Extended eigenvalue calibration method for overdetermined Mueller matrix polarimeters

Saúl A. Rosales; Enrique Garcia Caurel; Razvigor Ossikovski

doi:10.1364/OL.513929

Optics Letters
Vol. 49,
Issue 5,
pp. 1165-1168
(2024)
•https://doi.org/10.1364/OL.513929

Extended eigenvalue calibration method for overdetermined Mueller matrix polarimeters

Saúl A. Rosales, Enrique Garcia Caurel, and Razvigor Ossikovski

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Saúl A. Rosales, Enrique Garcia Caurel, and Razvigor Ossikovski, "Extended eigenvalue calibration method for overdetermined Mueller matrix polarimeters," Opt. Lett. 49, 1165-1168 (2024)

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Table of Contents Category
- Optical Sensors, Measurements, and Metrology
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About this Article
History
- Original Manuscript: November 20, 2023
- Revised Manuscript: January 26, 2024
- Manuscript Accepted: January 26, 2024
- Published: February 21, 2024

Abstract

The eigenvalue calibration method is a versatile approach that can be applied to any type of the Mueller matrix polarimetic setup because a precise knowledge of the optical response of the setup components is not required. The method has usually been employed in its original form to calibrate non-overdetermined polarimeters dealing with intensity data arranged in 4 × 4 matrices, but it can also be applied to calibrate overdetermined polarimeters with intensity data matrices of higher dimension. The main drawback with the original formulation of the method is its sensitivity to noise in the input data, especially if applied as it is to overdetermined intensity matrices. In the present work, we present a rigorous extension of the conventional eigenvalue calibration method to treat overdetermined data. We experimentally show that the proposed method does not enhance noise propagation, and therefore it does not degrade the quality of Mueller matrices measured with overdetermined polarimeters.

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Supplementary Material (1)

Name	Description
Supplement 1	Supplemental Material

Data availability

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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	Conventional ECM: States 1 to 4	Conventional ECM: States 5 to 8	Extended ECM: States 1 $\dots$ and 5 to 8
$⟨ W ⟩$	$(\begin{matrix} 1 & 0.999 (7) & 0.992 (6) & 0.992 (3) \\ - 0.215 (4) & 0.190 (4) & - 0.889 (3) & 0.345 (4) \\ 0.45 (1) & - 0.790 (9) & - 0.26 (1) & 0.179 (6) \\ 0.873 (5) & 0.577 (5) & - 0.360 (2) & - 0.913 (4) \end{matrix})$	$(\begin{matrix} 1 & 0.981 (3) & 0.991 (2) & 1.003 (3) \\ - 0.204 (4) & 0.203 (1) & - 0.886 (3) & 0.331 (4) \\ 0.438 (6) & - 0.776 (4) & - 0.285 (6) & 0.151 (4) \\ - 0.858 (3) & - 0.580 (3) & 0.354 (3) & 0.924 (5) \end{matrix})$	$(\begin{matrix} 1 & \dots & 0.992 (5) & 0.994 (9) & 1.000 (5) & 1.002 (3) \\ - 0.215 (4) & \dots & - 0.198 (6) & 0.190 (7) & - 0.894 (6) & 0.341 (5) \\ 0.45 (1) & \dots & 0.46 (1) & - 0.78 (1) & - 0.268 (9) & 0.166 (6) \\ 0.873 (5) & \dots & - 0.863 (5) & - 0.576 (5) & 0.354 (4) & 0.924 (5) \end{matrix})$
$⟨ A^{T} ⟩$	$(\begin{matrix} 1 & 1.015 (2) & 1.00 (1) & 1.001 (2) \\ - 0.389 (2) & 0.824 (2) & 0.409 (6) & - 0.160 (5) \\ 0.417 (3) & - 0.229 (5) & 0.585 (5) & - 0.685 (2) \\ - 0.817 (7) & - 0.546 (3) & 0.71 (1) & 0.706 (5) \end{matrix})$	$(\begin{matrix} 1 & 1.014 (3) & 1.025 (2) & 1.009 (4) \\ - 0.391 (1) & 0.836 (3) & 0.397 (2) & - 0.164 (2) \\ - 0.169 (3) & - 0.514 (3) & 0.905 (3) & - 0.159 (1) \\ 0.911 (5) & 0.297 (2) & - 0.248 (4) & - 0.985 (2) \end{matrix})$	$(\begin{matrix} 1 & \dots & 0.998 (4) & 1.014 (4) & 1.005 (5) & 1.006 (3) \\ - 0.389 (2) & \dots & - 0.386 (3) & 0.824 (5) & 0.406 (8) & - 0.166 (3) \\ 0.417 (3) & \dots & - 0.133 (7) & - 0.493 (6) & 0.89 (1) & - 0.14 (1) \\ - 0.817 (7) & \dots & 0.904 (3) & 0.292 (6) & - 0.251 (2) & - 0.977 (3) \end{matrix})$
$⟨ M_{a i r} ⟩$	$(\begin{matrix} 1 & 0.004 (1) & - 0.003 (2) & - 0.003 (1) \\ - 0.003 (2) & 0.995 (3) & 0.002 (4) & - 0.001 (2) \\ - 0.002 (3) & 0.000 (5) & 0.994 (4) & 0.006 (2) \\ - 0.002 (2) & - 0.002 (2) & - 0.001 (4) & 0.994 (2) \end{matrix})$	$(\begin{matrix} 1 & - 0.006 (1) & - 0.001 (3) & 0.002 (2) \\ - 0.002 (2) & 0.998 (2) & - 0.006 (5) & - 0.003 (4) \\ 0.003 (2) & - 0.003 (4) & 0.999 (4) & 0.003 (4) \\ - 0.001 (1) & - 0.004 (1) & 0.002 (4) & 1.000 (2) \end{matrix})$	$(\begin{matrix} 1 & - 0.0007 (9) & - 0.000 (1) & 0.000 (1) \\ - 0.002 (2) & 0.997 (1) & - 0.004 (4) & 0.0003 (9) \\ 0.002 (2) & 0.000 (4) & 0.9987 (8) & 0.003 (2) \\ - 0.001 (1) & - 0.002 (1) & - 0.001 (2) & 0.9978 (8) \end{matrix})$

Saúl A. Rosales	https://orcid.org/0009-0003-2865-4815
Enrique Garcia Caurel	https://orcid.org/0000-0001-8202-7810
Razvigor Ossikovski	https://orcid.org/0000-0002-7084-7579

Abstract

Supplementary Material (1)

Data availability

Cited By

Figures (3)

Tables (1)

Equations (8)

Optics Letters