Snapshot imaging Mueller matrix polarimeter using modified Savart polariscopes

Qizhi Cao; Min Jiang; Chenling Jia; Siyue Jiang; Jing Zhang; Jing Zhang; Baoli Yao; Mingwu Jin; Edward Dehoog; Lian Duan; Huahua Wang; Ting Deng; Dongxin Fan

doi:10.1364/AO.481493

Applied Optics
Vol. 62,
Issue 8,
pp. 2124-2129
(2023)
•https://doi.org/10.1364/AO.481493

Snapshot imaging Mueller matrix polarimeter using modified Savart polariscopes

Qizhi Cao, Min Jiang, Chenling Jia, Siyue Jiang, Jing Zhang, Baoli Yao, Mingwu Jin, Edward Dehoog, Lian Duan, Huahua Wang, Ting Deng, and Dongxin Fan

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Qizhi Cao, Min Jiang, Chenling Jia, Siyue Jiang, Jing Zhang, Baoli Yao, Mingwu Jin, Edward Dehoog, Lian Duan, Huahua Wang, Ting Deng, and Dongxin Fan, "Snapshot imaging Mueller matrix polarimeter using modified Savart polariscopes," Appl. Opt. 62, 2124-2129 (2023)

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Table of Contents Category
- Fourier Optics and Optical Processing
Optics & Photonics Topics
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About this Article
History
- Original Manuscript: November 24, 2022
- Revised Manuscript: February 4, 2023
- Manuscript Accepted: February 5, 2023
- Published: March 8, 2023

Abstract

We present a snapshot imaging Mueller matrix polarimeter using modified Savart polariscopes (MSP-SIMMP). The MSP-SIMMP contains both the polarizing optics and the analyzing optics encoding all Mueller matrix components of the sample into the interferogram by the spatial modulation technique. An interference model and the methods of reconstruction and calibration are discussed. To demonstrate the feasibility of the proposed MSP-SIMMP, the numerical simulation and the laboratory experiment of a design example are presented. The remarkable advantage of the MSP-SIMMP is easy to calibrate. Moreover, compared with conventional imaging Mueller matrix polarimeters with rotating parts, the advantage of the proposed instrument is simple, compact, snapshot-enabled, and stationary (no moving parts).

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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$n$	$S_{n}$ (Summations of MM elements)
$0$	$16 m_{11}$
$\pm 1$	$2 m_{23} - m_{33} - m_{44} \pm 2 i m_{24} \mp i m_{34} \pm i m_{43}$
$\pm 2$	$m_{33} - m_{44} \mp i m_{34} \mp i m_{43}$
$\pm 3$	$- 4 m_{13} - 2 m_{23} + m_{33} - m_{44} \mp 4 i m_{14} \pm 2 i m_{24} \mp i m_{34} \mp i m_{43}$
$\pm 4$	$- m_{33} - m_{44} \mp i m_{34} \pm i m_{43}$
$\pm 5$	$4 m_{13} + 2 m_{23} + m_{33} + m_{44} \mp 4 i m_{14} \pm 2 i m_{24} \pm i m_{34} \mp i m_{43}$
$\pm 6$	$- m_{33} + m_{44} \pm i m_{34} \pm i m_{43}$
$\pm 7$	$- 2 m_{23} - m_{33} + m_{44} \pm 2 i m_{24} \pm i m_{34} \pm i m_{43}$
$\pm 8$	$m_{33} + m_{44} \pm i m_{34} \mp i m_{43}$
$\pm 9$	$4 m_{22} + 2 m_{32} \mp 2 i m_{42}$
$\pm 10$	$- 2 m_{32} \pm 2 i m_{42}$
$\pm 11$	$4 m_{22} - 2 m_{32} \pm 2 i m_{42}$
$\pm 12$	$2 m_{32} \mp 2 i m_{42}$
$\pm 13$	$4 m_{31} \mp 4 i m_{41}$
$\pm 14$	$- 4 m_{31} \pm 4 i m_{41}$
$\pm 15$	$- 8 m_{12}$
$\pm 16$	$- 8 m_{21}$

