Understanding multi-layered transmission matrices

TL;DR

This paper provides a theoretical analysis of multi-layered models for transmission matrices in tissue optics, showing that sparse layers can effectively approximate complex matrices, aiding wavefront shaping.

Contribution

It introduces a theoretical framework for fitting transmission matrices with sparse multi-layered models, enhancing tissue aberration correction methods.

Findings

Transmission matrices can be accurately fitted with sparse layers.

Sparse multi-layer models enable wide field-of-view aberration correction.

The approximation quality depends on the number of layers used.

Abstract

Transmission matrices, mapping the propagation of light from one end of the tissue to the other, form an important mathematical tool in the analysis of tissue scattering and the design of wavefront shaping systems. To understand the relationship between their content and the volumetric structure of the tissue, we wish to fit them with multi-slice models, composed of a set of planar aberrations spaced throughout the volume. The number of layers used in such a model would largely affect the amount of information compression and the ease in which we can use such layered models in a wavefront-shaping system. This work offers a theoretical study of such multi-layered models. We attempt to understand how many layers are required for a good fit, and how does the approximation degrade when a smaller number of such layers is used. We show analytically that transmission matrices can be well fitted with very sparse layers. This leads to optimistic predictions on our ability to use them to design future wavefront shaping systems which can correct tissue aberration over a wide field-of-view.