Advanced Photonics Nexus, Volume. 4, Issue 3, 036010(2025)

Reciprocal polarization imaging of complex media

Zhineng Xie1... Weihao Lin1, Mengjiao Zhu1, Jianmin Yang1, Chenfan Shen1, Xin Jin1, Xiafei Qian2, and Min Xu13,* |Show fewer author(s)
Author Affiliations
  • 1Wenzhou Medical University, Institute of Lasers and Biomedical Photonics, Biomedical Engineering College, Wenzhou, China
  • 2Hangzhou First People’s Hospital, Hangzhou, China
  • 3The City University of New York, Hunter College and the Graduate Center, Department of Physics and Astronomy, New York, United States
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    Figures & Tables(8)
    (a) Lu–Chipman decomposition of a forward-scattering Mueller matrix. (b) Reciprocal polar decomposition of a backscattering Mueller matrix in reciprocal polarization imaging. The diattenuation and retardance matrices MD# and MR# in the backward path are specified by the reciprocal of their counterparts MD and MR in the forward path.
    Polarization imaging system. P, polarizer; QW, quarter-wave plate; L, lens; BS, beam splitter; M, mirror; PCCD, polarization camera; S1, sample position for backscattering Mueller matrix measurement; S2, sample position for forward-scattering Mueller matrix measurement.
    Polarization imaging of a birefringence resolution target in forward and backward geometries. The orientation angle, linear retardance, and depolarization from (a1), (b1), (c1) Lu–Chipman decomposition in forward geometry; (a2), (b2), (c2) Lu–Chipman decomposition; and (a3), (b3), (c3) reciprocal polar decomposition of the Mueller matrix measured in backward geometry. Profiles along the white arrow are displayed for (a4) the target orientation angle, (b4) linear retardance, and (c4) depolarization from Lu–Chipman decomposition of the Mueller matrix measured in forward geometry; Lu–Chipman and reciprocal polar decompositions of the Mueller matrix measured in backward geometry. Scale bar: 0.5 mm.
    Polarization imaging of fresh beef tissue sections in serial cuts with thicknesses of 100 and 300 μm. The orientation angle, linear retardance, and depolarization: (a1), (b1), (c1) Lu–Chipman decomposition of the Mueller matrix for the 100-μm section measured in forward geometry; Lu–Chipman decomposition of (a2), (b2), (c2) the 100-μm section and (a4), (b4), (c4) the 300-μm section; and reciprocal polar decomposition of (a3), (b3), (c3) the 100-μm section and (a5), (b5), (c5) the 300-μm section measured in backward geometry. Boxplots are shown for the orientation angle (a6), linear retardance (b6), and depolarization (c6) of the whole tissue section obtained by Lu–Chipman and reciprocal polar decompositions of the Mueller matrices measured in the forward and backward geometries. Only reciprocal polar decomposition correctly yields consistent orientation angles, approximately three times greater linear retardance, and greater linear retardance for the 300-μm section than for the 100-μm section. Scale bar: 0.5 mm.
    Polarization imaging of a 30-μm-thick unstained gastric cancerous tissue section. (a) Original image, (b) H&E stained histological image, and the orientation angle, linear retardance, depolarization, and depolarization anisotropy: (c), (e), (g), (i) Lu–Chipman decomposition of the forward scattering Mueller matrix, and (d), (f), (h), (j) reciprocal polar decomposition of the backscattering Mueller matrix. The red dashed line represents the boundary between the cancer [left (C)] and normal [right (N)] regions. Boxplots are shown for the orientation angle (k), linear retardance (l), depolarization (m), and depolarization anisotropy (n) of the cancerous and normal regions obtained by Lu–Chipman measured in the forward and reciprocal polar decomposition of the Mueller matrices measured in the backward geometry. Triple (linear retardance, depolarization, and depolarization anisotropy): (o) Lu–Chipman decomposition of the forward-scattering Mueller matrix and (p) reciprocal polar decomposition of the backscattering Mueller matrix. The latter better differentiates cancerous from normal gastric tissue. Scale bar: 0.5 mm.
    (a)–(b) Four configurations of the polarization imaging system.
    • Table 1. Mean and standard deviation of the orientation angle θ, linear retardance δ, and depolarization Δ for the birefringent (subscript “B”) and clear (subscript “C”) regions of the target measured in the forward and backward geometries. Erroneous values are in bold.

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      Table 1. Mean and standard deviation of the orientation angle θ, linear retardance δ, and depolarization Δ for the birefringent (subscript “B”) and clear (subscript “C”) regions of the target measured in the forward and backward geometries. Erroneous values are in bold.

      ParameterForward geometryBackward geometryGround truth from manufacturer
      Lu–ChipmanLu–ChipmanReciprocal polar
      θB (deg)34.7 (1.2)–58.7 (7.8)35.4 (0.5)34.5 (4.3)
      θC (deg)0.9 (0.7)–88.5 (9.8)0.1 (0.3)0.1 (3.8)
      δB (rad)2.45 (0.02)0.67 (0.01)2.47 (0.02)2.44 (0.08)
      δC (rad)2.37 (0.02)0.72 (0.01)2.43 (0.01)2.38 (0.07)
      ΔB0.03 (0.02)0.09 (0.04)0.10 (0.04)
      ΔC0.02 (0.02)0.03 (0.01)0.04 (0.01)
    • Table 2. Reciprocal polar decomposition of the Mueller matrix measured in the backward geometry for a multiple scattering chiral turbid medium and the extracted polarization parameters compared with the Lu–Chipman decomposition of the Mueller matrices measured in the forward and backward geometries for the same medium. Erroneous values are in bold.

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      Table 2. Reciprocal polar decomposition of the Mueller matrix measured in the backward geometry for a multiple scattering chiral turbid medium and the extracted polarization parameters compared with the Lu–Chipman decomposition of the Mueller matrices measured in the forward and backward geometries for the same medium. Erroneous values are in bold.

      Backscattering MSymmetrized [QM+(QM)T]/2
      (10.1150.0660.0230.1110.7590.0610.0010.0180.1510.4350.1390.0460.0060.1280.334)(10.1130.0240.0120.1130.7590.1060.0020.0240.1060.4350.1340.0120.0020.1340.334)
      MΔ              MRMD
      (0.99700000.79000000.42500000.359)(100000.9520.3050.03500.3070.9370.16600.0180.1680.986)(10.0660.0200.0130.06610.0010.0000.0200.0010.9980.0000.0130.0000.0000.998)
      Forward geometryBackward geometry
      ParameterLu–ChipmanLu–ChipmanReciprocal polar
      δ (rad)0.0550.1680.170
      α   (rad)0.0690.0340.157
      C (M)4.821.064.91
      Ground truth for C (M)5.05.05.0
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    Zhineng Xie, Weihao Lin, Mengjiao Zhu, Jianmin Yang, Chenfan Shen, Xin Jin, Xiafei Qian, Min Xu, "Reciprocal polarization imaging of complex media," Adv. Photon. Nexus 4, 036010 (2025)

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    Paper Information

    Category: Research Articles

    Received: Nov. 11, 2024

    Accepted: Mar. 20, 2025

    Published Online: May. 8, 2025

    The Author Email: Xu Min (minxu@hunter.cuny.edu)

    DOI:10.1117/1.APN.4.3.036010

    CSTR:32397.14.1.APN.4.3.036010

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