\documentclass[preprint]{aastex} % AASTeXv5.0
\usepackage{carma_memo}
\usepackage{psfig}

\begin{document}

%%
%% CARMA Memo number. Check web http://www.mmarray.org/memos
%% for most recent memo number.
%%
\carmamemo{41}

%%
%% Uncomment these if this is also an ALMA or BIMA memorandum.
%%
%\almamemo{222} % ALMA Memo number.
%\bimamemo{101} % BIMA Memo number.


\title{Fitting Antenna Gain, Pointing and Primary Beam Characteristics to Interferometric Mosaics}
\author{Melvyn Wright and David McMahon}
\affil{Radio Astronomy laboratory, University of California, Berkeley, CA, 94720}

\begin{abstract}

Mosaic observations of a strong compact source at the nominal pointing
center and half power points are used to determine the aperture
efficiency, pointing, and primary beam width of the CARMA antennas. The
data are self-calibrated to determine the antenna voltage gains. A
Gaussian fit to antenna voltage patterns is used to analyze the CARMA
beam patterns at 3mm and 1mm.  For multichannel observations the antenna
bandpass solution is also obtained.

Using a  hex7 mosaic pattern works very well at 3mm. At 1mm good
atmospheric phase stability is required to obtain reliable results.  We
measure antenna gains close to 65 and 145 Jy/K corresponding to aperture
efficiencies 50\% and  65\%  respectively for 10 and 6m antennas.
An elliptical primary beam pattern is observed in some antennas.

\end{abstract}

%%
%% Change Record/Revision History
%% This goes AFTER the abstract: the abstract is
%% printed on the front of the cover page and the
%% change record on the back of the cover page.
%% Use \addrevision to add additional revisions.
%% Columns are
%% | revision |date| author| sections/pages affected |
%% |          | remarks                              |

\ChangeRecordBegin
\addrevision{1.1}{2009-June-01}{MCHW}{1-14}{Draft memo}
\ChangeRecordEnd


\section{INTRODUCTION}

\clearpage
\section{Observations}

Mosaic observations were obtained using a standard hexagonal 7-pointing
mosaic of a strong compact source at the nominal pointing center and
half power points for the 10m antennas. The data are self-calibrated to
determine the antenna voltage gains.

Gaussian fits to the voltage gains are used to determine pointing
and primary beam width of each of the the CARMA antennas. 


Although 10m
antennas are sampled close to the half power
point, the 6m antennas are not. It would be better to sample each 

Mosaic observations

hex7 mosaic to derive pointing, PBFWHM,  jyperk and bandpass

-- pointings at center and FWHM points are best - for the
heterogeneous CARMA telescope this means best using az/el offsets
rather than ra/dec. delay/phase tracking
center on strong compact source.
These are 7 discrete pointings, and Gaussian fitting.
could be 5 pointings with no PA fit - which hex7 can determine,
or 13- or more to fit non Gaussian part of PB of 10m which is within 6m PB.
The frequency and number of pointings needed depends on image fidelity required.

Sounds like telescope software can handle this as is, but may need some
observing script writing ?

2. OTF mosaicing.  This is more ambitious, but from your email, it sounds
like this is possible by incrementing az and el offsets.  The advantage over
the standard discrete pointing mosaic is observing efficiency for large FOV.
I've argued that with OTF it would be difficult to control the synchronous slew
needed to maintain the x-corr PB stability illuminating the target FOV,
but now thinking it maybe possible to finesse this by incrementing az/el offsets
 in a more controlled way at CARMA.
Would need something like synchronized integrations and incrementing az/el
offsets every few seconds.  Does this sound possible ?

3. Array Rx response. This was my initial question.
An array Rx will give different pointings in 6 and 10m antennas. We need to
measure the cross correlation PB response for offset pointings.
We could try this with existing Rxs by using  different Az,El offsets in 6
and 10m antennas. Observations required are same as (1).

 hex7 - antenna voltage patterns
are a great way to analyze beam patterns and feed characteristics/problems -
squint, focus,  pbfwhm, alignment etc.,  Jy/K gains and antenna based bandpass come for free from mfcal on a hex7 mosaic on a calibrator.

using hex7 mosaic on strong source
to determine jyperk, bandpass, pointing, and PB FWHM
from antenna gains.  works very well at 3mm.
Results  on carma at 1mm do not look very stable.

