Unveiling the Relationship Between Amplitude-only Transmission Matrix and Third-Order Correlation of Light Fields in Wavefront Shaping

TL;DR

This paper reveals that the amplitude-only transmission matrix is a special case of the third-order correlation of light fields, explaining their relationship and differences in computational complexity within wavefront shaping techniques.

Contribution

It establishes the theoretical connection between amplitude-only TM and TCLF methods, clarifying their roles and computational efficiencies in wavefront shaping.

Findings

Amplitude-only TM is a special case of TCLF.

TCLF has lower computational complexity than TM.

Random pixel fluctuations in TCLF act as orthogonal bases.

Abstract

In the regime of wavefront shaping (WFS) techniques, both the transmission matrix (TM) methods and a recently proposed third-order correlation of light fields (TCLF) method are effective in overcoming light scattering. This letter details the relationship between the amplitude-only TM method and the amplitude-only TCLF. The random fluctuations of different pixels on a digital micromirror device (DMD) in the amplitude-only TCLF method can be regarded as orthogonal bases, sharing the same role as the Hadamard bases in the amplitude-only TM method. This insight explains why the computational complexity of the TCLF method is significantly lower than that of the TM methods and also indicates that the amplitude-only TM is essentially a special case of the TCLF method.