Complete Mueller matrix from a partial polarimetry experiment: the 12-element case

Oriol Arteaga; Razvigor Ossikovski

doi:10.1364/JOSAA.36.000416

Complete Mueller matrix from a partial polarimetry experiment: the 12-element case

Oriol Arteaga and Razvigor Ossikovski

Journal of the Optical Society of America A
Vol. 36,
Issue 3,
pp. 416-427
(2019)
•https://doi.org/10.1364/JOSAA.36.000416

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Oriol Arteaga and Razvigor Ossikovski, "Complete Mueller matrix from a partial polarimetry experiment: the 12-element case," J. Opt. Soc. Am. A 36, 416-427 (2019)

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Table of Contents Category
- Polizarization and Ellipsometry
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About this Article
History
- Original Manuscript: October 31, 2018
- Revised Manuscript: January 7, 2019
- Manuscript Accepted: January 8, 2019
- Published: February 22, 2019

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Abstract

Conventional generalized ellipsometry instrumentation is capable of measuring 12 out of the 16 elements of the Mueller matrix of the sample. The missing column (or row) of the experimental partial Mueller matrix can be analytically determined under additional assumptions. We identify the conditions necessary for completing the partial Mueller matrix to a full one. More specifically, such a completion is always possible if the sample is nondepolarizing; the fulfillment of additional conditions, such as the Mueller matrix exhibiting symmetries or being of a special two-component structure, are necessary if the sample is depolarizing. We report both algebraic and numerical procedures for completing the partial 12-element Mueller matrix in all tractable cases and validate them on experimental examples.

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Instrument	Partial Mueller Matrix
RPCE	$[\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ M_{21} & M_{22} & M_{23} & • \\ M_{31} & M_{32} & M_{33} & • \\ M_{41} & M_{42} & M_{43} & • \end{matrix}]$
RCAE	$[\begin{matrix} M_{11} & M_{12} & M_{13} & M_{14} \\ M_{21} & M_{22} & M_{23} & M_{24} \\ M_{31} & M_{32} & M_{33} & M_{34} \\ • & • & • & • \end{matrix}]$
Extended PME:RPPM	$θ_{m} = 0 ° (90 °) [\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ • & • & • & • \\ M_{31} & M_{32} & M_{33} & • \\ M_{41} & M_{42} & M_{43} & • \end{matrix}] & θ_{m} = \pm 45 ° [\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ M_{21} & M_{22} & M_{23} & • \\ • & • & • & • \\ M_{41} & M_{42} & M_{43} & • \end{matrix}] \Rightarrow [\begin{matrix} M_{11} & M_{12} & M_{13} & • \\ M_{21} & M_{22} & M_{23} & • \\ M_{31} & M_{32} & M_{33} & • \\ M_{41} & M_{42} & M_{43} & • \end{matrix}]$
Extended PME: PMRA	$θ_{m} = 0 ° (90 °) [\begin{matrix} M_{11} & • & M_{13} & M_{14} \\ M_{21} & • & M_{23} & M_{24} \\ M_{31} & • & M_{33} & M_{34} \\ • & • & • & • \end{matrix}] & θ_{m} = \pm 45 ° [\begin{matrix} M_{11} & M_{12} & • & M_{14} \\ M_{21} & M_{22} & • & M_{24} \\ M_{31} & M_{32} & • & M_{34} \\ • & • & • & • \end{matrix}] \Rightarrow [\begin{matrix} M_{11} & M_{12} & M_{13} & M_{14} \\ M_{21} & M_{22} & M_{23} & M_{24} \\ M_{31} & M_{32} & M_{33} & M_{34} \\ • & • & • & • \end{matrix}]$

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