A theory is developed for analyzing the structure of a focused random field in systems of large Fresnel numbers. The analysis provides a general expression for the cross-spectral density of the focused field in terms of the cross-spectral density of the random field on a spherical reference surface in the region of the diffracting aperture. The results are illustrated by considering the structure of the focal region in a field produced by focusing a partially coherent wave whose correlation function is frequently encountered in practice.
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Wang et al. (1997) studied this question.
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