Experimental compressive phase space tomography

TL;DR

This paper demonstrates an experimental method for reconstructing optical correlation functions using compressive sensing, significantly reducing the number of measurements needed compared to traditional techniques.

Contribution

First experimental demonstration of compressive reconstruction of the classical optical mutual intensity function utilizing a low-entropy source assumption.

Findings

Quantitative improvements over traditional methods in reconstructing mutual intensity.

Successful validation against ground-truth measurements from the van Zernike theorem.

Effective application of compressive sensing in phase space tomography.

Abstract

Phase space tomography estimates correlation functions entirely from snapshots in the evolution of the wave function along a time or space variable. In contrast, traditional interferometric methods require measurement of multiple two-point correlations. However, as in every tomographic formulation, undersampling poses a severe limitation. Here we present the first, to our knowledge, experimental demonstration of compressive reconstruction of the classical optical correlation function, i.e. the mutual intensity function. Our compressive algorithm makes explicit use of the physically justifiable assumption of a low-entropy source (or state.) Since the source was directly accessible in our classical experiment, we were able to compare the compressive estimate of the mutual intensity to an independent ground-truth estimate from the van Cittert-Zernike theorem and verify substantial quantitative improvements in the reconstruction.