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Chin. Phys. B, 2021, Vol. 30(10): 104202    DOI: 10.1088/1674-1056/abe92a

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

Xi-Cheng Zhang(张熙程), Zuo-Gang Yang(杨佐刚), Long-Jie Fang(方龙杰), Jing-Lei Du(杜惊雷), Zhi-You Zhang(张志友), and Fu-Hua Gao(高福华)
College of Physics, Sichuan University, Chengdu 610065, China
Abstract  Transmission matrix (TM) 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. Therefore, we make a quantitative comparison of the peak light intensity, signal-to-noise ratio, and average background of 24×24 = 576 focal points between paired samples (TM3-TM4) through the Wilcoxon rank sum test, 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 matrixes. The focusing effect of the former is significantly better than that of the latter; interest concentrates on the focal intensity and singular value. The reciprocal of the singular value is proportional to the squared intensity, which is in accordance with singular value theory. The results of comparison of peak light intensity and signal-to-noise ratio strongly suggest that 3-step phase shift should be selected and used in applying the phase shift method to the measurement of the transmission matrix; and the singular value is of great significance in quantifying the focusing, imaging, and communication quality of the transmission matrix.
Keywords:  scattering media      phase modulation      transmission matrix      focal point  
Received:  20 January 2021      Revised:  15 February 2021      Accepted manuscript online:  24 February 2021
PACS:  42.25.Hz (Interference)  
  42.30.Rx (Phase retrieval)  
  78.20.-e (Optical properties of bulk materials and thin films)  
Corresponding Authors:  Long-Jie Fang, Jing-Lei Du     E-mail:;

Cite this article: 

Xi-Cheng Zhang(张熙程), Zuo-Gang Yang(杨佐刚), Long-Jie Fang(方龙杰), Jing-Lei Du(杜惊雷), Zhi-You Zhang(张志友), and Fu-Hua Gao(高福华) Phase-shift interferometry measured transmission matrix of turbid medium: Three-step phase-shifting interference better than four-step one 2021 Chin. Phys. B 30 104202

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