Application of the Wigner distribution function in optics

Martin J. Bastiaans

This contribution presents a review of the Wigner distribution function and of some of its applications to optical problems. The Wigner distribution function describes a signal in space and (spatial) frequency simultaneously and can be considered as the local frequency spectrum of the signal. Although derived in terms of Fourier optics, the description of a signal by means of its Wigner distribution function closely resembles the ray concept in geometrical optics. It thus presents a link between Fourier optics and geometrical optics.

The concept of the Wigner distribution function is not restricted to deterministic signals; it can be applied to stochastic signals, as well, thus presenting a link between partial coherence and radiometry. Some interesting properties of partially coherent light can thus be derived easily by means of the Wigner distribution function.

Properties of the Wigner distribution function, for deterministic as well as for stochastic signals (i.e., for completely coherent as well as for partially coherent light, respectively), and its propagation through linear systems are considered; the corresponding description of signals and systems can directly be interpreted in geometric-optical terms. Some examples are included to show how the Wigner distribution function can be applied to problems that arise in the field of optics.

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