Compressive Optical Interferometry Under Structural Constraints

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 su ces to reconstruct the field modal structure despite the structural constraints of the measurement system set by its limited degrees of freedom. The distribution of the reduced (and structurally constrained) sensing matrices corresponding to random measurements is provably incoherent and isotropic, which helps us carry out CS successfully. We implement compressive interferometry using a generalized Mach-Zehnder interferometer in which the traditional temporal delay is replaced with a linear transformation corresponding to a fractional transform. By randomly sampling the order of the fractional transform, we e ciently reconstruct the modal content of the input beam in the Hermite-Gaussian and Laguerre-Gaussian bases.

Publication Date

3-5-2018

Publication Title

Optics Express

Volume

26

Issue

5

Number of Pages

5225-5239

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1364/OE.26.005225

Socpus ID

85042758429 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85042758429

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