Preliminary Progress Report on the Implementation of the
Bandwidth Transfer Technique for High Frequency
Observations
ALMA Technical Note Number: 9
Status: FINAL
Prepared by:

Organization:

Date:

Jennifer Donovan Meyer(NAASC/NRAO)

ALMA

08 August 2014

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CAPABILITIES SUMMARY
To: Takahashi Satoko (JAO), EOC Management
From: Jennifer Donovan Meyer (NAASC)
Date: 08/17/2014
Subject: Bandwidth Switching Progress Report
Reporting JIRA ticket:
http://jira.alma.cl/browse/CSV-3074

Datasets:
1 June, uid___A002_X83210a_Xfb, Band 7 (too much phase decorrelation)
3 June, uid___A002_X833c94_Xf37, Band 8 (too much phase decorrelation)
19 June, uid___A002_X84bb63_X2df, Band 3, wide FDM (3840) to narrow FDM (3840)(too much phase decorrelation)
19 June, uid___A002_X84bb63_X68, Band 3, PWV~1.8.
TDM (128) to narrow FDM (3840)
21 June, uid___A002_X84e1f2_X45, Band 7, PWV~1.6.
TDM (128) to narrow FDM (3840)
23 June, uid___A002_X8505d8_X1eae, Band 9, PWV~0.83.
ICT-331 fix required first.
TDM (128) to narrow FDM (3840)

8 July, uid___A002_X8658de_X3a4, Band 9, PWV~0.63.
TDM (128) to narrow FDM (3840), plus
intermediate FDM (3840) to narrow FDM
Motivation:
Calibrating ALMA high frequency observations in Bands 8, 9, and 10 will be limitedby the availability of nearby phase calibrators. This will be particularly problematicfor narrow band observations (bandwidths less than 300 MHz) at high frequency.
Observing with bandwidth switching will enable higher signal-to-noise observationsof faint calibrators found closer to the science targets, thus allowing better
atmospheric calibration of those targets than bright calibrators at larger distances.
This technique involves transferring the phase solutions of faint calibrators
observed in wide spectral windows to science targets observed in narrow spectral

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windows. Eventually, this technique will be combined with the Band-to-Band (B2B)
transfer technique in order to calibrate high frequency, narrow band observations
with lower frequency, wide band calibrator observations.

Testing method:
Observe two nearby bright quasars, one with wide spectral windows and one withnarrow spectral windows. Apply the phase solutions from the wide window quasar
observations to the narrow window quasar observations. In the first three usable
data sets (in Bands 3, 7, and 9), we demonstrate that this technique works. In the
final Band 9 dataset (X3a4), we add an intermediate resolution FDM window to theobserving setup to compare the noise in the final calibrated images, using first the
TDM window(s) and second the FDM window for the phase transfer.

Technique demonstration:
In the first three SBs, the script generator is used to make the data reduction script.
In each case, it recognized that the observation intended to use bandwidth
switching. Some modification of the generated script was necessary, and thechanges are summarized in the following section. The images resulting from thesedemonstration reductions are shown in Figures 1, 2, and 3.

Figure 1: Image of 3C274 in four 58.6 MHz (FDM) windows in Band 3 (X68), using
phase transfer from four Band 3 TDM windows.

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Figure 2: Image of J1923-210 in four 58.6 MHz (FDM) windows in Band 7 (X45),
using phase transfer from four Band 7 TDM windows.

Figure 3: Image of J1923-210 in four 58.6 MHz (FDM) windows in Band 9 (X1eae),
using phase transfer from four Band 9 TDM windows.

The observations are set up with four 2 GHz TDM windows and four 58.6 MHz FDM
windows. In each case, there is one-to-one correspondence between the TDM andFDM windows; no TDM windows are overlapping. A bright bandpass calibrator isobserved in the wide windows (field = ‘0’, spw = ‘0~3’) and in the narrow windows(field = ‘1’, spw = ‘4~7’), a flux calibrator is observed in the wide windows (field =‘2’, spw = ‘0~3’), and then observations of the phase calibrator (field = ‘3’, spw =‘0~3’) and target (field = ‘4’, spw = ‘4~7’) are alternated until the end of the SB.

