Dual beam mapping with a maximum entropy algorithm

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Abstract
The problem of making images of the sky from dual beam (or differential) maps is a linear inversion problem in which the data are related to the unknown sky brightness distribution via a convolution with a point spread function which in general varies across the map. A solution to this problem based on the maximum entropy method has been implemented and tested, and is described in detail with particular reference to data obtained at the James Clerk Maxwell Telescope. The algorithm deconvolves a general beam function from the data and simultaneously accounts for the rotation of the local coordinate system which occurs during the map. Tests have been performed on synthetic and real data using both the maximum entropy algorithm and the existing two-step algorithm (which uses a Fourier filter followed by regridding to reconstruct the sky brightness). Both algorithms perform well in recovering source structure and fluxes, but the maximum entropy algorithm appears to be the method of choice because it deconvolves the beam response. The new algorithm makes a clear distinction between image and data space which makes general and consistent image reconstruction possible: separate dual beam maps of the same patch of sky can be combined into a single image, arbitrarily small image pixels can be used and total power observations of the source can be straightforwardly incorporated into the mapping algorithm to constrain the absolute flux level in a region of the image.

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