[evlatests] Closure, Dynamic Range, and Aliasing

[Rick Perley]

    I have carefully reduced a 7.5 hour observation of the prominent 
source 3C273, taken at X-band on 29 December, for the purpose of 
examining whether the EVLA antennas have a higher, or more variable 
'closure' corrections.    The observations were taken in mode 'PA', with 
12.5 MHz BW, with 16 channels for each of the four correlations.  Each 
channel is hence 0.78 MHz wide. 

    3C273 is ideal for 'closure' studies for three reasons:

    1) It is very strong, with a 33 Jy unresolved nucleus, which makes 
calibration and self-calibration very easy.
    2) Is has a well known , and relative faint, one-sided extended 
jet.  This is useful to see if the quality of the images are as they 
should be.
    3) It is at a declination of only +2 degrees.  This means that all 
the (u,v) tracks are nearly perfectly horizontal, which has the very 
useful consequence (for people like me) that constant offset errors in 
the visibilities (a.k.a. 'closure') are readily visible in the image as 
a vertical 'stripe'.  [This effect of geometry is a nuisance for real 
astronomers, but provides a vital clue for diagnosticians].  The 
presence of closure errors, and the effectiveness of their removal via 
processing, are readily apparent from the image. 

    The short answer (for the impatient) is that the EVLA antennas are 
perfectly equivalent to VLA antennas in terms of sensitivity and imaging 
capabilities.  There is no indication that closure is higher, or more 
variable amongst the EVLA antennas than on the VLA antennas. 

    However, the full story is more complicated.  The statement above 
applies only to those channels numbered 3 through 9.  For higher 
numbered channels (the baseband end) the effects of the now-infamous 
aliasing are increasingly seen.  Note that in this experiment, channel 
10 is ~4.7 MHz from the edge frequency!   Great care must be taken in 
interpreting this statement, however -- the precision in the imaging is 
of order 300,000:1 -- so the aliasing effects are very small indeed at 
this distance from the baseband.    Read on, for a deeper understanding.

    A)  Calibration

    The data were of excellent quality, with 27 antennas operating 
smoothly.  There were 13 EVLA antennas, and 14 VLA antennas -- a very 
convenient balance for comparison of imaging and sensitivity.  As the 
data were taken at X-band, where the EVLA receivers are identical to 
those of the VLA, we are expecting equivalent results for the two arrays.

    Observations of 3C273 (a 33 Jy quasar with a famous one-sided jet) 
were taken in 76 5-minute long scans.  In addition, we observed the flux 
density calibrator 3C286 seven times, each of 2 minutes duration.  
Overhead took up the rest of the time. 
    Very little flagging was required, and I was very stringent in the 
application of these flags.  Anything that appeared less than perfect 
(in amplitude and phase, for each of the 16 channels, in all four 
correlations) was rubbed out.  No mercy was shown.  Probably less than 
1% of all the data were removed via flagging. 

    A bandpass caliabration was made, separately for each scan, for each 
source.  Inspection showed no evident variability in the bandpasses, 
either in time, or between sources.  (A closer inspection, using a 
differential method, is probably warranted, but has not yet been done). 

    B) Imaging

    I generated the 'ideal model' by extracting channel 8 data, and 
performing the usual routine of antenna-based calibration and 
baseline-based (closure) corrections.  The resulting image has almost 
300,000 ratio between the noise far from the source, and the peak of the 
quasar emission.  This is as good as any image I have made of this 
source in the past.  The length of the jet (about 15 arcseconds) is a 
little too long for this B-configuration -- 'echos' of the jet are seen 
extending north and south, at a level of about .1% of the jet. 
    The amplitude and phases of the closure corrections are very small 
-- typically 0.1%, and 0.05 degrees.  The maximum closure errors are 
about 1%, and 1 degree -- and these seem to be associated with VLA-VLA 
baselines.   A single closure correction was made for the entire 7.5 
hour run -- no attempt to make it time-variable (a tempting but 
dangerous procedure) was made.
    After applying the 'closure' corrections, the 'Channel 8' image 
showed *no* residual 'closure' stripe -- indicating that to the level of 
the noise, the closure errors are indeed constant over the length of the 
observation. 

