Proposal for optical implementation of the wigner distribution function

The Wigner distribution function (WDF) offers comprehensive insight into a signal, for it employs both space (or time) and frequency simultaneously. Whenever optical signals are involved, the importance of the WDF is significantly higher because of the diffraction (or dispersion) behavior of optical signals. Novel optical implementations of the WDF and of the inverse Wigner transform are proposed. Both implementations are based on bulk optics elements incorporating joint transform correlator architecture. A similar implementation is derived for the ambiguity function, which is related to the WDF through Fourier transformation.