| Subject: | A METHOD FOR HANDLING
SMA DATA FROM SWARM CORRELATOR - |
| Solving for bandpass of high- or full- spectral resolution data |
Date: | October 2, 2017$ |
From: | Jun-Hui Zhao (SAO) |
___________________
$| Updated from the versions since February 25, 2016; Submitted September 21, 2017 |
Along with the wideband development for SMA, we are implementing Miriad[1] software
to accommodate large volumes of SMA data. For the reduction of high spectral
resolution and wideband data generated from SMA observations with the newly upgraded
SWARM correlator, a considerable amount of software upgrading and further development
is indispensable concerning software infrastructure and advanced algorithms in the
era of wideband SMA. This technical memo reports a progress of Miriad software
development for the reduction of SWARM data, specifically for the program of bandpass
corrections. Given a general calibrator, the effects owing to emission structure and
variability of sources are discussed along with a visibility model. A method of
separating between the distortion functions in terms of complex antenna gains,
instrumental bandpass, and residual delays is also discussed. This method has been
applied to Miriad software. Three processes prior to passing the data to the
bandpass solver are discribed: (1) visibility weighting in both variance and source
structure, (2) normalization, and (3) enhancement of signal-to-noise ratio with moving
smoothing and/or orthogonal polynomials' fitting algorithms. The relevant subroutines
have been implemented in the Miriad task smamfcal. A test data set was produced on
February 11, 2016 from observations of Sgr B2 North, a site of forming a massive star
cluster, producing four sub-band of high-resolution spectral data (0.1 MHz/channel)
with a part of the SWARM correlator. An example for reduction of SWARM data, utilizing
the method described in this technical memo, is demonstrated based on the test data.
1. Motivation -
As the SMA SWARM correlator comes online, reliable bandpass corrections become a pressing
issue for probing fine structure of kinematics in imaging molecular lines with a high
spectral-resolution as well as for imaging comprehensive distributions of continuum
emission sampled with wideband (WB) data. For some special objects, the line width
appears to be narrow; for example, the velocity widths of molecular lines from brown
dwarf or proto brown dwarf candidates are as narrow as 1 km/s or even less[2,3,4]. The
full spectral resolution, 0.1 MHz per channel or 0.1 km/s at 1 mm, provided by the
SWARM correlator is needed for the study of the narrow line systems. However, a poor
signal-to-noise ratio (S/N) provided for such high-spectral resolution data becomes
an issue in solving for a reliable bandpass, given a lack of strong QSOs at higher
frequencies and highly variable cores of blazars in the range of wavelengths covered
in the radio, millimeter and submillimeter (RMS) bands as well as extended structures
of disc-like emission from strong thermal objects in the Solar system. The bandpass
solvers that were developed early need to be upgraded with more advanced algorithms
to address the inadequate budget in S/N for both spectrally and angularly high
resolution observations at submillimeter wavelengths. On other hand, wideband
continuum imaging employs the multiple-frequency synthesis (MFS) imaging technique[5],
which requires well-calibrated data across the sampled spectral band. In addition to
bandpass and delay corrections, the phase between individual spectral chunks or
sub-bands (hereafter) must be aligned well and also corrections for time-dependent
residual delays need to be carried out in order to achieve high-dynamic range images;
both errors in phase become critical issues in sub-arcsec resolution imaging. The
relevant algorithms have been developed and implemented in Miriad software. The
goal of the efforts is to match the specifications required by a variety of science
cases in the reduction of wideband data produced from the SMA SWARM correlator.
In Section 2, a visibility model for a celestial object is discussed concerning
calibrations. In Section 3, a method of pre-processing data prior to solving for
antenna-based bandpass as well as auto-editing the bandpass solutions are described
and discussed. The relevant algorithms have been implemented in a Miriad program
smamfcal. Sections 4 and 5 give the in-line document from help deck of smamfcal,
and a usage for setting up variables in a c-shell script, respectively. A test data
set was given from SMA observations of Sgr B2 North on Feburary 11, 2016 with
four SWARM sub-bands. Application and demonstration for this software
technique with the test data are given in Section 6. The names of relevant subroutines
and functions for SMA Miriad implementation are given in Appendix.
