Spectral behavior of partially coherent beam passing through an aperture

Based on the Rayleigh diffraction integral and the expansion of the hard-aperture function into a finite series of complex Gaussian functions, an approximate analytical spectrum expression for a Gaussian schell-model (GSM) beam passing through an aperture is given. The spectral shifts and spectral switches of near-zone off-axis are studied. The effect of the coherence and hard-edge on the spectral behavior are also presented.