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Journal of Physics A Mathematical Nuclear and General

Spatial properties of quasi-stationary gaussian optical fields

Bahaa E. A. Saleh, J. M. Minkowski

Published Dec 1, 1973• 0 citations
Publisher

Abstract

The spatial coherence properties of quasi-stationary gaussian optical fields are discussed using a terminology that shows the importance of coherence functions of order N not=M. It is shown that this field is spatially less coherent than a thermal field.
DOI
10.1088/0305-4470/6/12/002

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In the general theory of optical coherence, the following problem discussed in the present paper, arises: to determine the statistical properties of a field represented by an analytic signal from the knowledge of the statistical properties of the corresponding real field. It is shown by the use of the characteristic functionals that in order to determine the joint probability distributions of the complex field at N space-time points, the knowledge of the complete statistical description of the real field is required; on the other hand, the moments of the complex field up to that order can be determined from the knowledge of the moments of the real field up to the same order. The results are illustrated by explicit calculations relating to the Gaussian random process, which, as is well known, characterizes the fluctuations of thermal light. A converse of a well-known theorem of Kac and Siegert relating to a Gaussian random process is derived as an immediate consequence of our analysis.