2. Visibility model -
In the era of new generation interferometer arrays at RMS wavelengths with a capability
of wideband sampling, telescope sensitivities in detections of weaker objects have
been dramatically improved in recent years. Source structure and variability of a
celestial object used as a calibrator become noticeable issues in data calibration
and imaging. Previous assumptions of point source models for core-dominant QSOs or
blazars in data calibrations appear to be inappropriate, and the issues owing to the
nature of sources require special attention and treatment. A visibility function in
modeling a calibrator concerning its variability and structure is introduced and
discussed. A transformation of actual source structure into a pseudo point-source model
and a process of removal of time variability are reviewed as follows.
2.1. Structure and variability
Given a (u, v) plane, observing frequency ν, and time t, a visibility function sampled
with a wideband interferometer array towards a target source, in general, can be
expressed as:
V(u, v, ν, t) = VS(u, v, ν, t) e2πiντA GA(ν, t), (2.1)
where GA(ν, t) and τA correspond to time-dependent complex gains and a delay caused
by both instrumental errors and atmospheric effects, respectively; both terms are
antenna-based. For a QSO or a blazar, its source function can be simply described as a
core-dominant source with a strong point-like function in the (u, v) plane,
VC(u, v, ν, t), an initial model separated from the extended emission structure
VExt(u, v, ν), namely:
VS(u, v, ν, t) = VC(u, v, ν, t) + VExt(u, v, ν). (2.2)
For a planet in the Solar system, the visibility function becomes:
VS(u, v, ν, t) = VExt(u, v, ν), (2.3)
assuming that time variability in both the distribution of emission brightness over a
planet disc and the total intensity can be ignored during an observing period.
2.2. Source model and creation of pseudo point source
As improvement of an interferometer array in both sensitivity and angular resolution,
the previous assumption of a calibrator (a QSO or a small planet) as a point source
is no longer suitable. The extended structure and variability of a calibrator appear
to generate significant effects, leading to limitations in both calibration precision
and quality of interferometer imaging. Given a celestial object, a time-invariant or
a stable structure of its emission can be constructed as shown in radio observations
and wideband imaging[6]. Then, a model for the structure of stable emission from
a calibrator can be expressed as:
VS(u, v, ν) = VC(u, v, ν) + VExt(u, v, ν). (2.4)
In principal, given a calibrator, a pseudo-point visibility function modulated by
atmospheric attenuation and delay as well as antenna-based instrumental effects can
be formed by the sampled visibilities, Eq(2.1), divided by the relevant model of
the stable emission structure Eq(2.4):
VP(u, v, ν, t) = V(u, v, ν, t) / VS(u, v, ν). (2.5)
For a QSO with a variable intensity I0+ΔI(t) of the radiation from its core which
is assumed to be placed at the phase center, Eq (2.5) can be expressed as,
VP(u, v, ν, t) = {1 + ΔI(t)/[I0 + VExt(u, v, ν)]}e2πiντA GA(ν, t), (2.6)
where the spectrum of the core is further assumed to be flat for simplicity. The
term caused by time-variable radiation from the core requires a special process to
remove it prior to further complex gain calibration[6]. For a planet or
a calibrator with no time-variability issues,
VP(u, v, ν, t) = e2πiντA GA(ν, t). (2.7)
And the antenna-based delay can be further written as,
τA = τ0 + Δτ. (2.8)
For the SMA concern, τ0 is assumed to be removed by an on-line process and Δτ
is the residual delay that depends on time. Furthermore, the frequency-dependent and
time-dependent functions in the complex gain can be decoupled if the instrumental
bandpass is stable enough,
GA( ν, t) = gA(t) gB(ν). (2.9)
Thus, Eq(2.7) can be re-written to,
VP(u, v, ν, t) = gA(t) gB(ν)e2πiν Δτ. (2.10)
The rest of this technical memo discusses a method of corrections for bandpass
term gB(ν) and residual delay Δτ. It is obvious that the normalization process
using the mean visibility over a sub-band at a time interval of an integration
record discussed in section 3.2 effectively eliminates the term gA(t). The
function of the pseudo-point source normalized by each of the pseudo-continuum
integrations for each baseline describes the solutions for bandpass shape and
residual delays, i.e.,
VP(ν, t) = gB(ν)e2πiν Δτ. (2.11)
We also note that normalization of the visibility data divided by a baseline-based
pseudo-continuum at each integration time interval can eliminate the variability
of the core emission in the case of a blazar, which is described in Eq(2.6). Before
discussion of the detailed algorithm for a wideband bandpass in next section, caveats
for the visibility model discussed above are noted:
1) A perfect source model for the stable emission Eq(2.4) is assumed. In practice,
at the submillimeter wavelengths, efforts to build reliable models for relevant
calibrators are needed.
