Abstract

Paraxial propagation of a partially coherent Hermite–Gaussian beam through aligned and misaligned ABCD optical systems is investigated based on the generalized Collins formula for treating the propagation of a partially coherent beam through such optical systems. Analytical formulas for the cross-spectral density of a partially coherent Hermite–Gaussian beam propagating through such optical systems are derived. As an application example, we derive the propagation formulas for a partially coherent flattened Gaussian beam by expressing it as a superposition of a series of partially coherent Hermite–Gaussian beams by using polynomial expansion. The focusing properties of a partially coherent Hermite–Gaussian beam focused by a thin lens are studied as a numerical example.

© 2007 Optical Society of America

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