The paper presents a review of the Wigner distribution function (WDF) and of some of its applications to optical problems, especially in the field of partial coherence. The WDF describes a signal in space and in spatial frequency simultaneously and can be considered the local spatial-frequency spectrum of the signal. Although derived in terms of Fourier optics, the description of an optical signal by means of its WDF closely resembles the ray concept in geometrical optics; the WDF thus presents a link between partial coherence and radiometry. Properties of the WDF and its propagation through linear optical systems are considered; again, the description of systems by WDF’s can be interpreted directly in geometric-optical terms. Some examples are included to show how the WDF can be applied to practical problems that arise in the field of partial coherence.
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ErrataWojciech Nasalski, "Aberrationless effects of nonlinear propagation," J. Opt. Soc. Am. B 13, 1736-1747 (1996)