2) In the equations from Eq(2.1) to Eq(2.11), the visibility and the relevant
modulation models are assumed to be continuous functions of the variables
u, v, ν, t. In the sampling process of an interferometer array, the sampled
data are discrete. Thus, in computer programming, the formulas need to be
written in a numerical way, e.g., Eq(2.10) and Eq(2.11) can be re-written as:
VPij(νk,tl) = gAij(tl)gBij(νk)e2πiνkΔτij(νk,tl) (2.12)
and
VPij(νk,tl) = gBij(νk)e2πiνkΔτij(νk,tl). (2.13)
3) The indices i, j, k, and l are integers; the antenna pair or baseline indices i and
j are from 0 to nA-1, and nA is a number of antennas used in an array; the frequency
index k is in the range between 0 and nchan-1 that is a total number of spectral
channels sampled by a correlator; the time sampling or integration index l is from
0 to nt-1, where nt is a total number of time sampling intervals used for the
calibrators given a data set.
4) The next section is to present a method of pre-processing the visibility data to
optimize the ratio of signal-to-noise for solving antenna-based complex bandpass gB
as well as antenna-based residual delay Δτ which may be also dependent on sub-bands
in the case of multiple sub-bands used for wideband spectral sampling. The two
terms can be decoupled if the instrumental bandpass does not change over a relevant
period of data sampling. Then, the instrumental bandpass term can be corrected
with solutions derived from the data acquired in a snapshot observation of a
strong calibrator.
5) The residual delay Δτ may be a small quantity and frequently varies in time.
Phase slopes produced from this term in sub-bands generate noticeable artifacts
near a strong compact source in high-angular resolution images, limiting dynamic
range of imaging[6]. The algorithm discussed in Section 3 provides a way to derive
solutions in phase caused by the residual delays. Linear fitting to the phase
slopes as function of frequency over each of the sub-bands may be carried out to
derive solutions for residual delays in the case of poor S/N, given a time
interval. For high S/N data, the phase solutions can be directly applied to a
target source.
3. Bandpass solver SMAmfcal -
The program smamfcal is a Miriad task which determines calibration solutions for antenna-
based corrections in aspects of antenna gains, delay terms and passband shapes from a
multi-frequency observation. This task is developed based on the original Miriad program
mfcal coded by Bob Sault according to the Miriad code signature. In the past decade,
smamfcal has been powered by implementing new algorithms as discussed below for handling
poor S/N data from observations at submillimter wavelengths. The algorithm of matrix
solver in mfcal is retained in smamfcal. The algorithms used for pre-processing
visivilities and editing bandpass solutions are listed below along with descriptions
and discussions in the following sub-sections.
3.1 Weight
In addition to uniform weighting, two methods of visibility weighting have been
implemented in smamfcal: 1) use variance (σ2) of visibility; 2) use amplitude
(A) of visibility, usually with the n-th power of the amplitude (An and n>1). The
second method is dependent on the source structure, less weighting the contribution
from the visibilities with lower S/N data due to the emission structure in a resolved
or a partially-resolved source. A subroutine accumwt accumulates the visibility
weight in paralle to the visibility accumulation with one-to-one mapping for each
data point. Three options have been provided for weighting in smamfcal:
1. weight = 1/σ2 or 1, the same way as that used in mfcal
2. weight = 1/(A/σ)2
3. weight = 1/(A/σ)4Option 3 can effectively give less weighting to the lower S/N visibilities near nulls
for a disc-like object.
