Analysis of Light Fluctuations from Photon Counting Statistics

Abstract Reconstrution of light intensity fluctuations from photon-counting data is a typical ill-posed inverse problem for non-Hermitian transforming operator. Such problems cannot be solved with the help of eigenfunction representation which diagonalizes the operator and simplifies the regularization of a quasi-solution. We describe an analytical method to solve this inverse problem using the Poisson transform operator representation in a mixed basis which diagonalizes the Poisson transform. On the base of the proposed method we performed numerical experiments with typical intensity distributions. We showed that the reconstruction procedure is stable and may be used even when the level of statistical errors is relatively high. In conclusion we describe the results of the inversion procedure in application to the processing of experimental data on photon counts statistics.