Pade approximates used for the inversion of the Poisson transform

Fraidoun Sultani; Claude Aime; Henri Lanteri

doi:10.1117/12.226727

10 November 1995 Padé approximates used for the inversion of the Poisson transform

Fraidoun Sultani, Claude Aime, Henri Lanteri

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Proceedings Volume 2647, International Conference on Holography and Correlation Optics; (1995) https://doi.org/10.1117/12.226727
Event: International Conference on Holography and Correlation Optics, 1995, Chernivsti, Ukraine

Abstract

An analytical method to recover the high light level probability density function (PDF) of a random field from its PDF in counting mode is presented. The high light PDF is related to the photo-detected PDF by the Poisson transform. The inversion of this transformation is performed as follows: the characteristic function (CF), the Fourier transform of the PDF, is first calculated as a Taylor type series where the coefficients are the photo-counting PDF. Unfortunately the limited number of p(n) that can be obtained experimentally makes this expression of (Phi) ((omega) ) valid only for very low values of (omega) , and prevents the recovering of the PDF by an inverse Fourier transform. We have proposed recently to use Pade approximants to overcome this problem and to extend the validity of the expression of (Phi) ((omega) ) towards the high values of (omega) where the Taylor series diverges. We propose here a summary of this technique and its generalization to two dimensions. A procedure making use of the application of physical constraints allows us to select the most appropriate rational approximation of the CF. We present applications of this method to astronomical speckle interferometry and show that good results can be obtained for simulated data in the case of one and two fold PDFs.

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Fraidoun Sultani, Claude Aime, and Henri Lanteri "Padé approximates used for the inversion of the Poisson transform", Proc. SPIE 2647, International Conference on Holography and Correlation Optics, (10 November 1995); https://doi.org/10.1117/12.226727

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