The fractional Fourier transform (FRT) is applied to partially coherent twisted anisotropic Gaussian–Schell model (GSM) beams based directly on the cross-spectral density. An analytical and concise formula is derived for the cross-spectral density of partially coherent twisted anisotropic GSM beams passing through a FRT system in terms of the tensor method. The corresponding tensor ABCD law for performing a FRT is obtained. The connection between the FRT formula and the generalized Collins formula for partially coherent beams is discussed. The formulas derived provide a powerful tool for analyzing and calculating the FRTs of partially coherent beams.
© 2002 Optical Society of America
(030.1640) Coherence and statistical optics : Coherence
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
Qiang Lin and Yangjian Cai, "Fractional Fourier transform for partially coherent Gaussian–Schell model beams," Opt. Lett. 27, 1672-1674 (2002)