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Moment estimator approach to the retrieval problem in coherence theory

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Abstract

The purpose of this paper is to suggest a possible approach to the recovery of the spectral density function g(ω) through a knowledge of the first few measured complex zeros of the complex degree of coherence γ(τ). The assumption that γ(τ) is band-limited allows us to express the sums of inverse powers of the complex zeros of γ(τ) in terms of the moments of g(ω). Only the lowest-order moments can be evaluated in this manner with any accuracy for reasons discussed in the text. We use two estimation-type solutions that utilize lower-order moments: beta distribution model and the Shannon maximum entropy model to estimate g(CD). Representative numerical calculations are discussed.

© 1980 Optical Society of America

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