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Additions/alterations to the data reduction script:-- Bandpass. The automatically generated script does not account for the bandpass
calibration in the narrow windows; in the bandpass calibration step (12), add asecond (solint=int, field=1) gaincal for the narrow window, and set append=True. At
band 9 (and likely 10), additional averaging will likely be necessary in both time andfrequency, but try to average more in frequency than time. Also create a second callto bandpass for the field=1 source, and specify the spw range in both calls (field=0
and spw=0~3 in the first, and field=1 and spw=4~7 in the second). Add
append=True to the second call. These should both be solint=inf, and again in band
9 (and 10) some additional averaging in frequency will likely be necessary.
-- Gain calibration. In the gain calibration step (14), the instrumental phase offsets
are determined in the .phase_pre_offsets_inf table with field=0, solint=inf (this table
does not need to be changed). The generated spwmap maps the narrow windows to
the wide ones:
phasemap = range(8)phasemap[0] = 0
phasemap[1] = 1
phasemap[2] = 2
phasemap[3] = 3
phasemap[4] = 0
phasemap[5] = 1
phasemap[6] = 2
phasemap[7] = 3

The second gaincal finds the offset between the wide and narrow windows in the.phase_offsets_inf table; set this to field=1, solint=inf, and add interp = ['', 'linear'],spwmap = [ [], phasemap].

The third gaincal corrects the short timescale variability in the wide window
calibrators (.phase_int). Remove '1' from the list of fields and add spw='0~3' and set
gaintable = ['uid___A002_X84e1f2_X45.ms.split.bandpass',‘file.ms.split.phase_pre_offsets_inf']. I have also been creating a narrow band shorttimescale variability plot, with field='1', spw='4~7', interp = [‘’, ‘linear’], gaintable =[‘file.ms.split.bandpass', ‘file.ms.split.phase_pre_offsets_inf',‘file.ms.split.phase_offsets_inf'], spwmap = [ [], phasemap, [] ].

The fourth gaincal sets the amplitude solutions; again split out field = ‘1’ into its own
call to gaincal and set append = True. In the field = ‘0,2,3’ call, use gaintable =[‘file.ms.split.bandpass', ‘file.ms.split.wide.phase_int',‘file.ms.split.phase_pre_offsets_inf']), and in the field = ‘1’ call, use gaintable =[‘file.ms.split.bandpass', ‘file.ms.split.phase_int', ‘file.ms.split.phase_pre_offsets_inf',‘file.ms.split.phase_offsets_inf'], spwmap = [[], [], phasemap, []]). Note that theAtacama Large Millimeter/
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reductions described in this document are largely phase calibrations only, but this is
how the amplitude calibration would work.
The fifth gaincal sets the long timescale phase variations in the wide window gain
calibrator (.phase_inf). Remove ‘1’ from the field list and add spw=’0~3’. Heregaintable = [‘file.ms.split.bandpass',’file.ms.split.phase_pre_offsets_inf']).

-- Applycal.
For the wide window bandpass calibrator (field = ‘0’), gaintable =[‘file.ms.split.bandpass', ‘file.ms.split.wide.phase_int',‘file.ms.split.phase_pre_offsets_inf'], gainfield = ['', '0', '0'], spwmap = [ [], phasemap,[] ].
For the narrow window bandpass calibrator (field = ‘1’), gaintable =[‘file.ms.split.bandpass', ‘file.ms.split.phase_int',’file.ms.split.phase_pre_offsets_inf',‘file.ms.split.phase_offsets_inf'], gainfield = ['1', '1','', ''], spwmap = [ [],[], phasemap,[]].
For the flux calibrator (field = ‘2’, though I only phase calibrated most of the data
shown here), gaintable = [‘file.ms.split.bandpass', ‘file.ms.split.phase_int',‘file.ms.split.flux_inf', ‘file.ms.split.phase_pre_offsets_inf'], gainfield = [‘0’, ‘2’, ‘2’,’’],
spwmap = [ [], [], [], [] ].

For the phase calibrator (field = '3'), gaintable = [‘file.ms.split.bandpass',‘file.ms.split.phase_inf',’file.ms.split.phase_pre_offsets_inf', ‘file.ms.split.flux_inf'],
gainfield = ['0', '3','', '3'], interp = ['', 'linearPD', '', ''], spwmap = [[], [], [], []].
*Note that interp = ‘linearPD’ has created some problems; this may need to
be changed to interp = ‘linear’.

