Compressively sampling the optical transmission matrix of a multimode fibre

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.

Learning and avoiding disorder in multimode fibers

“…The second vector U 2 shows a well defined symmetric pattern that corresponds to an energy conversion between modes with close-by radial and angular momenta l and m (see Fig 4b, d). This is consistent with the previous observations of mode coupling [36] and is analogous to the conversion between ballistic and single scattered photons in scattering media. This physical interpretation is made possible thanks to the precise correction of the aberrations that would otherwise destroy the symmetries of H modes .…”

Calibration-free speckle matrix imaging

“…On the one hand, compressed sensing is well established and routinely used to image a scene from an underdetermined set of measurements. Recently, reconstructing the matrix—as opposed to the scene—from compressive measurements was explored 11 , but Choi’s team does not even need to explicitly reconstruct the compressively sampled RM in their approach. On the other hand, calibration-free imaging with speckle illumination is known from blind structured-illumination microscopy 12 but not in the context of matrix imaging.…”

Multiview Virtual Confocal Microscopy Through A Multimode Fiber

“…Bending sensitivity of the fiber is another challenge and any perturbations after calibration lead to systematic errors in the image reconstruction. However, various approaches exist to mitigate fiber perturbations, including feedback mechanisms [51,[57][58][59][60][61], fiber selection [62] or illumination pattern optimization [63,64].…”