Transmission-matrix-based point-spread-function engineering through a complex medium

TL;DR

This paper introduces a method to engineer the spatial profile of transmitted light through complex media using a transmission matrix, enabling super-resolution focusing and beam shaping in scattering environments.

Contribution

The authors develop a novel technique based on the transmission matrix to control light propagation through scattering media, extending Fourier optics concepts to complex environments.

Findings

Successfully generated sub-diffraction limited foci

Demonstrated control over various beam shapes including Bessel, donut, and helical beams

Analyzed fundamental limitations and 3D profiles of the engineered foci

Abstract

We report a method to design at will the spatial profile of transmitted coherent light after propagation through a scattering sample. We compute an operator based on the experimentally measured transmission matrix, obtained by numerically adding an arbitrary mask in the Fourier domain prior to focusing. We demonstrate the strength of the technique through several examples: propagating Bessel beams, thus generating foci smaller than the diffraction limited speckle grain, donut beams, and helical beams. We characterize the 3D profile of the achieved foci and analyze the fundamental limitations of the technique. Our approach generalizes Fourier optics concepts for random media, and opens in particular interesting perspectives for super-resolution imaging through turbid media.