Abstract
The measurement of the optical transmission matrix (TM) of an opaque material is an advanced form of space-variant aberration correction. Beyond imaging, TM-based methods are emerging in a range of fields, including optical communications, micro-manipulation, and computing. In many cases, the TM is very sensitive to perturbations in the configuration of the scattering medium it represents. Therefore, applications often require an up-to-the-minute characterisation of the fragile TM, typically entailing hundreds to thousands of probe measurements. Here, we explore how these measurement requirements can be relaxed using the framework of compressive sensing, in which the incorporation of prior information enables accurate estimation from fewer measurements than the dimensionality of the TM we aim to reconstruct. Examples of such priors include knowledge of a memory effect linking the input and output fields, an approximate model of the optical system, or a recent but degraded TM measurement. We demonstrate this concept by reconstructing the full-size TM of a multimode fibre supporting 754 modes at compression ratios down to ∼5% with good fidelity. We show that in this case, imaging is still possible using TMs reconstructed at compression ratios down to ∼1% (eight probe measurements). This compressive TM sampling strategy is quite general and may be applied to a variety of other scattering samples, including diffusers, thin layers of tissue, fibre optics of any refractive profile, and reflections from opaque walls. These approaches offer a route towards the measurement of high-dimensional TMs either quickly or with access to limited numbers of measurements.
Highlights
The scattering of light was long thought to be an insurmountable barrier preventing imaging through opaque materials
Examples of such priors include knowledge of a memory effect linking the input and output fields, an approximate model of the optical system, or a recent but degraded transmission matrix (TM) measurement. We demonstrate this concept by reconstructing the full-size TM of a multimode fibre supporting 754 modes at compression ratios down to ∼5% with good fidelity
An unknown TM is often measured by injecting a sequence of orthogonal input probe fields, where the nth input is denoted by an, and recording how each input field is transformed by propagation through the scatterer into the corresponding output field bn
Summary
The scattering of light was long thought to be an insurmountable barrier preventing imaging through opaque materials. Light that has undergone multiple scattering can be unscrambled to see through opaque media, such. Once the TM has been characterised, it encodes how any linear combination of probe fields will be scrambled and, more importantly, how to unscramble them again[11]. This versatile approach simplifies the task of ‘un-doing’ scattering effects, connecting the light fields on either side of a scatterer and thereby circumventing the need to consider the interaction of the light with the nano-scale structure of the scatterer itself[12,13]
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