For the science target (field = ‘4’), gaintable = [‘file.ms.split.bandpass',‘file.ms.split.phase_inf', ‘file.ms.split.phase_pre_offsets_inf',‘file.ms.split.phase_offsets_inf', ‘file.ms.split.flux_inf'], gainfield = ['1', '3', '', '', '3'],
interp = ['', 'linearPD', '', '', ''], spwmap = [[], phasemap, phasemap, [], phasemap].
*Note that interp = ‘linearPD’ has created some problems; this may need to
be changed to interp = ‘linear’.

A note on interp = ‘linearPD’: as reported in CAS-6797, adding ‘PD’ to theinterpolation setting leads to (incorrect) residual phase offsets when using phasesolutions averaged to the central frequency of an SPW. This is due to the fact thatthe phase delays are calculated using the frequency at the edge of the SPW. These
residual phases are of order 1.5-2 degrees in Band 3, up to 0.5 degree in Band 7, andup to 0.2 degree in Band 9. I have left the phase delay correction in the applycals
only for the .phase_inf table applications to fields 3 and 4; with further testing, thisAtacama Large Millimeter/
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makes very little difference in the rms of the final image (at the 1-2% level), with the‘linearPD’ case being marginally worse than the ‘linear’ case.

Suggestions for changes to the observing setup and observations still needed:-- As the narrow bandpass calibration is very signal-to-noise limited in the
narrowest (62.5 MHz) windows, investigate the possibility of using a solar systemobject to do the narrow bandpass calibration-- Currently, the phase offsets between the wide and narrow window are measured
using observations of fields 0 and 1, which are generally observed separated by 1520 minutes. Any change in the atmosphere over this time, which results in more
phase offset than is purely instrumental, is therefore included. Adding an additional
bandpass calibration (in the wide windows) at the end of the SB, or even
immediately following the narrow bandpass observation, to re-measure the phaseoffset between the wide and narrow window bandpasses will yield an idea of how
much phase offset is instrumental and how much is due to changes in theatmosphere.
-- Nagging issues with phase decorrelation (reported in PRTSPR-5946 and ICT3186) are occasionally seen when switching between FDM and TDM setups (seeFigure 4). Turning off scan sequences, an expert mode option, has been identified asa workaround solution. This suggestion was implemented in a successful Band 10
execution during the 8 July EOC week, but the weather was not conducive to highfrequency observing. Further testing of this option in the bandwidth switchingobservations is suggested. In addition, as reported in PRTSIR-3082, this observation
caused strange behavior in the numbering of target fields in the imported SB, which
is hopefully not related to the scan sequence fix but should also be re-tested.

Figure 4: (Left to right) Band 7 (Xfb), Band 8 (Xf37), Band 3 (X68) uncalibrated
amplitude vs. time in field 3 (phase calibrator, green) and field 4 (science target, brown).
Generally the first 30 seconds – the first few subscans of an observation – are affected. In
Xfb, it affects the first and last FDM subscans and the first (all) TDM subscans; in Xf37,
it affects the first FDM and TDM subscans; and in X68, it affects the first FDM subscans.

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The issue is intermittent in all cases and especially so in X68.
-- In addition to the items listed above, testing observations still needed include:demonstration that this method works in Band 10 (using narrow windows for thescience target that are at least 125 or 250 MHz), inclusion of the 7m antennas in the
bandwidth switching experiments (since these antennas will be the most signal-tonoise limited at high frequencies) now that the technique has been successfully
demonstrated for the 12m array, and observations in varying conditions to test thelimits of this calibration method with PWV, width of the narrow bandpass windows,
flux of the phase calibrator, and the length of the longest baselines for B9/10.
The necessity of the narrow bandpass measurement:
Since we are signal-to-noise limited in the narrow SPWs at high frequencies, testingis performed to check whether the narrow bandpass correction is really necessary.
The results are tabulated in Table 1 below. Specifically, we compare the applicationof the wide bandwidth bandpass (low frequency resolution) and narrow bandwidth
bandpass (high frequency resolution), and in Band 9 we also compare the imaging
results using no bandpass correction at all. Since these are only calibrated in phase,the relative results are meaningful and are presented normalized to the narrow
bandwidth run. The lack of amplitude calibration may also lead to some bias in the
final “no bandpass” case for Band 9. Finally, we test the effect of including the WVR
correction in the Band 9 SB (for the median PWV of 0.83).
Table 1: Results of testing the inclusion of the bandpass correction.

