[evlatests] Comparison of 3-bit to 8-bit 'absolute' calibration

[rperley]

I wrote on Tuesday about the accuracy of 3-bit and 8-bit relative 
calibration -- the ability to transfer gain between two sources.  In 
short,  there is no significant difference, for well-behaved data for 
objects of similar flux and elevation, between 3-bit and 8-bit.

I also noted that, for 8-bit, 'absolute' calibration -- using the 
recorded system constants (Tcal and antenna efficiency) with the 
observed switched power to derive calibrated visibilities in real 
Janskys, is good to better than 5%, once obvious outlier antennas are 
removed.  The only exception to this is the upper half of Q-band, where 
the calculated visibilities are too low by about 20%, likely due to a 
declining antenna efficiency (or pointing) that is not accounted for in 
the system constants.

This leaves the question of how accurate is application of the switched 
power for deriving correct fluxes, for 3-bit data.  Due to the known 
non-linearity of the digital switched power compared to the analog 
power, we are confident that attempting to use the switched power for 
3-bit data in general will lead to erroneous results when the sources 
are very strong (or the sky very bright), or when the elevations are 
low, so the system temperature is unusually high.

But what if the elevation is high, the source is weak (compared to the 
system power), and the elevation high?  This is the situation employed 
for the test data taken last weekend.

I did this today, and generated the 'voltage gain histograms' for 
comparison to those generated Tuesday for the 8-bit data (taken at the 
same time and elevation).

The result summary, for the impatient, is:

Once discrepant antennas are removed, the means, and medians, of the 
antenna voltage gains, are similar to those for the 8-bit system.  
However, for Ku, K, Ka, and Q bands, the spread in antenna gains is 
*very* much wider.  The tight grouping seen in the 8-bit gains is absent 
in the 3-bit gains.  The ratio of highest to lowest gains (expressed in 
power) is generally over an order of magnitude in the 3-bit data.

For those seeking a better summary, read on ...

The conversion of raw correlation, for the JVLA, to visibilities, is 
described in detail in EVLA Memo 145.  In short, the correlation value 
for a given baseline is multiplied by two antenna-based factors.  Each 
looks like:  sqrt(Tcal)/[(sqrt(PDif)*sqrt(AntEff)]
(There is also a constant which converts this to Jy).

The Tcal and AntEff values are stored in tables. The former were 
measured in the lab with quite fine frequency spacing.  (I don't recall 
the spacing value).  The latter were determined by Bob Hayward and me 
for ea24 (the 'poster child' antenna), and are assumed to be the same 
for all other antennas.  The details of these measurements are in 
various EVLA Memos.  These measurements are, in short, painful and slow 
to make...

For the data reported on here, the analysis was done in AIPS, which 
knows about all that is written above.  To determine the gain voltages, 
the resulting visibilities from 3C286 were input to CALIB, which, using 
my 3C286 models, and the P&B flux values, generated voltage gains for 
both polarizations, and each SPW.  There are *a lot* of values, so I 
selected a single SPW, located near opposite ends of each band from X 
through Q, for the comparison.  The 3-bit data were not taken with 
exactly the same frequency values for the individual SPWs, so the 
closest match to the 8-bit value, was chosen.  (This can matter, since 
the Tcals are on a different grid, and some interpolative scheme 
determined the appropriate value to be used in the conversion).


<Whew>.  With all that done, here are the detailed comparisons:

X-band.

The results are remarkably similar between 3 and 8 bits.  The major 
difference is that for 3-bits, there are many more antenna whose gain 
values are far too high.  (In AIPSese, this means the calibrated 
visibilities are too low, so that the product of Tcal/(PDif*AntEff) is 
too low).   Discarding these discrepant antennas, the spread in the 
remaining gains is about 0.2, and the means/medians are low by 2 to 5%.  
The offset from 1.0 is greater in 3-bit than 8-bit.


Ku-band.

For 13.936 GHz, the spread in gains for 3-bit is about twice that seen 
in 8-bit.  There are more than 5 antennas in 3-bit with gain corrections 
exceeding 1.2 (that is, their correlated power is more than 50% too 
low).  At 16.424 GHz, both histograms are wide, but the 3-bit one has 
many more antennas with very large gain corrections, especially on the 
LCP side.

K-band.

Things really fall apart for the 3-bit mode in this band.  For 8-bits, 
the histograms are tight, with a width of about 0.2 (full).  For 3-bit, 
the voltage gains span more than 1.0, not including the 6 - 12  antennas 
with values (in power) a factor of 3 too low, or too high.  So although 
the medians are within 0.1 of 1.0, I doubt any discerning user would be 
comfortable with utilizing the wide spread of values.

Ka-band.

Similar to K-band, except the spreads are not as wide -- about 0.4 for 
the 3-bit case, and less than half that for the 8-bit case.  As 
elsewhere, a significant fraction of antennas have values between a 
factor of 2 to 5 too high (in power) in the 3-bit data.

Q-band.

Similar to the above, except that the 8-bit spreads are wider here -- 
about 0.3.  This likely reflects a variation in antenna efficiencies -- 
in the software, all antennas are assumed to be identical.  In the 3-bit 
data, even more antennas are seen with extremely high voltage gains -- 
these include those seen also in the 8-bit case, but have included many 
others with apparently normal values in the 8-bit data.

----------------------------

Recommendation:

With a modest effort, involving 8-bit interferometer data only, we could 
measure and adjust the Tcal values to reduce the spread in the observed 
gain values.  This should be done on a frequency grid similar to that of 
the default SPW width -- 128 MHz from 2 to 50 GHz.  There is ample 
evidence that these values are very stable -- the histograms generated 
this week are indistinguishable from those generated about a decade ago. 
  (Note:  this is a statistical statement -- I haven't attempted to 
compare individual antennas).

For 3-bits, I don't recommend this.  The very wide spread in generated 
visibilities (evidenced by the wide spread in gains) indicates something 
is amiss with the PDif values.  (Since the Tcal and antenna efficiency 
values are the same as for 8-bit).  This is in addition to the known 
problem with sensitivity to system power -- the experiment described 
above ensured intermediate elevation and similar observing (same day, 
same time, same frequency).

Hence, for wideband experiments, the suggested method of having the user 
spend ~5 minutes observing their phase calibrator in 8-bit mode should 
be sufficient to determine the flux scale to better than 5%.