    This 'ideal model' was then used for each channel, separately.  I 
produced a Hanning-smoothed file for each channel from 2 through 14 
(channels 1 and 15 can't be properly smoothed, but nobody should use 
them anyway).  Each of these 13 databases was then calibrated (both 
antenna-based, and baseline-based) ysubg the best model generated from 
channel 8.   An image (using all antennas, and including all 
corrrections) was made for each of these 13 separate files.  The results 
immediately showed we have a problem at the high end of the band:
       The RMS noise, away from the source, was (including ALL antennas):
    - 0.25 mJy in channel 2,
    - 0.17 mJy in channels 3 and 4,
    - 0.16 mJy in channel 6 through 9,
    - 0.17 in chan 10,
    - 0.18 in ch 11,
    - 0.26 in ch 12,
    - 0.47 in ch 13, and
    - 2.96 (!) in chan 14. 
    More importantly, the 'north-south' residual closure line is absent 
in channel 2 through 9, appears faintly in channel 10, and steadily 
increases in magnitude through channel 14. 
    To establish whether this rise at the high-frequency end was due to 
aliasing, or due to something associated with the mis-matched bandpass, 
I made images of the VLA-only, and EVLA-only, baselines for these 
channels. 
    In channel 8, the rms noise, and the two images, are exactly 
equivalent -- rms - 0.31 mJy.  The VLA x EVLA baseline image has noise 
0.21 mJy -- exactly as it should be, given there are twice the number of 
bsselines.  More importantly, there is no sign of the North-South 
closure 'line' in any of these images. 
    As I go up in frequency towards the baseband end, the difference 
between EVLA and VLA-only images dramatically worsens.  For channel 10, 
the rms's are 0.31 and 0.34 for VLA and EVLA.  For channel 12, it is 
0.30 and 0.54 mJy.  For channel 14, it is 0.63 and 2.42 mJy.  (All these 
are with the closure errors determined from those particular channels 
removed -- the difference are considerably greater without closure 
corrections). 
    More importantly -- the VLA-only closure-corrected images show no 
sign of residual closure errors (seen as an absence of the north-south 
stripe), while for EVLA-only images, the vertical stripe becomes 
dramatically larger and larger.  What this means is that the closure 
errors in the EVLA-EVLA baselines are variable in these high-numbered 
channels, while those for VLA-VLA baselines remain constant (and hence 
are nicely removed through the baseline-based calibration). 

    All this is exactly as expected from a small 'aliased' contribution 
which (vectorially speaking) is slowly rotating w.r.t. the in-band 
signal.  (I may try a time-variable baseline-calibration, to see if I 
can remove the observed residual).  What has surprised me is that the 
effects are still seen nearly 5 MHz away from the edge.  However, be 
careful in interpreting this -- the effects are very subtle indeed -- at 
the level of 0.001% or less -- and can only been seen in a source like 
this one, at a declination of essentially zero. 

    Returning to the 'safe' channels (3 through 10):  I concatenated 
these eight single-channel databases, each of which were individually 
calibrated, to make a single image.  The noise, away from the structure, 
was 96 microJy (compared to a peak of  31.3 Jy).  There was no hint of a 
vertical closure stripe.  A lovely image. 
    I then split these same channels from the  originating spectral-line 
file, to a single-channel file, utilizing the bandpass solutions, then 
followed the same self-calibration path.   The difference in this 
approach is that the eight channels are handled as a block, with no 
separate solutions for each. 
    An image was then made, with the same rms noise as the concatenated 
single-channel file.  This is a very satisfying result -- it 
demonstrates that the 'closure errors', (away from the channels 
containing the aliased response), are independent of the channel 
number.  A single 'closure' correction will serve for all channels. 

    The polarization data will be reported on separately.