Validity of the Wigner Distribution Function for Ray-based Imaging

Abstract

In this work we provide an introduction to the Wigner Distribution Function (WDF) using geometric optics principles. The WDF provides a useful model of wave-fields, allowing simulation of diffraction and interference effects. We attempt to explain these Fourier optics concepts to computational photography researchers by clarifying the relationship between the WDF and position-angle representations. We demonstrate how the WDF can be used to simulate diffraction effects using a light field representation and discuss its validity in the near-field, far-field, and under the paraxial approximation. Finally, we demonstrate that although the WDF representation contains negative values, any projection always yields a non-negative intensity value.