Band 3, wide
Band 3,narrow
Band 7, wide
Band 7,
narrow
Band 9, wide
Band 9,narrow
Band 9, nobandpass
Band 9,narrow, no
WVR

Normalized
rms
1.02
1.0

Normalized
peak
0.99
1.0

Normalized
flux density
0.99
1.0

SNR
(peak/rms)
163
167

0.89
1.0

0.91
1.0

0.92
1.0

29
28

1.01
1.0

0.91
0.81

1.0
1.0

0.93
0.57

0.99
1.0

0.95
0.86

124
126

28
19

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In Bands 3 and 7, the narrow bandpass yields a better image of the final calibrator
with a lower rms and higher peak/flux density/SNR of the calibrator itself at the 12% level.

In Band 9, where we are more signal-to-noise limited, the case is less clear. The rms
is better in the wide bandpass (and potentially biased) no bandpass cases, but thephase errors lead to flux being distributed farther from the peak. Here thedifferences are of order 10%. However, the SNR is very similar in all three cases.

Including the WVR correction increases the rms noise in the final image by 20%, but
it does a much better job of recovering flux at the phase center than the “no WVR”
case (though in fact, the phase center in the “no WVR” case is closer to the real
location of the target; see the section on position offsets below).

The reduction of X3a4:
In the second Band 9 observation, the observing setup includes an intermediate
resolution FDM SPW (SPW 4) and an additional high resolution FDM SPW (SPW 5)
in addition to the eight usual SPWs (four TDM, SPW 0~3, and four FDM 58.6 MHz
wide, SPW 6~9). The central frequencies of the four TDM windows are the same, thefrequencies of SPW 5 and 6 are the same, and those of SPW 7 and 8 are the same.
The FDM windows are all located within the frequency range of the TDM windows.
Phase transfer is applied in this reduction from the wide windows (SPW 0,2), as well
as from the intermediate window (SPW 4), to the narrow windows (SPW 5~9).
Currently the script generator fails with this type of observation; a script isgenerated by hand which matches the updates described above. The observation istaken in better weather than the previous Band 9 SB, but the elevation is lower,
resulting in an elongated beam shape in the final images. The images with the TDM
phase transfer and FDM phase transfer look very similar; the TDM phase transfer
image is shown in Figure 5. Transferring phase solutions from the wide TDM
windows and intermediate FDM windows does not make much of a difference in the
final images; their rms values are very similar.

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Figure 5: Image of 3C274 in four 58.6 MHz (FDM) windows in Band 9 (X3a4), using
phase transfer from one Band 9 TDM window (or one Band 9 intermediate
resolution FDM window).

Position offsets when doing bandwidth switching:
In the Band 3 demonstration data, the peak pixel of the science target (a quasar witha known position, which should be located at the phase center) is offset from thephase center by 0.14”. The beam size is 1.2”x0.93”, so the offset is well less than one
beam.
In the Band 7 demonstration data, the peak pixel of the science target is offset fromthe phase center by 0.28”. The beam size is 0.32”x0.28”, so the offset is roughly thesize of one beam.

In the Band 9 demonstration data, the peak pixel of the science target is offset fromthe phase center by 0.08”. The beam size is 0.19”x0.15”, so the offset is roughly half
the size of the beam. In the no WVR case, the offset drops to 0.03”, less than aquarter of the beam size.

In the Band 9 (X3a4) data, the peak pixel of the science target is offset from thephase center by 0.03” when using a TDM window for the transfer and 0.02” whenusing the FDM window for the transfer. The beam size is 0.36”x0.18”, so the offset iswell less than one beam in both cases.