3.2. Normalization
Solving bandpass is usually carried out before phase corrections are made. A
pseudo continuum visibility is computed by vector averaging each sub-band at a
time of each integration record. A normalization of the visibility for each
spectral channel is carried out with the pseudo continuum visibility. Thus,
such a self-normalization can remove any temporal phase drifts while retaining
bandpass variations across a sub-band. The normalization is accomplished with
two subroutines avgchn and divchz. The former determines the vector average
of spectral visibilities in the basis of per baseline and per sub-band given
an integration. Then, a normalized spectrum is computed.
For a calibrator partially resolved or with extended emission rather than a point
source, its visibilites need to be normalized by a model of its emission structure
before processing in smamfcal. As discussed in Section 2, the normalization of the
emission-structure model will remove the calibrator phase structure across the
frequency band within which the data are sampled. The issues concerning calibrator
structure become more critical for wideband data at the RMS wavelengths when
the overall sensitivity gets better. A catalog for calibrator models needs to be
built so that an automatic normalization with an emission-structure model can be
programmed given a relevant calibrator.
3.3. Smooth and LSQ fit
The subroutine smoothply hosts two micro-processes, i.e. moving smooth[4] and
orthogonal polynomials' fitting[4] to each of the visibility spectra prior to solving
for bandpass. Options msmooth and opolyfit are given for users to select one of
the two micro-processes to handle poor S/N spectral data. For high spectral
resolution data, such as SWARM data, msmooth appears to be a better choice.
The algorithm of msmooth is discussed as follows.
For a sub-band with a total number of channels n, the complex quantity in each
channel visibility consists of two parts, the true value of the measured quantity η
and a measurement error ε,
yi = ηi+εi, i = 1, 2, ..., n (3.1)We assume that ηi is a polynomial in frequency ν and the error εi to be normally
distributed about zero. In the high-spectral resolution case δν ~ 0.1 MHz, such as
in the spectral production from the SMA SWARM correlator, the variation trend ηi
is often embedded in the fluctuation of error εi for most of QSOs at submillimter
wavelengths. Thus a smoother function of ν is needed to replace every value
of yi,
i+k
ui = Σyi / (2k+1), (3.2)
j=i-k
If η is a linear function of ν in the frequency interval Δν = νi+k-νi-k = (2k+1) δν,
ηj = α + βνj, j = −k, −k+1, ..., k (3.3)α and β are constant. They can be determined from the data by linear regression.
For a higher order polynominal η,
ηj = a1 + a2νj + a3νj2 + ... + al+1νjl, (3.4)
The coefficients of the polynomial function can be determined from the data by least
square fitting to the smoother function ui, Eq(3.2).
If the variance of yi is σ2, then the variance corresponding to the smoother function
ui is,
σu2 = σ2/(2k+1), (3.5)
The ratio of the variance from the original data to that of the smoother function is
proportional to (2k+1),
σ2/σu2 = 2k+1, (3.6)For k=5, the variance of a spectral smoother is an order in magnitude smaller than
that of the original spectrum. The default provided in smamfcal for moving smooth is
k=3 and linear regression l=1. For the SWARM spectra, the linear regression
approaching appears to be appropriate for even larger value of k. For the trial data
used in Section 6, a smoother with k=7 is applied. The pre-process for options=msmooth
in smamfcal should be adequate in solving for the bandpass trend of a telescope
with data taken from a relatively weak calibrator. For SMA SWARM high-spectral
resolution sub-bands, a smoother with k=10 can greatly enhance S/N ratio of the
spectral data while a slow variation of bandpass response is retained. Thus with
the pre-process of moving smooth, we can correct for the bandpass of SWARM spectral
data with a high confidence level.
3.4. Auto-editing bandpass solutions
Solutions of bandpass may be contaminated due to individual channels with large
errors, e.g. spectral spikes produced from an instrumental part of a telescope.
A function for auto-editing of bandpass solutions is implemented, which rejects
solutions that are highly deviated from the actual bandpass trend; and replacements
can be made with the values derived from orthogonal polynomials' fitting to overall
solutions.
