Semilinear Gravitational Lens Inversion

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Abstract
We describe a new method for analyzing gravitational lens images, for the case in which the source light distribution is pixelized. The method is suitable for high-resolution, high signal-to-noise ratio (S/N) data of a multiply imaged extended source. For a given mass distribution, we show that the step of inverting the image to obtain the deconvolved pixelized source light distribution, and the uncertainties, is a linear one. This means that the only parameters of the nonlinear problem are those required to model the mass distribution. This greatly simplifies the search for a minimum χ2 fit to the data and speeds up the inversion. The method is extended in a straightforward way to include linear regularization. We apply the method to simulated Einstein ring images and demonstrate the effectiveness of the inversion for both the unregularized and regularized cases.
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