The elliptical PB pattern is probably real and results from
the astigmatism which we saw in the holography at that time,
and later corrected by adjusting the panels
 agree.
This hex7 measurement was at 30" radius  . Gaussian fitting of the pointing and voltage patterns are far from optimum. Also, I had to average for 50min, and there are some pointing changes within the 50min measurement cycle which mess up
the fits.


Suggest we try the standard hex7 script again in a stronger source
at the nominal 10m FWHM points, and see how robust and repeatable the results are.

Better would be to observe with both 6 and 10m at their nominal
FWHM points. This is possible as I understand it from Marc and
Steve, but is not a standard script. We can try that later.

\section{ANALYSIS}

FYI CARMA antenna efficiencies:

 100 and 230 GHz.  If we get consistent results
 we should change the nominal FWHM.  Since
 these observations are similar to mosaic projects
 we should get better mosaic imaging performance
 using the measured PB FWHM.


 The aperture efficiencies can be calculated
 from the pkval fitted to the hex7 voltage patterns
 ( and therefore corrected for pointing)

 The pkval is  w.r.t. the adopted flux for 3c273
 and the nominal jyperk values in the data

 jyperk in data are  65 and 145.337
 corresponding to aperture efficiencies
  32.5/65 = 50\%, and  94.5/145.337 = 65\%.
 respectively for 10 and 6m antennas,

 I used flux 3c273 10 Jy at 230 GHz and 22 Jy at 100 GHz. which gives a
 pkval
 around 1. lower values
 mean  lower aperture efficiency.


 i.e

 aperture efficiency

 $10m (230GHz) = pkval^2  \times  (10/ 3c273_flux)  \times 50$

 $10m (100GHz) = pkval^2  \times  (22/ 3c273_flux)  \times 50$

 $6m  (230GHz)  = pkval^2  \times  (10/ 3c273_flux)  \times 65$

 $6m  (100GHz)  = pkval^2  \times  (22/ 3c273_flux)  \times 65$

\clearpage
\section{Data Reduction}

FWIW, 

1. I got carma 230 GHz hex7 on 4 Jy source to work using line=wide
      i.e. 6 x 500 MHz channels to beat down the noise in the gains.

2. integration times chosen to give same Number of solution intervals= 3,2, and 1 for each pointing.

thanks for your help with this.

plots in
/home/obs/mchw/carma/ct007.1D_2303C454.2009mar31


Mel.



#!/bin/csh -vf

goto start

start:

echo "integration times chosen to give Number of solution intervals: 3,2,1"
foreach INT ( 50 100 10000)
  echo "integration time =  $INT"
  foreach FILE ( --0.0 30.0 -30.0 15.26 -15.26 15.-26 -15.-26 )
    mfcal vis=$FILE.uv flux=3.9 interval=$INT,$INT line=wide | grep "Number of solution intervals
:"
  end
  /home/davidm/mmm/davidm/gpfit.rb vis='*.*.uv' options=verbose > gpfit.$INT
  /home/davidm/mmm/davidm/plotpbfits.rb -r 0.6 -n 4,4 -d /xs gpfit.$INT
  /home/davidm/mmm/davidm/plotpbfits.rb -r 0.6 -n 4,4 -d gpfit.$INT.ps/ps gpfit.$INT
end


