Deconvolving Primary Beam Patterns from Mosaic and Polarization Images

Melvyn Wright & Stuartt Corder
Radio Astronomy laboratory, University of California, Berkeley,
& Caltech, Pasadena, CA.


In this memo we present a method for deconvolving the primary beam
response from interferometric images of astronomical sources.
The measured primary beam may be time variable, non axi-symmetric and
different on each antenna in the interferometer array. The method is a
simple extrapolation of existing software which subtracts a model of the
sky brightness distribution from uv data.  After subtracting the best
estimate of the sky brightness distribution weighted by the measured
primary beam pattern, the residual uv data can be re-imaged to provide
an improved model of the sky brightness distribution and the process
iterated if needed until the residual uv data are consistent with thermal
noise and other residual instrumental errors. The data are imaged using
canonical, time invariant primary beam patterns, and deconvolved using
the measured primary beam voltage patterns for each antenna.

In this memo we simulate observations with the CARMA telescope and
calculate the errors which result from the measured primary beam voltage
patterns at 100 GHz.  We show that the effects of the measured ~1 - 5%
deviations from the canonical beam patterns can be devastating, reducing
the image fidelity from ~8000 to ~50 for a source which fills the primary
beam FWHM. The image fidelity can be greatly improved by using the measured
voltage patterns in the deconvolution.

The primary beam pattern is the product of the
voltage patterns for each antenna pair, and is complex valued if the
voltage patterns are not identical. This results in a complex valued
image of a real, total intensity, sky brightness distribution; i.e.
the image shows a polarized flux distribution which varies across the
primary beam, and any real polarization distribution is confused by
flux scattered from the total intensity by primary beam errors.
Polarization images can be corrected by subtracting a model
of the source weighted by the complex valued primary beam patterns from
the uv data.