Phase-space interpretation of spatial stationarity for coherence holography

TL;DR

This paper extends the concept of spatial stationarity in coherence holography into phase-space using the Wigner distribution function, demonstrating equivalence of ensemble and space averages and providing numerical insights.

Contribution

It introduces a phase-space framework for coherence holography, linking Wigner distribution functions with spatial stationarity and optical-field transformations.

Findings

WDF from ensemble-averaged and space-averaged coherence functions are equivalent.

Numerical simulations validate the phase-space interpretation.

The approach applies to incoherent light sources and optical propagation kernels.

Abstract

We extend the wide-sense spatial stationarity concept of coherence holography in the regime of phase-space using the wigner distribution function. We focus mainly on the incoherent light source and the Fourier and Fresnel propagation kernels for the optical-field transformation rule (inputoutput relation) and derive the same analogy in WDF. We further show that in phase-space the WDF obtained from the ensemble-averaged and space-averaged coherence functions are the same. Finally, we interpret behaviour of these results through numerical simulations.