1. ct007.1C_1003C273.1.gpfit.0.2

\begin{verbatim}

#ant pol fit iters  :  pkval     az_off   el_off  az_fwhm  el_fwhm  |residual|
###############################################################################
01 I fit 1 iters 7  : 9.96e-01   -0.072   -0.034    1.162    1.224  |X|= 0.0151
02 I fit 1 iters 7  : 1.00e+00   -0.016    0.020    1.198    1.167  |X|= 0.0198
03 I fit 1 iters 7  : 1.04e+00   -0.041   -0.065    1.148    1.183  |X|= 0.0076
04 I fit 1 iters 7  : 9.77e-01   -0.036   -0.030    1.227    1.221  |X|= 0.0128
05 I fit 1 iters 7  : 9.63e-01   -0.051   -0.088    1.216    1.203  |X|= 0.0180
06 I fit 1 iters 7  : 9.80e-01   -0.006   -0.007    1.216    1.195  |X|= 0.0203
07 I fit 1 iters 8  : 9.75e-01    0.005   -0.034    2.044    1.948  |X|= 0.0032
08 I fit 1 iters 9  : 9.61e-01    0.007   -0.075    2.055    2.160  |X|= 0.0083
09 I fit 1 iters 9  : 9.48e-01    0.032   -0.007    1.841    1.950  |X|= 0.0142
10 I fit 1 iters 8  : 9.55e-01    0.019   -0.142    1.920    1.991  |X|= 0.0036
11 I fit 1 iters 8  : 9.98e-01    0.053   -0.030    1.944    1.989  |X|= 0.0087
12 I fit 1 iters 8  : 9.51e-01   -0.026   -0.105    1.972    2.022  |X|= 0.0043
13 I fit 1 iters 8  : 9.77e-01    0.043   -0.083    1.911    1.915  |X|= 0.0050
14 I fit 1 iters 8  : 9.57e-01   -0.021    0.023    1.906    1.945  |X|= 0.0139
15 I fit 1 iters 8  : 9.71e-01    0.045   -0.187    2.009    2.035  |X|= 0.0064
\end{verbatim}

\clearpage
\begin{figure}
\psfig{figure=ct007.1C_1003C273.1.gpfit.0.2.ps,angle=-90,width=6.0in}
\caption{ct007.1C_1003C273.1.gpfit.0.2.ps}
\end{figure}

\clearpage
2. ct007.1C_1003C273.2.gpfit.0.2

\begin{verbatim}

#ant pol fit iters  :  pkval     az_off   el_off  az_fwhm  el_fwhm  |residual|
###############################################################################
01 I fit 1 iters 7  : 9.97e-01    0.001   -0.002    1.182    1.213  |X|= 0.0025
02 I fit 1 iters 7  : 1.01e+00   -0.015    0.013    1.177    1.155  |X|= 0.0177
03 I fit 1 iters 7  : 1.04e+00   -0.028   -0.015    1.183    1.163  |X|= 0.0033
04 I fit 1 iters 7  : 9.83e-01   -0.039   -0.042    1.211    1.161  |X|= 0.0051
05 I fit 1 iters 7  : 9.66e-01   -0.034   -0.004    1.227    1.188  |X|= 0.0125
06 I fit 1 iters 7  : 9.88e-01   -0.005    0.024    1.199    1.185  |X|= 0.0147
07 I fit 1 iters 8  : 9.89e-01    0.033   -0.073    1.984    1.997  |X|= 0.0013
08 I fit 1 iters 8  : 9.67e-01    0.002   -0.061    2.033    1.989  |X|= 0.0030
09 I fit 1 iters 8  : 9.50e-01    0.018   -0.105    1.974    1.962  |X|= 0.0022
10 I fit 1 iters 8  : 9.65e-01    0.042   -0.067    1.975    1.952  |X|= 0.0025
11 I fit 1 iters 8  : 9.97e-01    0.018   -0.100    1.992    1.965  |X|= 0.0012
12 I fit 1 iters 8  : 9.51e-01   -0.006   -0.090    1.971    2.038  |X|= 0.0034
13 I fit 1 iters 8  : 9.70e-01    0.059   -0.044    2.014    2.018  |X|= 0.0045
14 I fit 1 iters 8  : 9.59e-01    0.006   -0.015    2.071    1.984  |X|= 0.0014
15 I fit 1 iters 8  : 9.85e-01    0.020   -0.074    2.008    1.993  |X|= 0.0021
\end{verbatim}

\clearpage
\begin{figure}
\psfig{figure=ct007.1C_1003C273.2.gpfit.0.2.ps,angle=-90,width=6.0in}
\caption{ct007.1C_1003C273.2.gpfit.0.2.ps}
\end{figure}