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Phase offsets between wide and narrow windows:
Instrumental phase offsets exist between the TDM and FDM windows contained
within them. These are measured using the bandpass calibrator observations inboth sets of spectral windows. First, the instrumental phase offsets relative to the
SPWs of the reference antenna are derived using solint = ‘inf’ and field = ‘0’ for thewide windows (with the bandpass solutions applied on the fly); this is the.phase_pre_offsets_inf table. Next, the narrow bandpass solutions and wide window
instrumental phase offsets table are applied on the fly to the narrow window
observation of the bandpass calibrator (field = ‘1’); the resulting phase residuals,
contained in the .phase_offsets_inf table, are the offsets between the wide andnarrow windows. There is some atmospheric change that is currently incorporated
into these solutions since the two observations of the bandpass calibrator are taken
15-20 mintues apart; in the “suggestions” section, we recommend to take anothermeasurement of the bandpass calibrator later in the SB to quantify how stable themeasured offset table is with time.
In Band 3 (X68), the phase offsets between the TDM and FDM windows range from–10 to 10 degrees with a few outliers reaching 20 degrees, and the phase offsets inthe two polarizations track each other to within roughly 5 degrees. The four SPWs
on each antenna generally vary in the same direction (Figure 6).

Figure 6: FDM to TDM window phase offsets in Band 3 (X68).

In Band 7 (X45), the phase offsets vary between roughly –50 and 50 degrees, withoutliers up to 100 degrees of offset. Again, the two polarizations and four SPWs
exhibit fairly consistent behavior to each other (Figure 7).

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Figure 7: FDM to TDM window phase offsets in Band 7 (X45).

In Band 9 (X1eae), the behavior is similar to Band 7 (X45); the phase offsets
generally range between –40 to 40 degrees with only one outlier at larger offset.
Here the two polarizations do not track as closely as at the lower frequencies, but
their behavior trends in the same direction (with a couple of exceptions that havelarger, tens of degrees, of offset between them). The behavior is roughly similar
between SPWs (Figure 8). SPW 6 has fewer solutions than the other windows.

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Figure 8: FDM to TDM window phase offsets in Band 9 (X1eae).

To examine the effect of the WVR correction on the phases in the Band 9 SB (X1eae),
the same reduction is also run without applying the WVR table. Phase offsets on
individual antennas generally change compared to the version of the reduction
using WVR, but both versions have similar offset absolute values overall (Figure 9).

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Figure 9: FDM to TDM window phase offsets in Band 9 (X1eae), the same as in
Figure 8, with no WVR correction applied.

Finally, we address the phase offsets measured in the second Band 9 SB (X3a4).
First, the TDM-to-FDM phase transfer is performed twice using both SPW 0 and
SPW 2 as the wide band reference window. Next, the FDM-to-FDM phase transfer isperformed using SPW 4 as the reference window. Remember that in this case, allfour TDM windows and the intermediate FDM window have (roughly) the same
central frequency, and all four narrow FDM windows lie within them.

When using SPW 0 as a reference, the magnitude of the phase offsets in SPW 6 aresimilar to those seen in B9/X1eae (roughly ranging from –40 to 40 degrees), but theother three SPWs display much larger phase offsets (up to roughly –160/160
degrees). When using SPW 2 as a reference, the same behavior is seen for SPW 8(offsets are in the range of –40/40 degrees, while the other three SPWs display
much larger phase offsets). In the SPW 0/SPW 6 match and in the SPW 2/SPW 8
match, the phase offsets of the two polarizations also tend to agree with each othermore than in the other three SPWs, where they differ anywhere from a few degrees
to a hundred degrees or more. When looking at the phase offsets relative to theintermediate resolution SPW 4, the findings are similar to those of SPW 0 and SPWAtacama Large Millimeter/
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2; here SPW 7 seems to “match” best. These phase offset tables are shown in Figures
10, 11, and 12.

Figure 10: TDM-to-FDM phase offsets in Band 9 (X3a4) using (wide) SPW 0 as thereference. SPW 6 seems to “match” best, similar to the behavior in the other Band 9
TDM-to-FDM transfer.

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Figure 11: TDM-to-FDM phase offsets in Band 9 (X3a4) using SPW 2 as thereference. SPW 8 seems to “match” best, similar to the behavior in the other Band 9
TDM-to-FDM transfer.

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Figure 12: FDM-to-FDM phase offsets in Band 9 (X3a4) using SPW 4 as thereference. SPW 7 seems to “match” best, similar to the behavior in the other Band 9
TDM-to-FDM transfer.