4. Help deck -
Task: smamfcal
Responsible: Jun-Hui Zhao
SmaMfCal is a Miriad task which determines calibration corrections
(antenna gains, delay terms and passband shapes) from a
multi-frequency observation. The delays and passband are
determined from an average of all the selected data. The gains
are worked out periodically depending upon the user selected
interval. SmaMfcal implements algorithms for weighting,
continuum vector normalization, and moving smooth prior to solving
for bandpass and gains, which are necessary for handling data
at submillimeter wavelength when the S/N is poor and phase dispersion
is large. The basic solving algorithms are the same as in MfCal.
Keyword: vis
Input visibility data file. No default. This can (indeed should)
contain multiple channels and spectral windows. The frequency
set-up can vary with time.
Keyword: line
Standard line parameter, with standard defaults.
Keyword: edge
The number of channels, at the edges of each spectral window, that
are to be dropped. Either one or two numbers can be given, being the
number of channels at the start and end of each spectral window to be
dropped. If only one number is given, then this number of channels
is dropped from both the start and end. The default value is 0.
Keyword: select
Standard uv selection. Default is all data.
Keyword: flux
Three numbers, giving the source flux, the reference frequency
(in GHz) and the source spectral index. The flux and spectral index
are at the reference frequency. If no values are given, then SmaMfCal
checks whether the source is one of its known sources, and uses the
appropriate flux variation with frequency. Otherwise the default flux
is determined so that the rms gain amplitude is 1, and the default
spectral index is 0. The default reference frequency is the mean of
the frequencies in the input data. Also see the `oldflux' option.
(This function has not been implemented for SMA data).
Keyword: refant
The reference antenna. Default is 3. The reference antenna needs
to be present throughout the observation. Any solution intervals
where the reference antenna is missing are discarded.
Keyword: minants
The minimum number of antennae that must be present before a
solution is attempted. Default is 2.
Keyword: interval
This gives one or two numbers, both given in minutes, both being
used to determine the extents of the gains calibration solution
interval. The first gives the max length of a solution interval. The
second gives the max gap size in a solution interval. A new solution
interval is started when either the max times length is exceeded, or a
gap larger than the max gap is encountered. The default max length is
5 minutes, and the max gap size is the same as the max length.
Keyword: weight
This gives different ways to determine weights (wt) prior to
solving for bandpass:
-1 -> wt = 1; the same weighting method as used in MfCal.
1 -> wt ~ amp0**2/var(i); for a normalized channel
visibility, the reduced variance is proportional
to amp0**2/var(i), where amp0 is the amplitude
of the pseudo continuum and var(i) is the variance
of visibility for the ith channel.
2 -> wt ~ amp0**4/var(i)**2;
Default is 2 for SMA and -1 for other telescopes.
if you have stable phase, use -1;
if the phase stability is poor, use 1 or 2;
for a larger planet, 2 is recommended.
For antenna gains' solver:
-1 -> wt = 1; the same weight method that is used in MfCal.
>0 -> wt = 1/var, where var is the visibility variance.
Defualt is 1/var.
Keyword: options
Extra processing options. Several values can be given, separated by
commas. Minimum match is used. Possible values are:
delay Attempt to solve for the delay parameters. This can
be a large sink of CPU time.
nopassol Do not solve for bandpass shape. In this case if a bandpass
table is present in the visibility data-set, then it will
be applied to the data.
interpolate Interpolate (and extrapolate) via a spline fit (to
the real and imaginary parts) bandpass values for
channels with no solution (because of flagging). If
less than 50% of the channels are unflagged, the
interpolation (extrapolation) is not done and those
channels will not have a bandpass solution.
oldflux This causes SmaMfCal to use a pre-August 1994 ATCA flux
density scale. See the help on "oldflux" for more
information. (not relevant to SMA data)
msmooth Do a moving average of the uv data (the real and
imaginary parts) using the keyword smooth parameters
specified prior to solving for bandpass.
opolyfit Do a least-square fit to the bandpass solutions
(the real and imaginary parts) with an orthogonal
polynomial of degree n which can be given in keyword
polyfit.
wrap Don't unwrap phase while doing fit or smoothing
the uv data.
averrll In the case of solving for bandpass of dual
polarizations, averrll gives vector average of rr and
ll bandpass solutions; the mean value is written into
the bandpass table for each of rr and ll.
