Comparison of two configurations of a Stokes polarimeter measuring three wavelengths simultaneously

Eusebio Aguilar F.; Neil C. Bruce

doi:10.1364/AO.475807

Applied Optics
Vol. 62,
Issue 1,
pp. 83-90
(2023)
•https://doi.org/10.1364/AO.475807

Comparison of two configurations of a Stokes polarimeter measuring three wavelengths simultaneously

Eusebio Aguilar F. and Neil C. Bruce

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Eusebio Aguilar F. and Neil C. Bruce, "Comparison of two configurations of a Stokes polarimeter measuring three wavelengths simultaneously," Appl. Opt. 62, 83-90 (2023)

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Abstract

In this paper, we study two configurations of a full-Stokes polarimeter that measures three wavelengths simultaneously. A recently developed fitting calibration process is used to reduce the error in the final Stokes vector. The first configuration uses an optimized setup for the central wavelength that fixes the non-optimized setups for the other two wavelengths. The second configuration is the result of a search for the best simultaneous setups for all three wavelengths. It is found that this second setup gives smaller errors in the measured Stokes parameters before calibration, but the first configuration gives smaller errors after calibration. These results demonstrate the need for a method of finding the best polarimeter configuration for this type of measurement. It seems clear that the condition number by itself is not a metric that provides sufficient information to determine whether a particular configuration is better by giving smaller errors. It is also important to point out that the results presented here are for the particular calibration scheme used. Additionally, it may be that a different calibration method is required to give better results, but that is outside the scope of the present work.

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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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Equations (14)

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	Polarizer 30°	Polarizer 130°	Half-wave plate 30°	Half-wave plate 130°	Quarter-wave plate 30°	Quarter-wave plate 130°
633 nm			$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.25 \end{matrix} \\ \begin{matrix} 0.433 \\ 0 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.47 \end{matrix} \\ \begin{matrix} 0.171 \\ 0 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ 0.125 \end{matrix} \\ \begin{matrix} 0.217 \\ 0.433 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ 0.015 \end{matrix} \\ \begin{matrix} 0.086 \\ - 0.492 \end{matrix} \end{matrix})$
543 nm	$(\begin{matrix} \begin{matrix} 0.5 \\ 0.25 \end{matrix} \\ \begin{matrix} 0.433 \\ 0 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.087 \end{matrix} \\ \begin{matrix} 0.492 \\ 0 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.213 \end{matrix} \\ \begin{matrix} 0.411 \\ 0.189 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.421 \end{matrix} \\ \begin{matrix} 0.163 \\ - 0.215 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ 0.013 \end{matrix} \\ \begin{matrix} 0.282 \\ 0.413 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.13 \end{matrix} \\ \begin{matrix} 0.111 \\ - 0.47 \end{matrix} \end{matrix})$
450 nm			$(\begin{matrix} \begin{matrix} 0.5 \\ 0.05 \end{matrix} \\ \begin{matrix} 0.26 \\ 0.424 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.082 \end{matrix} \\ \begin{matrix} 0.103 \\ - 0.483 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.098 \end{matrix} \\ \begin{matrix} 0.346 \\ 0.348 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.274 \end{matrix} \\ \begin{matrix} 0.136 \\ - 0.396 \end{matrix} \end{matrix})$

		450 nm	543 nm	633 nm
Optimized polarimeter	Polarizer (uncalibrated)	0.0465	0.0731	0.0471
	Polarizer (calibrated)	0.0391	0.0731	0.0465
	Half-wave plate (uncalibrated)	0.0850	0.0751	0.0538
	Half-wave plate (calibrated)	0.0789	0.0728	0.0487
	Quarter-wave plate (uncalibrated)	0.0696	0.0778	0.0596
	Quarter-wave plate (calibrated)	0.0627	0.0720	0.0475
Non-optimized polarimeter	Polarizer (uncalibrated)	0.1119	0.0876	0.0821
	Polarizer (calibrated)	0.0314	0.0336	0.0242
	Half-wave plate (uncalibrated)	0.1427	0.0905	0.0960
	Half-wave plate (calibrated)	0.0751	0.0344	0.0252
	Quarter-wave plate (uncalibrated)	0.1388	0.1164	0.0997
	Quarter-wave plate (calibrated)	0.0779	0.0348	0.0332

	Polarizer 30°	Polarizer 130°	Half-wave plate 30°	Half-wave plate 130°	Quarter-wave plate 30°	Quarter-wave plate 130°
633 nm			$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.25 \end{matrix} \\ \begin{matrix} 0.433 \\ 0 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.47 \end{matrix} \\ \begin{matrix} 0.171 \\ 0 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ 0.125 \end{matrix} \\ \begin{matrix} 0.217 \\ 0.433 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ 0.015 \end{matrix} \\ \begin{matrix} 0.086 \\ - 0.492 \end{matrix} \end{matrix})$
543 nm	$(\begin{matrix} \begin{matrix} 0.5 \\ 0.25 \end{matrix} \\ \begin{matrix} 0.433 \\ 0 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.087 \end{matrix} \\ \begin{matrix} 0.492 \\ 0 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.213 \end{matrix} \\ \begin{matrix} 0.411 \\ 0.189 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.421 \end{matrix} \\ \begin{matrix} 0.163 \\ - 0.215 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ 0.013 \end{matrix} \\ \begin{matrix} 0.282 \\ 0.413 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.13 \end{matrix} \\ \begin{matrix} 0.111 \\ - 0.47 \end{matrix} \end{matrix})$
450 nm			$(\begin{matrix} \begin{matrix} 0.5 \\ 0.05 \end{matrix} \\ \begin{matrix} 0.26 \\ 0.424 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.082 \end{matrix} \\ \begin{matrix} 0.103 \\ - 0.483 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.098 \end{matrix} \\ \begin{matrix} 0.346 \\ 0.348 \end{matrix} \end{matrix})$	$(\begin{matrix} \begin{matrix} 0.5 \\ - 0.274 \end{matrix} \\ \begin{matrix} 0.136 \\ - 0.396 \end{matrix} \end{matrix})$

		450 nm	543 nm	633 nm
Optimized polarimeter	Polarizer (uncalibrated)	0.0465	0.0731	0.0471
	Polarizer (calibrated)	0.0391	0.0731	0.0465
	Half-wave plate (uncalibrated)	0.0850	0.0751	0.0538
	Half-wave plate (calibrated)	0.0789	0.0728	0.0487
	Quarter-wave plate (uncalibrated)	0.0696	0.0778	0.0596
	Quarter-wave plate (calibrated)	0.0627	0.0720	0.0475
Non-optimized polarimeter	Polarizer (uncalibrated)	0.1119	0.0876	0.0821
	Polarizer (calibrated)	0.0314	0.0336	0.0242
	Half-wave plate (uncalibrated)	0.1427	0.0905	0.0960
	Half-wave plate (calibrated)	0.0751	0.0344	0.0252
	Quarter-wave plate (uncalibrated)	0.1388	0.1164	0.0997
	Quarter-wave plate (calibrated)	0.0779	0.0348	0.0332

Abstract

Data availability

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Tables (2)

Equations (14)

Applied Optics