Finally, instrumental phase offsets on individual antennas depend on the reference
antenna specified as well as the observing frequency. They are not constant fromone observation to another if the frequency changes even if the reference antenna is
kept consistent. The offsets between the wide and narrow windows are also
observed to change.
Future work and related testing:Currently, testing is ongoing to determine the stability of the bandpass in the wideand narrow windows; these seem to be very stable, but recommendations may
result from these tests indicating the best way to derive the narrow bandpasses,
especially in the low signal to noise regime. One possibility is to use a more
complicated bandpass solution fitting, like spline fitting (gaintype=BPOLY) or
smoothing in real and imaginary space.

The usage of DiffGainCal will also be added soon to the observing setup forbandwidth switching (and band-to-band observing). This will enable quick
switching back and forth between the wide and narrow bandpass calibrators.
Depending on the needs of the band-to-band data reduction, the timing of the
bandpass calibration within the SB may be different than it is currently, which is fineAtacama Large Millimeter/
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for running bandwidth switching as long as enough signal-to-noise can be achievedin the narrow bandpass observations. The usage of DiffGainCal will be testable soon.
Additionally, a new observing strategy will soon be implemented in the automatic
script generator for flux calibration transfer between the flux and bandpass
calibrators. This will affect the way that the amplitude calibration is done inbandwidth switching data reductions.

Finally, this method should be combined with the band-to-band transfer method ofhigh frequency calibration once both are adequately characterized on their own.
The addition of the DiffGainCal to the observing strategy and new flux/bandpass
calibration data reduction strategy will be necessary to combine these techniques.

Summary:-- Bandwidth switching from TDM to FDM windows within the same frequency bandis a viable way to calibrate high frequency observations; it has been demonstrated
in B3, B7, and B9.
-- Wide FDM window to narrow FDM window phase solution transfer can also beused; this does not appear to perform better than the TDM transfer (in the X3a4 B9scheduling block).
-- Alterations to the automatically generated script are described. The usage of‘linearPD’ should be avoided (though it appears to only make a 1-2% difference inthe final image rms).

-- Suggestions to improve the observing setup (using solar system objects, taking an
extra bandpass calibration) are described and testing fixes to the documented phasedecorrelation and target numbering problems are recommended, as is testing invarious conditions to determine the limits of bandwidth switching capabilities.
-- Including a bandpass measurement in the narrow windows improves the final
image in Bands 3 and 7. In Band 9, the SNR is similar regardless of the inclusion of anarrow window bandpass calibration (though this should be tested in data takenwith better weather). In the same Band 9 SB, including the WVR correction
increases the rms in the final image by 20% but does a better job of recovering flux
at the phase center than the “no WVR” case, though the “no WVR” case finds thetarget closer to its true location on the sky.
-- Position offsets are seen in all of the final images ranging from 10% of the beam
(B3, B9) to 100% of the beam (B7). In the B9 “no WVR” case, the offset is halved
compared to the offset seen with the WVR applied; the weather was fairly bad in
this observation. In the FDM-to-FDM transfer B9 data, the offset is smaller than the
TDM-to-FDM transfer, though they are both quite small (7-11% of the beam size).

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Vitacura - Santiago Chile-- Phase offsets are measured between the wide TDM and narrow FDM windows
when the wide windows do not overlap and have a one-to-one correspondence with
the narrow windows. For an individual antenna, the offsets change with SPW andfrequency band (and reference antenna). In Band 3, the magnitude of the offsets isroughly ±10 degrees, and in Bands 7 and 9, the offsets are roughly ±40-50 degrees.
In Bands 3 and 7, the offsets in the two polarizations are within ~5 degrees of eachother; this proximity is not always seen in Band 9, regardless of the weather.

-- Phase offsets are measured in Band 9 between TDM and FDM windows, as well as
between wide FDM and narrow FDM windows, when the wide windows all have thesame central frequency. In this case, depending on which TDM/wide FDM window isused as the reference, one of the narrow FDM windows exhibits the roughly ±40
degree behavior seen previously. The rest of the narrow windows exhibit up to±160 degree offsets; there appears to be one “matching” narrow SPW in each case.
-- Instrumental phase offsets on individual antennas depend on the reference
antenna specified as well as the observing frequency. They are not constant fromone observation to another if the band changes even if the reference antenna is kept
consistent.
-- Related testing is summarized (bandpass stability), as is future work, including
the usage of DiffGainCal, an update to the method to be used in the script generator,
and the (eventual) combination of this technique with the Band-to-Band transfer
technique.