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Compressively sampling the optical transmission matrix of a multimode fibre

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Document pages: 17 pages

Abstract: Measurement of the optical transmission matrix (TM) of an opaque material isan advanced form of space-variant aberration correction. Beyond imaging,TM-based methods are emerging in a range of fields including opticalcommunications, optical micro-manipulation, and optical computing. In manycases the TM is very sensitive to perturbations in the configuration of thescattering medium it represents. Therefore applications often require anup-to-the-minute characterisation of the fragile TM, typically entailinghundreds to thousands of probe measurements. In this work we explore how thesemeasurement requirements can be relaxed using the framework of compressivesensing: incorporation of prior information enables accurate estimation fromfewer measurements than the dimensionality of the TM we aim to reconstruct.Examples of such priors include knowledge of a memory effect linking input andoutput fields, an approximate model of the optical system, or a recent butdegraded TM measurement. We demonstrate this concept by reconstructing afull-size TM of a multimode fibre supporting 754 modes at compression ratiosdown to ~5 with good fidelity. The level of compression achievable isdependent upon the strength of our priors. We show in this case that imaging isstill possible using TMs reconstructed at compression ratios down to ~1 (8probe measurements). This compressive TM sampling strategy is quite general andmay be applied to any form of scattering system about which we have some priorknowledge, including diffusers, thin layers of tissue, fibre optics of anyknown refractive profile, and reflections from opaque walls. These approachesoffer a route to measurement of high-dimensional TMs quickly or with access tolimited numbers of measurements.

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