Compressive Direct Imaging of a Billion-Dimensional Optical Phase-Space

TL;DR

This paper introduces a compressive sensing method for direct, high-dimensional optical phase-space measurement, enabling efficient imaging of billion-dimensional spaces with high resolution and broad applicability.

Contribution

It presents a novel compressive sensing approach that overcomes previous dimensionality limitations in direct phase-space imaging, achieving billion-dimensional measurements.

Findings

Measured a 1.07-billion-dimensional phase-space.

Achieved high spatial and scalable frequency resolution.

Demonstrated accurate numerical propagation to an object.

Abstract

Optical phase-spaces represent fields of any spatial coherence, and are typically measured through phase-retrieval methods involving a computational inversion, interference, or a resolution-limiting lenslet array. Recently, a weak-values technique demonstrated that a beam's Dirac phase-space is proportional to the measurable complex weak-value, regardless of coherence. These direct measurements require scanning through all possible position-polarization couplings, limiting their dimensionality to less than 100,000. We circumvent these limitations using compressive sensing, a numerical protocol that allows us to undersample, yet efficiently measure high-dimensional phase-spaces. We also propose an improved technique that allows us to directly measure phase-spaces with high spatial resolution and scalable frequency resolution. With this method, we are able to easily measure a 1.07-billion-dimensional phase-space. The distributions are numerically propagated to an object placed in the beam path, with excellent agreement. This protocol has broad implications in signal processing and imaging, including recovery of Fourier amplitudes in any dimension with linear algorithmic solutions and ultra-high dimensional phase-space imaging.