Error analysis of channeled Stokes polarimeters

Luis Oscar González-Siu; Neil C. Bruce; Neil C. Bruce

doi:10.1364/AO.423739

Applied Optics
Vol. 60,
Issue 16,
pp. 4511-4518
(2021)
•https://doi.org/10.1364/AO.423739

Error analysis of channeled Stokes polarimeters

Luis Oscar González-Siu and Neil C. Bruce

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Luis Oscar González-Siu and Neil C. Bruce, "Error analysis of channeled Stokes polarimeters," Appl. Opt. 60, 4511-4518 (2021)

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Abstract

This work presents an analysis of passive polarimeters with spectral channeling, referred to as Stokes channeled spectropolarimeters (SCS). The SCS setup comprises two thick birefringent retarders, followed by a horizontal linear polarizer. The simulation of these polarimeters and two extraction methods for the incident Stokes vector is presented as well. The effects of different retarders thickness ratios, the global retardance factor, retardance errors, axes alignment error, and Gaussian noise on root mean square (RMS) errors of the recovered Stokes parameters are described. Furthermore, two different, previously published data extraction methods are presented and compared. We found the best polarimeter configurations from the cases studied, and our results suggest that a mixed extraction process, using different extraction methods for different Stokes parameters, could give better results by reducing RMS errors by about a factor of 5. It is worth mentioning that although calibration is needed to account for the effect of errors, this is out of the scope of this 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 (24)

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			Channel Relative Position
Case	$d_{1}$	$(d_{1} : d_{2})$	$τ_{1}$	$τ_{2}$	$τ_{1} + τ_{2}$	$τ_{1} - τ_{2}$	$N_{C}$
1	$< d_{2} / 2$	(1, 3)	1	3	4	−2	9
2	$= d_{2} / 2$	(1, 2)	1	2	3	−1	7
3	$> d_{2} / 2$	(1, 1.5)	2	3	4	−1	9
4	$> 2 d_{2}$	(3, 1)	3	1	4	2	9
5	$= 2 d_{2}$	(2, 1)	2	1	3	1	7
6	$< 2 d_{2}$	(1.5, 1)	3	2	4	1	9

Index	OPD	$S_{0}$	$S_{1}$	$S_{2}$	$S_{3}$
4	$+ τ_{1} - τ_{2}$			$+ 1 / 8$	$- j 1 / 8$
3	$+ τ_{1} + τ_{2}$			$- 1 / 8$	$+ j 1 / 8$
2	$+ τ_{2}$		$+ 1 / 4$
1	$+ τ_{1}$		0
0	0	$+ 1 / 2$
$- 1$	$- τ_{1}$		0
$- 2$	$- τ_{2}$
$- 3$	$- τ_{1} - τ_{2}$			$- 1 / 8$	$- j 1 / 8$
$- 4$	$- τ_{1} + τ_{2}$			$+ 1 / 8$	$+ j 1 / 8$

			Channel Relative Position
Case	$d_{1}$	$(d_{1} : d_{2})$	$τ_{1}$	$τ_{2}$	$τ_{1} + τ_{2}$	$τ_{1} - τ_{2}$	$N_{C}$
1	$< d_{2} / 2$	(1, 3)	1	3	4	−2	9
2	$= d_{2} / 2$	(1, 2)	1	2	3	−1	7
3	$> d_{2} / 2$	(1, 1.5)	2	3	4	−1	9
4	$> 2 d_{2}$	(3, 1)	3	1	4	2	9
5	$= 2 d_{2}$	(2, 1)	2	1	3	1	7
6	$< 2 d_{2}$	(1.5, 1)	3	2	4	1	9

Index	OPD	$S_{0}$	$S_{1}$	$S_{2}$	$S_{3}$
4	$+ τ_{1} - τ_{2}$			$+ 1 / 8$	$- j 1 / 8$
3	$+ τ_{1} + τ_{2}$			$- 1 / 8$	$+ j 1 / 8$
2	$+ τ_{2}$		$+ 1 / 4$
1	$+ τ_{1}$		0
0	0	$+ 1 / 2$
$- 1$	$- τ_{1}$		0
$- 2$	$- τ_{2}$
$- 3$	$- τ_{1} - τ_{2}$			$- 1 / 8$	$- j 1 / 8$
$- 4$	$- τ_{1} + τ_{2}$			$+ 1 / 8$	$+ j 1 / 8$

Abstract

Data Availability

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Tables (2)

Equations (24)

Applied Optics