\clearpage
3. ct007.1C_2303C273.1.gpfit.60

\begin{verbatim}


#ant pol fit iters  :  pkval     az_off   el_off  az_fwhm  el_fwhm  |residual|
###############################################################################
01 I fit 1 iters 7  : 1.01e+00    0.008    0.009    0.545    0.521  |X|= 0.0369
02 I fit 1 iters 7  : 1.05e+00   -0.009   -0.001    0.544    0.507  |X|= 0.0168
03 I fit 1 iters 7  : 1.01e+00   -0.013    0.023    0.519    0.519  |X|= 0.0095
04 I fit 1 iters 7  : 9.05e-01    0.025    0.020    0.554    0.524  |X|= 0.0112
05 I fit 1 iters 7  : 1.01e+00    0.016    0.019    0.541    0.508  |X|= 0.0062
06 I fit 1 iters 7  : 7.96e-01    0.035   -0.032    0.576    0.530  |X|= 0.0162
07 I fit 1 iters 50 : 7.71e-01   10.840   -9.220    9.981   11.584  |X|= 0.0080
08 I fit 1 iters 8  : 9.03e-01   -0.004    0.083    0.887    0.918  |X|= 0.0059
09 I fit 1 iters 8  : 9.47e-01   -0.045    0.021    0.837    0.855  |X|= 0.0052
10 I fit 1 iters 8  : 9.11e-01   -0.036   -0.013    0.843    0.868  |X|= 0.0011
11 I fit 1 iters 8  : 1.01e+00   -0.007   -0.002    0.834    0.894  |X|= 0.0018
12 I fit 1 iters 8  : 9.61e-01   -0.006   -0.030    0.846    0.834  |X|= 0.0126
13 I fit 1 iters 8  : 9.94e-01   -0.025   -0.052    0.849    0.805  |X|= 0.0048
14 I fit 1 iters 8  : 9.93e-01    0.013    0.023    0.930    0.890  |X|= 0.0047
15 I fit 1 iters 8  : 8.92e-01   -0.021    0.035    0.852    0.851  |X|= 0.0068
\end{verbatim}


\clearpage
\begin{figure}
\psfig{figure=ct007.1C_2303C273.1.gpfit.60.ps,angle=-90,width=6.0in}
\caption{ct007.1C_2303C273.1.gpfit.60.ps}
\end{figure}

\clearpage
3. ct007.1C_2303C273.2.gpfit.60

\begin{verbatim}

#ant pol fit iters  :  pkval     az_off   el_off  az_fwhm  el_fwhm  |residual|
###############################################################################
01 I fit 1 iters 8  : 1.07e+00   -0.013   -0.037    0.510    0.485  |X|= 0.0391
02 I fit 1 iters 50 : 8.36e-02   -4.176   -9.600    5.218    8.550  |X|= 0.0013
03 I fit 1 iters 7  : 1.06e+00    0.062   -0.029    0.522    0.479  |X|= 0.0344
04 I fit 1 iters 7  : 9.50e-01    0.055   -0.050    0.554    0.468  |X|= 0.0204
05 I fit 1 iters 7  : 1.01e+00    0.055   -0.034    0.548    0.485  |X|= 0.0107
06 I fit 1 iters 7  : 8.69e-01    0.028   -0.050    0.553    0.483  |X|= 0.0065
07 I fit 1 iters 50 : 4.98e-01   -2.862   10.928   13.647    8.472  |X|= 0.0033
08 I fit 1 iters 8  : 9.43e-01   -0.077    0.006    0.869    0.818  |X|= 0.0050
09 I fit 1 iters 8  : 9.73e-01   -0.098   -0.061    0.877    0.792  |X|= 0.0023
10 I fit 1 iters 8  : 9.37e-01   -0.026   -0.097    0.845    0.777  |X|= 0.0043
11 I fit 1 iters 8  : 1.05e+00   -0.085   -0.015    0.844    0.823  |X|= 0.0048
12 I fit 1 iters 8  : 9.89e-01   -0.034   -0.068    0.850    0.836  |X|= 0.0038
13 I fit 1 iters 8  : 1.02e+00   -0.005   -0.106    0.862    0.804  |X|= 0.0054
14 I fit 1 iters 8  : 1.03e+00   -0.048   -0.053    0.864    0.841  |X|= 0.0067
15 I fit 1 iters 8  : 9.33e-01   -0.068   -0.022    0.879    0.818  |X|= 0.0070
\end{verbatim}

\clearpage
\begin{figure}
\psfig{figure=ct007.1C_2303C273.2.gpfit.60.ps,angle=-90,width=6.0in}
\caption{ct007.1C_2303C273.2.gpfit.60.ps}
\end{figure}

\end{document}
