Extraction of relative magnification matrices from VLBI observations of gravitational lens systems

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To get more reliable constraints on the reconstruction of gravitational lenses, we are working on a method to extract relative magnification matrices of the lensed images directly from VLBI visibilities. Instead of independently reconstructing multiple images of the source, we describe the sky brightness distribution by that of one of the images, plus a set of linear coordinate transformations for the other images characterising the action of the lens; parameters then are to be adjusted by fitting visibilities.
To parameterise the brightness profile of the source we use the shapelet formalism as introduced by Refregier (2001). Within this formalism a localised object is linearly decomposed with respect to a complete set of orthonormal basis functions. These basis functions have a number of remarkable mathematical properties -- simple behaviour under Fourier transform, convolution and coordinate transformations. This makes them a promising candidate to model compact sources as observed in strong gravitational lensing.

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