Optimal extraction of multiple overlapping spectra: a new algorithm based on the maximum entropy method

A general algorithm of slit spectra extraction for a system of point-like sources (e.g. multiple lensed images of the same quasar) has been developed, assuming that the point-spread function (PSF) of the measuring instrument 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, relative magnitudes between the components, astrometry, etc.) to compute the initial parameter sets. After careful testing, the algorithm was applied to extract the spectra of the gravitationally lensed system Q1009-0252 A & B (I[SUB]B[/SUB]/I[SUB]A[/SUB]=0.1, θ[SUB]AB[/SUB]=1.''55, 1{pxl}=0.''44, typical seeing FWHM=0.''8).