$m_{11} = \| I_{r 0} \| / \| I_{s 0} \|$	$m_{31} = - 2 Re {c_{13} - c_{14}}$
$m_{12} = - 2 Re {c_{15}}$	$m_{32} = - 4 Re {c_{9} - c_{11}}$
$m_{13} = - 4 Re {c_{2} + c_{7} - c_{3} - c_{6}}$	$m_{33} = 8 Re {c_{8} - c_{6}}$
$m_{14} = 4 Im {c_{2} + c_{7} - c_{3} - c_{6}}$	$m_{34} = - 8 Im {c_{8} + c_{6}}$
$m_{21} = - 2 Re {c_{16}}$	$m_{41} = 2 Im {c_{14} - c_{13}}$
$m_{22} = 4 Re {c_{11} + c_{12}}$	$m_{42} = - 4 Im {c_{11} - c_{9}}$
$m_{23} = 8 Re {c_{7} - c_{6}}$	$m_{43} = 8 Im {c_{6} - c_{8}}$
$m_{24} = 8 Im {c_{7} - c_{6}}$	$m_{44} = - 8 Re {c_{8} + c_{6}}$

$n$	$S_{n}$ (Summations of MM elements)
$0$	$16 m_{11}$
$\pm 1$	$2 m_{23} - m_{33} - m_{44} \pm 2 i m_{24} \mp i m_{34} \pm i m_{43}$
$\pm 2$	$m_{33} - m_{44} \mp i m_{34} \mp i m_{43}$
$\pm 3$	$- 4 m_{13} - 2 m_{23} + m_{33} - m_{44} \mp 4 i m_{14} \pm 2 i m_{24} \mp i m_{34} \mp i m_{43}$
$\pm 4$	$- m_{33} - m_{44} \mp i m_{34} \pm i m_{43}$
$\pm 5$	$4 m_{13} + 2 m_{23} + m_{33} + m_{44} \mp 4 i m_{14} \pm 2 i m_{24} \pm i m_{34} \mp i m_{43}$
$\pm 6$	$- m_{33} + m_{44} \pm i m_{34} \pm i m_{43}$
$\pm 7$	$- 2 m_{23} - m_{33} + m_{44} \pm 2 i m_{24} \pm i m_{34} \pm i m_{43}$
$\pm 8$	$m_{33} + m_{44} \pm i m_{34} \mp i m_{43}$
$\pm 9$	$4 m_{22} + 2 m_{32} \mp 2 i m_{42}$
$\pm 10$	$- 2 m_{32} \pm 2 i m_{42}$
$\pm 11$	$4 m_{22} - 2 m_{32} \pm 2 i m_{42}$
$\pm 12$	$2 m_{32} \mp 2 i m_{42}$
$\pm 13$	$4 m_{31} \mp 4 i m_{41}$
$\pm 14$	$- 4 m_{31} \pm 4 i m_{41}$
$\pm 15$	$- 8 m_{12}$
$\pm 16$	$- 8 m_{21}$

$m_{11} = \| I_{r 0} \| / \| I_{s 0} \|$	$m_{31} = - 2 Re {c_{13} - c_{14}}$
$m_{12} = - 2 Re {c_{15}}$	$m_{32} = - 4 Re {c_{9} - c_{11}}$
$m_{13} = - 4 Re {c_{2} + c_{7} - c_{3} - c_{6}}$	$m_{33} = 8 Re {c_{8} - c_{6}}$
$m_{14} = 4 Im {c_{2} + c_{7} - c_{3} - c_{6}}$	$m_{34} = - 8 Im {c_{8} + c_{6}}$
$m_{21} = - 2 Re {c_{16}}$	$m_{41} = 2 Im {c_{14} - c_{13}}$
$m_{22} = 4 Re {c_{11} + c_{12}}$	$m_{42} = - 4 Im {c_{11} - c_{9}}$
$m_{23} = 8 Re {c_{7} - c_{6}}$	$m_{43} = 8 Im {c_{6} - c_{8}}$
$m_{24} = 8 Im {c_{7} - c_{6}}$	$m_{44} = - 8 Re {c_{8} + c_{6}}$

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Applied Optics