Keyword: smooth
This gives three parameters of moving smooth calculation of the
bandpass/gain curves:
smooth(1) = K parameter k giving the length 2k+1 of the averaging
interval; default is 3.
smooth(2) = L order of the averaging polynomial l; default is 1.
smooth(3) = P probability P for computing the confidence limits;
default is 0.9.
Keyword: polyfit
polyfit gives a degree of orthogonal polynomial in least-sqaure
fit to the bandpass/gain curves. Default is 3.
polyfit: 1 (linear), 2 (parabolic), 3 (cubic), ....
Keyword: tol
Solution convergence tolerance. Default is 0.001.
5. Usage -
The reduction of SMA data has been suggested to use msmooth in bandpass calibration, e.g.
CalibrationProcedure₤ for data produced from the ASIC correlator. The function msmooth
appears to be critical in solving high-spectral resolution bandpass of ASIC data. This
pre-process appears to be essential for handling the high-spectral resolution SWARM
data. Here, an example is given for a usage of smamfcal in a C-shell script if
one uses a QSO as a bandpass calibrator:
#!/bin/csh -f
set fname = 160211_rx0.lsb
set bcal = 3c273
set edge = 500
set refant = 1
set smooth = 7,1,0.9
... (see CalibrationProcedure₤)
smamfcal vis=$fname.swarm.tsys select='source('$bcal')' edge=$edge,$edge \
refant=$refant interval=1000000 options=msmooth smooth=$smooth
___________________
₤https://www.cfa.harvard.edu/sma/miriad/swarm/pscripts/swarmcali_a.csh.html
6. Application & Testing -
Using a recent test data from the observation track on February 11, 2016 with a hybrid
configuration of both ASIC and SWARM correlators. This is the first real data set that
was produced from a part of the SWARM correlator, consisting of four high-resolution
sub-band while the SMA was in an array of five antennas. Here is a report for
the lower-side band (LSB) data set, which is produced with uvindex:
6.1. Description of the testing track on 2016-02-11
UVINDEX: version 5-sept-2013
Summary listing for data-set 160211_rx0.lsb
-----------------------------------------------
Time Source Antennas Spectral Wideband Freq Record
Name Channels Channels Config No.
16FEB11:17:20:13.8 3c273 8 71681 0 1 1
16FEB11:17:50:54.1 nrao530 8 71681 0 1 611
16FEB11:18:10:05.3 sgrb2n 8 71681 0 1 1991
16FEB11:18:25:55.1 nrao530 8 71681 0 1 2301
16FEB11:18:31:21.6 sgrb2n 8 71681 0 1 2411
16FEB11:18:46:41.8 nrao530 8 71681 0 1 2721
16FEB11:18:52:08.3 sgrb2n 8 71681 0 1 2831
16FEB11:19:07:28.5 nrao530 8 71681 0 1 3141
16FEB11:19:12:55.0 sgrb2n 8 71681 0 1 3251
16FEB11:19:28:15.2 nrao530 8 71681 0 1 3561
16FEB11:19:33:41.7 sgrb2n 8 71681 0 1 3671
16FEB11:19:49:01.8 nrao530 8 71681 0 1 3981
16FEB11:19:54:28.4 sgrb2n 8 71681 0 1 4091
16FEB11:20:09:48.5 nrao530 8 71681 0 1 4401
16FEB11:20:15:15.0 sgrb2n 8 71681 0 1 4511
16FEB11:20:30:35.2 nrao530 8 71681 0 1 4821
16FEB11:20:36:01.7 sgrb2n 8 71681 0 1 4931
16FEB11:20:51:21.9 nrao530 8 71681 0 1 5241
16FEB11:20:54:20.0 Total number of records 5310
------------------------------------------------
Total observing time is 3.55 hours
The input data-set contains the following frequency configurations:
Frequency Configuration 1
Spectral Channels Freq(chan=1) Increment
1 218.94975 -0.416000 GHz
128 220.94094 -0.000812 GHz
128 220.85894 -0.000812 GHz
128 220.78375 -0.000812 GHz
128 220.70175 -0.000812 GHz
128 220.61294 -0.000812 GHz
128 220.53094 -0.000812 GHz
128 220.45575 -0.000812 GHz
128 220.37375 -0.000812 GHz
