A fractional cross-spectral density is defined by use of an optical fractional Fourier transform based on the rotation of a Wigner distribution function within the accuracy of the paraxial approximation. The properties of the planar Gaussian Schell-model (GSM) source field in a fractional Fourier plane are analyzed theoretically. As a result, it becomes clear that the extent, the wave-front-curvature radius, and the spectral shift of the fractional Fourier field depend strongly on the fractional order of the Fourier transform, the Fresnel number associated with the GSM source size, and the scaled spatial-coherence length of the GSM source.
© 1997 Optical Society of America
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