Phase-shift interferometry measured transmission matrix of turbid medium: Three-step phase-shifting interference better than four-step one

Abstract

The transmission matrix is an important tool for controlling light focusing, imaging, and communication through turbid media. It can be measured by 3-step (TM3) or 4-step (TM4) phase-shifting interference, but the similarities and differences of the transmission matrices obtained by the two methods are rarely reported. For this reason, we quantitatively compared the peak light intensity, signal-to-noise ratio, and average background of 24×24 = 576 focal points through the Wilcoxon rank sum test for paired samples (TM3-TM4), and discuss the singular value of the transmission matrix and the focal peak. The comparative results of peak light intensity and signal-to-noise ratio show that there is a significant difference between the 3-step phase shift and the 4-step phase shift transmission matrix. The focus effect of the former is significantly better than of the latter; interest centers on the focal intensity and singular value. The reciprocal of the singular value is proportional to the square of the intensity, in accordance with singular value theory. The comparison results of peak light intensity and signal-to-noise ratio strongly suggest that 3-step phase shift should be selected in the process of applying the phase shift method to measure the transmission matrix; and the singular value is of great significance in quantifying the focus, imaging, and communication quality of the transmission matrix.