Memo 103 Deconvolving Primary Beam Patterns from SKA Images

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 at each station 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 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 station. In this memo we simulate observations with the heterogeneous CARMA telescope and calculate the errors which result from the measured primary beam voltage patterns. 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 station 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.