Complete Mueller matrix from a partial polarimetry experiment: the nine-element case

Razvigor Ossikovski; Oriol Arteaga

doi:10.1364/JOSAA.36.000403

Journal of the Optical Society of America A
Vol. 36,
Issue 3,
pp. 403-415
(2019)
•https://doi.org/10.1364/JOSAA.36.000403

Complete Mueller matrix from a partial polarimetry experiment: the nine-element case

Razvigor Ossikovski and Oriol Arteaga

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Razvigor Ossikovski and Oriol Arteaga, "Complete Mueller matrix from a partial polarimetry experiment: the nine-element case," J. Opt. Soc. Am. A 36, 403-415 (2019)

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Abstract

We show that an incomplete, nine-element Mueller matrix with a row and a column missing, obtained in a partial polarimetry experiment, can be completed to a full, 16-element Mueller matrix, provided depolarization is absent experimentally. There exist exactly two solutions for the missing row and column, differing from one another only by the signs of the respective row and column elements. To select the correct solution, additional information on the sample properties, such as weak anisotropy or special symmetry, is needed. We provide analytical and numerical procedures for completing the partial Mueller matrix for the cases of practical interest and illustrate the approach on an experimental example.

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Corrections

Razvigor Ossikovski and Oriol Arteaga, "Complete Mueller matrix from a partial polarimetry experiment: the nine-element case: erratum," J. Opt. Soc. Am. A 40, 530-530 (2023)
https://opg.optica.org/josaa/abstract.cfm?uri=josaa-40-3-530

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Instrument	Partial Mueller Matrix
RPAE	$[\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ M_{21} & M_{22} & M_{23} & • \\ M_{31} & M_{32} & M_{33} & • \\ • & • & • & • \end{matrix}]$
Extended PME	PM in PSA	PM in PSG
Extended PME	$\begin{array}{c} θ_{m} = 0 ° (90 °) & θ_{m} = \pm 45 ° \\ [\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ • & • & • & • \\ M_{31} & M_{32} & M_{33} & • \\ M_{41} & M_{42} & M_{43} & • \end{matrix}] & [\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ M_{21} & M_{22} & M_{23} & • \\ • & • & • & • \\ M_{41} & M_{42} & M_{43} & • \end{matrix}] \end{array}$	$\begin{matrix} θ_{m} = 0 ° (90 °) & θ_{m} = \pm 45 ° \\ [\begin{matrix} M_{11} & • & M_{13} & M_{14} \\ M_{21} & • & M_{23} & M_{24} \\ M_{31} & • & M_{33} & M_{34} \\ • & • & • & • \end{matrix}] & \begin{matrix} [\begin{matrix} M_{11} & M_{12} & • & M_{14} \\ M_{21} & M_{22} & • & M_{24} \\ M_{31} & M_{32} & • & M_{34} \\ • & • & • & • \end{matrix}] \end{matrix} \end{matrix}$
2-MGE	PM1 in PSG & PM2 in PSA
2-MGE	$\begin{matrix} θ_{m 1} = 0 ° (90 °); θ_{m 2} = \pm 45 ° & θ_{m 1} = \pm 45 °; θ_{m 2} = 0 ° (90 °) \\ [\begin{matrix} M_{11} & • & M_{13} & M_{14} \\ M_{21} & • & M_{23} & M_{24} \\ • & • & • & • \\ M_{41} & • & M_{43} & M_{44} \end{matrix}] & [\begin{matrix} M_{11} & M_{12} & • & M_{14} \\ • & • & • & • \\ M_{31} & M_{32} & • & M_{34} \\ M_{41} & M_{42} & • & M_{44} \end{matrix}] \end{matrix}$	$\begin{matrix} θ_{m 1} = 0 ° (90 °); θ_{m 2} = 0 ° (90 °) & θ_{m 1} = \pm 45 °; θ_{m 2} = \pm 45 ° \\ [\begin{matrix} M_{11} & • & M_{13} & M_{14} \\ • & • & • & • \\ M_{31} & • & M_{33} & M_{34} \\ M_{41} & • & M_{43} & M_{44} \end{matrix}] & [\begin{matrix} M_{11} & M_{12} & • & M_{14} \\ M_{21} & M_{22} & • & M_{24} \\ • & • & • & • \\ M_{41} & M_{42} & • & M_{44} \end{matrix}] \end{matrix}$

