Optimal extraction of multiple overlapping spectra using a maximum entropy algorithm

A general algorithm of slit spectra extraction for a system of point-like sources (e.g. multiple lensed images of a quasar) has been developed, assuming that the point-spread function (PSF) induced by the measuring instrument and/or atmosphere and the positions of the spectra relative to the CCD frame are unknown. The main idea of the algorithm is to successively apply the maximum entropy method to each set of parameters, such as the spectra, the PSF, and the spectra positions, in order to iteratively improve their values. The algorithm uses all the a priori knowledge about the spectra (e.g. flux positivity, flux ratios between the components, astrometry, etc.) to compute the initial parameter sets. The main features of the algorithm, its implementation, as well as some important aspects of its practical use, are discussed in detail. Two sets of simulated spectroscopic data have been built in order to show the most characteristic properties of the algorithm and to justify its aplication to the spectra extraction of the gravitational lens system Q1009-0252 A & B (=LBQS1009-0252 A & B). Further applications of the algorithm are suggested.