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

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.