128 220.28494 -0.000812 GHz
128 220.20294 -0.000812 GHz
128 220.12775 -0.000812 GHz
128 220.04575 -0.000812 GHz
128 219.95694 -0.000812 GHz
128 219.87494 -0.000812 GHz
128 219.79975 -0.000812 GHz
128 219.71775 -0.000812 GHz
128 219.62894 -0.000812 GHz
128 219.54694 -0.000812 GHz
128 219.47175 -0.000812 GHz
128 219.38975 -0.000812 GHz
128 219.30094 -0.000812 GHz
128 219.21894 -0.000812 GHz
128 219.14375 -0.000812 GHz
128 219.06175 -0.000812 GHz
128 218.94094 -0.000812 GHz
128 218.85894 -0.000812 GHz
128 218.78375 -0.000812 GHz
128 218.70175 -0.000812 GHz
128 218.61294 -0.000812 GHz
128 218.53094 -0.000812 GHz
128 218.45575 -0.000812 GHz
128 218.37375 -0.000812 GHz
128 218.28494 -0.000812 GHz
128 218.20294 -0.000812 GHz
128 218.12775 -0.000812 GHz
128 218.04575 -0.000812 GHz
128 217.95694 -0.000812 GHz
128 217.87494 -0.000812 GHz
128 217.79975 -0.000812 GHz
128 217.71775 -0.000812 GHz
128 217.62894 -0.000812 GHz
128 217.54694 -0.000812 GHz
128 217.47175 -0.000812 GHz
128 217.38975 -0.000812 GHz
128 217.30094 -0.000812 GHz
128 217.21894 -0.000812 GHz
128 217.14375 -0.000812 GHz
128 217.06175 -0.000812 GHz
16384 212.79985 0.000102 GHz
16384 217.09965 -0.000102 GHz
16384 216.79985 0.000102 GHz
16384 221.09965 -0.000102 GHz
------------------------------------------------
The input data-set contains the following polarizations:
There were 5310 records of polarization XX
------------------------------------------------
The input data-set contains the following pointings:
Source RA DEC dra(arcsec) ddec(arcsec)
3c273 12:29:06.70 +02:03:08.60 0.00 0.00
nrao530 17:33:02.70 -13:04:49.55 0.00 0.00
sgrb2n 17:47:19.88 -28:22:18.38 0.00 0.00
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This is a 4hr observation track pointing on sources interleaved between 3c273
(bandpass calibrator), nrao530 (gain calibrator) and sgrb2n (Sgr B2 North, target).
The data consist of a total of 52 sub-bands, excluding the first single channel
of the pseudo continuum sub-band. The first 48 uniform spectral resolution
sub-bands (0.812 MHz per channel, 128 channels per sub-band) are produced from the
ASIC correlator. Highlighted in red, the bottom four high spectral resolution
sub-bands (0.102 MHz per channel, 16384 channels per sub-band) are produced from a
part of the SWARM correlator, producing four sub-bands.
Fig. 1 - Raw spectra of 3C 273 from the ten baselines. Each row consists of four sub-bands
produced from a part of the SWARM correlator. Each of the spectra shows the amplitudes
(top) and phases (bottom). Click the figure for enlargement (for webpage version only)€.
Below, using the data extracted for the four high spectral resolution SWARM sub-bands,
we demonstrates the process of solving bandpass with smamfcal, showing the results
from the Miriad task smamfcal.
Using an SMA pre-process program swarmsplt, we binned every two channels together
before solving for bandpass. We note that the current code works for 8192 spectral
channels per sub-band or the original spectral data binned every two channels from
the full resolution (16384 channels) data due to some issues. Miriad is being
upgraded towards a full capacity in handling SWARM data for SMA science.
6.2. Raw spectra of 3C 273 - bandpass calibrator
The beginning of the observation tracks was on 3C 273, bandpass calibrator, for 30
minutes. Fig. 1 shows a set of spectra of the four SWARM sub-bands from 10 baselines.