DI experimental	DI recovered	$λ_{2}$ recovered	rms deviation
0.9955	0.9997	0.0004	0.0052
0.9936	0.9981	0.0017	0.0083
0.9866	0.9970	0.0027	0.0142
0.9826	0.9960	0.0039	0.0179
0.9775	0.9950	0.0051	0.0225
0.9712	0.9938	0.0065	0.0282
0.9605	0.9921	0.0081	0.0379

Instrument	Partial Mueller Matrix
RPAE	$[\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ M_{21} & M_{22} & M_{23} & • \\ M_{31} & M_{32} & M_{33} & • \\ • & • & • & • \end{matrix}]$
Extended PME	PM in PSA	PM in PSG
Extended PME	$\begin{array}{c} θ_{m} = 0 ° (90 °) & θ_{m} = \pm 45 ° \\ [\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ • & • & • & • \\ M_{31} & M_{32} & M_{33} & • \\ M_{41} & M_{42} & M_{43} & • \end{matrix}] & [\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ M_{21} & M_{22} & M_{23} & • \\ • & • & • & • \\ M_{41} & M_{42} & M_{43} & • \end{matrix}] \end{array}$	$\begin{matrix} θ_{m} = 0 ° (90 °) & θ_{m} = \pm 45 ° \\ [\begin{matrix} M_{11} & • & M_{13} & M_{14} \\ M_{21} & • & M_{23} & M_{24} \\ M_{31} & • & M_{33} & M_{34} \\ • & • & • & • \end{matrix}] & \begin{matrix} [\begin{matrix} M_{11} & M_{12} & • & M_{14} \\ M_{21} & M_{22} & • & M_{24} \\ M_{31} & M_{32} & • & M_{34} \\ • & • & • & • \end{matrix}] \end{matrix} \end{matrix}$
2-MGE	PM1 in PSG & PM2 in PSA
2-MGE	$\begin{matrix} θ_{m 1} = 0 ° (90 °); θ_{m 2} = \pm 45 ° & θ_{m 1} = \pm 45 °; θ_{m 2} = 0 ° (90 °) \\ [\begin{matrix} M_{11} & • & M_{13} & M_{14} \\ M_{21} & • & M_{23} & M_{24} \\ • & • & • & • \\ M_{41} & • & M_{43} & M_{44} \end{matrix}] & [\begin{matrix} M_{11} & M_{12} & • & M_{14} \\ • & • & • & • \\ M_{31} & M_{32} & • & M_{34} \\ M_{41} & M_{42} & • & M_{44} \end{matrix}] \end{matrix}$	$\begin{matrix} θ_{m 1} = 0 ° (90 °); θ_{m 2} = 0 ° (90 °) & θ_{m 1} = \pm 45 °; θ_{m 2} = \pm 45 ° \\ [\begin{matrix} M_{11} & • & M_{13} & M_{14} \\ • & • & • & • \\ M_{31} & • & M_{33} & M_{34} \\ M_{41} & • & M_{43} & M_{44} \end{matrix}] & [\begin{matrix} M_{11} & M_{12} & • & M_{14} \\ M_{21} & M_{22} & • & M_{24} \\ • & • & • & • \\ M_{41} & M_{42} & • & M_{44} \end{matrix}] \end{matrix}$

DI experimental	DI recovered	$λ_{2}$ recovered	rms deviation
0.9955	0.9997	0.0004	0.0052
0.9936	0.9981	0.0017	0.0083
0.9866	0.9970	0.0027	0.0142
0.9826	0.9960	0.0039	0.0179
0.9775	0.9950	0.0051	0.0225
0.9712	0.9938	0.0065	0.0282
0.9605	0.9921	0.0081	0.0379

Abstract

Corrections

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Figures (3)

Tables (2)

Equations (41)

Journal of the Optical Society of America A