[evlatests] Flux Density Accuracy via Switched Power Alone
Rick Perley
rperley at nrao.edu
Wed Jul 10 16:27:50 EDT 2013
Knowing both the antenna efficiencies and the values of Tcal, we
should -- in principle -- be able to pre-calibrate our visibility data
with an accuracy set by the knowledge of the above quantities (and of
the effects of atmospheric extinction). To do this, the raw
cross-correlations need to be multiplied by a factor of
sqrt(Tc1.Tc2/(e1.e2))
where e is the antenna efficiency, and Tc the value of the cal (in K).
(There are also some constant factors, which we think we know).
We know that this system actually works 'pretty well' -- Vivek and I
have both stated that it should be good to 5%. But until now, nobody
has tried to quantify this statement.
Using the 'flux density data', taken May 2, I have used the
observations of 3C286, (taken in excellent dry weather) at an elevation
of 55 degrees, and the associated switched power calibration data, to
see how close we get to the right answer.
I note here that getting this system to work correctly would often
remove the need for users to observe a 'standard' radio source to set
their flux density scale.
The bottom-line result is: Not bad, but the 5% claim is 'a little
optimistic' at some bands.
Below I give a table which summarizes the essential results.
Attached are the data from which the table comes, and histograms of the
gain factors.
The method I used was to used CALIB to generate antenna-based
voltage gains, after the visibilities were modified by the switched
power. Corrections due to atmospheric opacity were applied, but no
elevation gain correction was applied. (Hence, I used only the 55
degree elevation data). The gain solutions represent the antenna-based
error: A value less than 1.0 indicates the antenna has been
over-corrected, a value less than this means the antenna has been
under-corrected.
A gain value less than 1.0 means that the actual antenna efficiency
is higher than that applied, and/or the true Tcal is lower than that
value applied.
A gain value greater 1.0 means the actual antenna efficiency is
lower than that applied, and/or the true Tcal value is higher than that
applied.
In the analysis, I squared the derived gain factors, so they are now
proportional to power. The error factors are then directly applicable
to the efficiency or Tcal. I computed, for each of the 16 frequencies,
the mean gain factor, and the rms of the distribution about this mean.
Nearly all mean factors are with 10% of unity, however note the
distressingly high deviations -- particularly at S, Ka, and Q bands.
Band Frequency RCP LCP
MHz mean rms mean rms
----------------------------------------------------------------------
L 1465 0.98 0.11 0.99 0.17
L 1865 1.02 0.40 0.93 0.20
S 2565 1.09 0.39 1.11 0.44
S 3565 0.99 0.37 0.98 0.43
C 4885 0.98 0.16 0.98 0.11
C 6885 0.89 0.10 0.90 0.13
X 8435 0.87 0.13 0.90 0.13
X 11062 0.87 0.13 0.83 0.10
Ku 14965 0.95 0.17 0.97 0.17
Ku 17422 1.01 0.12 1.06 0.25
K 22450 0.90 0.12 0.90 0.18
K 25836 0.89 0.15 0.85 0.19
Ka 28450 1.04 0.20 0.99 0.20
Ka 36435 0.933 0.27 0.90 0.22
Q 43340 1.03 0.28 1.01 0.30
Q 48425 1.39 0.60 1.29 0.56
------------------------------------------------------------------------
More interesting and useful information is shown in the histograms
of the gain power distribution amongst antennas. Attached are eight
plots showing these for the two frequency pairs and two polarization for
each band.
I haven't bothered to put the antenna numbers into the histograms
(this is not easy to do with the software I use). For those interested
in the actual gain values for each antenna/IF, a table is attached.
Note the entries here are the *amplitude* antenna solutions.
Comments:
1) About half of the average power gains are within the 5% limit
quoted by Vivek and me.
2) The histograms illustrate that most antennas are within about 10%
of each other, and that at most bands, there are a few very discrepant
antennas responsible for the very high dispersions seen in the table.
The most discrepant antennas are generally not shown in the histograms
(for reasons of maintaining a decent horizontal scale).
3) There are curious and real mean offsets by band: A good example
is X-band, where the corrected amplitude scale is 10 to 15% too high
(gains values less than 0.9). This implies that the efficiency we are
using is too low by that same factor, or that the Tcal values -- on
average -- are too high by that factor. (Or, a combination of both).
The K-band discrepancies are of the same value. But note that Ku band,
and the lower half of Ka band, are very close to the correct value.
4) The higher end of Q-band values are far too low (power gain
values typically 1.3) -- but this is easy to explain as an efficiency
considerably lower than that being applied. This is as expected -- AIPS
only allows a single efficiency per band (at this time) -- we know the
efficiency sharply decreases in Q-band towards higher frequency. Also,
the very large dispersion in the Q-band values likely reflects a larger
variation in efficiency between antennas (unsurprising!) at this band.
(Or, it reflects pointing errors due to (say) collimation errors).
5) The very high dispersion in the values, particularly at S band,
and in the upper half of L-band, is a worry. This is very unlikely to
be due to efficiency errors, so likely reflects errors in the Tcals.
These are large errors -- tens of percent! In general (except at
Q-band), I'd have expected the dispersion in these values to be at the
5% level. The best we have at present is about 10%, and 20% is more
typical. This is far too large for reliable gain calibration.
6) So -- the question for everybody is: What should we do about
this? We could 'fudge' either the efficiencies or the Tcal values to
make things come out right. We could define a 'peculiar gain' factor
which is updated as needed, and is applied when the switched power is
applied. Individual in-situ measurement of the receiver temperatures
and antenna efficiencies is out of the question (we don't have the
people or the time).
I propose we discuss some of this at the 'test' meeting tomorrow.
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