Each SWARM sub-band is marked in different color. 3C 273 at 1.3 mm is a strong point
source (~11 Jy). Thus, weighting with visibility variance (default) would be good
enough. Using the setup given as an example in Section 5, we run smamfcal to
solve for bandpass.
Fig. 2 - Antenna-based solutions in amplitude derived from the bandpass solver smamfcal.
Click the figure for enlargement (for webpage version only)€.
6.3. Bandpass solutions
The bandpass solutions are obtained from the solver smamfcal in Miriad. Fig. 2 shows
the antenna-based bandpass solutions in amplitude for the four SWARM sub-bands (color
coded). We note that 500 channels, or 1000 channels for the data with the
original channel resolution, have been cut off from both edges of each sub-band.
The sub-band 2 at the large channel series number end may have more low signal
channels that need to be thrown away.
Fig. 3 shows the antenna-based bandpass solutions in phase for the four SWARM
sub-bands coded with the same color corresponding to the amplitude solutions. We note
that the antenna 1 is used as reference and the rest of antennas show significant
phase offsets between the sub-bands while small phase variaitions appear in each
sub-bands. The alignment in phase is critical in continuum imaging. Applying
the bandpass solutions to the target sources, the instrumental issues are taken
care automatically.
Fig. 3 - Antenna-based solutions in phase derived from the bandpass solver smamfcal,
corresponding to the solutions in amplitude shown in Fig. 2. Antenna 1 is the reference
antenna. Click the figure for enlargement (for webpage version only)€.
SWARM sub-band 1 -
SWARM sub-band 2 -
SWARM sub-band 3 -
SWARM sub-band 4 -
Fig. 4 - A stack of 10 spectra from each baseline in each of the four SWARM
sub-bands towards Sgr B2 North after apply corrections for bandpass. From top to bottom
are the sub-bands 1, 2, 3 and 4 produced from a part of the SWARM correlator.
Click each of the figures for enlargement (for webpage version only)€.
6.4. Spectra of Sgr B2 North
We apply the bandpass solutions derived from 3C 273 to the target Sgr B2 North. Fig. 4
shows a stack of 10 corrected spectra from each baseline in each of the four SWARM
sub-bands. A forest of molecular lines is present in the SWARM spectra; some show a
broad absorption (for example, a feature at around 214.2 GHz in SWARM sub-band 1) and
some are associated with very strong emission lines. The hydrogen recombination line
H30α is hidden in the line forest of the upper sideband (USB) spectra (not shwon
in this Memo).
Finally, we note that the scale of flux density and complex gain corrections have
not been applied to the spectra of the target source yet as shown in Fig. 4.
Appendix: Source code -
The Fortran code of the entire smamfcal program exceeds 4600 coding lines. For interested
users, a copy of the source code can be found from the SMA Miriad distribution. The code
of the Fortran 77 subroutines for the relevant pre-processes is highlighted below:
accumwt - weight
avgchn - vector average
divchz - normalization
smoothply - moving smooth & orthogonal polynomial fit
Reference -
[1]Sault, R. J., Teuben, P. J., & Wright, M. C. H. 1995, in ASP Conf. Ser. 77,
Astronomical Data Analysis Software and Systems IV, ed. R. A. Shaw,
H. E. Payne, & J. J. E. Hayes (San Francisco, CA: ASP), 433
[2]Basmah Riaz, 2016, personel communication based on her SMA project: 2015B-S044
[3]Long, F. et al. 2017, ApJ, 844, 99
[4]Ricci, L. et al. 2012, ApJL, 761, L20
[5]Rau, U. & Cornwell, T. J. 2011, AA, 532, A71, for example
[6]Jun-Hui Zhao, Mark, R. Morris, & W. M. Goss 2017, in preparation
[7]Siegmund Brandt, 1999, Data Analysis - Statistical and Computational Methods for
Scientists and Engineers, Third Edition, Springer-Verlag New York Inc.
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€https://www.cfa.harvard.edu/sma/miriad/swarm/SMAmemSWARMBpass/SMAmemSWARMBpass.html