An analytical method to recover the two-dimensional probability density function (PDF) of a random light field from the PDF of photon counts is presented. Some illustrations of the inversion procedure are given with application to the problem of light intensity interferometry.
One ofthe major limitations of intensity interferometry both in space and time domain is that only the linearly filtered signals could be registered in photon-counting mode. However, this restriction can be removed by a prior processing ofthe registered signal in a simple way before image formation from the field correlation function. This is a typical example of ill-posed inverse problems for non-symmetric transforms. We investigate the implementation of eigenfunction method to the problem of correlation function restoration from the photocount data. The effectiveness of the restoration procedure for the typical examples of astronomic images is investigated by computer simulation, both for symmetric and non-symmetric objects with phase restoration by the application of incoherent reference source.
A numerical method of estimating the probability density function of light intensity fluctuations from photon counting data is described. The solution is found as an orthogonal series of the functions which are the eigen functions of left and right iterated kernels of Mandel transformation. Inverse operator in such representation has diagonal form and provides powerful regularization of inverse problem solution by simple restriction of eigen values taken into account. The efficiency of proposed method is illustrated with results of restoration of light intensity probability functions for some typical models of speckle formation.
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