X66. See the caption to Figure 26 for a full description.

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Figure 29: Corrected phase r.m.s. for each antenna as a function of baseline distance for all
Band 6/Band 9 observations as labeled, using interp=‘linear’ (no scaling of the solutions by
the frequency ratio).

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Figure 30: Fractional increase in the corrected phase r.m.s. for each antenna as a functionof baseline distance for all Band 6/Band 9 observations as labeled, using interp=‘linear’ (noscaling of the solutions by the frequency ratio).

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Figure 31: Mean corrected phase for each antenna as a function of baseline distance for theobservation X1c5+X202. The Band 9 data were calibrated using the Band 6 gain solutions
with interp=‘linearPD’ (scaling of the solutions by the frequency ratio). The blue circles
show the mean phase offset averaged over all scans, and the blue error bars show the standard
deviation. The black error bars centered on zero show the standard deviation of the corrected
phases using Band 9 gain solutions (self-cal). Figures 32 to 33 show the same thing for theother Band6/Band9 observations.

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Figure 32: Mean corrected phase for each antenna as a function of baseline distance for theobservation X6e+Xab. See the caption to Figure 31 for a full description.

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Figure 33: Mean corrected phase for each antenna as a function of baseline distance for theobservation X6e+Xab. See the caption to Figure 31 for a full description.

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Figure 34: Corrected phase r.m.s. for each antenna as a function of baseline distance for all
Band 6/Band 9 observations as labeled, using interp=‘linearPD’ (scaling of the solutions by
the frequency ratio).

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Figure 35: Fractional increase in the corrected phase r.m.s. for each antenna as a functionof baseline distance for all Band 6/Band 9 observations as labeled, using interp=‘linearPD’(scaling of the solutions by the frequency ratio).

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