Abstract

Orthogonal expansion of a partially coherent source with a given cross-spectral density W is used to define an effective number Nof degrees of freedom and an effective number N of uncorrelated random variables characterizing the source. Relations NNTrW/λ0(TrW/W)2=Ve/Vce are established and discussed. Here Tr W, ‖W‖, and λ0 are, respectively, the trace, the norm, and the largest eigenvalue of W used as the kernel of a homogeneous Fredholm equation; Ve is an effective volume of the source; and Vce is its effective coherence volume. The main results are illustrated by a Gaussian Schell-model source.

© 1982 Optical Society of America

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