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
Lasers and Laser Optics
Original Manuscript: February 13, 2007
Revised Manuscript: April 13, 2007
Manuscript Accepted: April 16, 2007
Published: July 11, 2007
Yangjian Cai and Chiyi Chen, "Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems," J. Opt. Soc. Am. A 24, 2394-2401 (2007)