# Compressive optical interferometry

## TL;DR

This paper demonstrates that compressive sensing can be applied directly within optical hardware to efficiently reconstruct sparse optical fields from fewer measurements without additional components.

## Contribution

It introduces a method to perform compressive sensing in native optical hardware using random sub-Nyquist sampling of interferograms, avoiding extra components.

## Key findings

- Random sub-Nyquist sampling aids in reconstructing optical fields.
- Sensing matrices are provably incoherent and isotropic.
- CS can be effectively implemented in optical hardware without added complexity.

## Abstract

Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random spatial patterns that are selected from an appropriate random ensemble. We show here that CS can be exploited in `native' optics hardware without introducing added components. Specifically, we show that random sub-Nyquist sampling of an interferogram helps reconstruct the field modal structure. The distribution of reduced sensing matrices corresponding to random measurements is provably incoherent and isotropic, which helps us carry out CS successfully.