Optimization analysis of a Stokes polarimeter for&#x00A0;broadband liquid crystal variable retarders under&#x00A0;the optimal objective function

Lingying Chang; Jiayi Li; Youbiao Zhang; Yuping Yin; Jingyi Liu

doi:10.1364/JOSAA.515239

Journal of the Optical Society of America A
Vol. 41,
Issue 4,
pp. 606-614
(2024)
•https://doi.org/10.1364/JOSAA.515239

Optimization analysis of a Stokes polarimeter for broadband liquid crystal variable retarders under the optimal objective function

Lingying Chang, Jiayi Li, Youbiao Zhang, Yuping Yin, and Jingyi Liu

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Lingying Chang, Jiayi Li, Youbiao Zhang, Yuping Yin, and Jingyi Liu, "Optimization analysis of a Stokes polarimeter for broadband liquid crystal variable retarders under the optimal objective function," J. Opt. Soc. Am. A 41, 606-614 (2024)

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Abstract

A liquid crystal variable retarder (LCVR) is the core device to realize fast and high-precision broadband polarization imaging, and its ability to suppress the noise will have an impact on the polarization measurement results. In order to obtain better imaging quality and measurement accuracy, it is crucial to solve the optimization problem of the LCVR. In this paper, the optimal objective function for solving the optimization problem of the LCVR is analytically derived and verified based on the genetic algorithm in the band range of 350–700 nm. Meanwhile, considering that the minimum number of four measurements at this time cannot achieve the optimal state, the relationship between the number of measurements and the overall performance relative to the error propagation (optimized conditions number) is discussed. The results show that a better optimal set of angles can be obtained by using the optimal objective function. In this paper, a set of the most favorable angles is obtained, and the optimized average of the CN is 2.0000, which is reduced by 0.32% compared with previous optimization results and is closer to the ideal value of the CN. In addition, in this paper, the noise immunity of the set of most favorable angles is simulated and analyzed, and the optimized system can effectively improve the measured performance of the wide-band liquid crystal variable retarder polarimeter.

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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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Parameter Setting	Value
Population size	100
Maximal generation	1000
Crossover rate	0.7
Mutation rate	0.003

Objective		$ε$		CN Average
Function		$\geq 90 %$	$\geq 95 %$	Average	Best	Worst
$e_{1}$	$N = 350$	4	1	2.40094	2.3458	2.5869
	$N = 70$	3	0	2.50814	2.3211	2.8836
	$N = 35$	4	1	2.36614	2.3447	2.383
	$N = 7$	4	2	2.42148	2.3311	2.5978
$e_{2}$	$N = 350$	3	0	2.41304	2.3222	2.552
	$N = 70$	2	1	2.55802	2.463	2.9602
	$N = 35$	4	0	2.44062	2.3423	2.6633
	$N = 7$	3	2	2.43642	2.333	2.5589
$e_{3}$	$N = 350$	4	2	2.39308	2.34	2.4566
	$N = 70$	2	1	2.50304	2.3649	2.6331
	$N = 35$	5	2	2.36874	2.335	2.436
	$N = 7$	4	4	2.45056	2.3547	2.6674
$e_{4}$	$N = 350$	4	1	2.55248	2.3467	3.2227
	$N = 70$	2	0	2.60046	2.3467	2.7654
	$N = 35$	5	3	2.33816	2.3211	2.3534
	$N = 7$	4	4	2.50502	2.3893	2.879

	$θ$ of ${L C V R}_{1}$ (°)	$θ$ of ${L C V R}_{2}$ (°)	Voltages of ${L C V R}_{1}$ (V)	Voltages of ${L C V R}_{2}$ (V)	CN Average
$2 \times 2$	−67.44	−44.96	4.06, 1.75	7.55, 2.25	2.3211
$2 \times 3$	−17.31	48.09	1.55, 2.09, 5.50	4.10, 1.98	2.0000
$2 \times 4$	18.91	43.2	1.50, 9.89, 2.33, 1.76	4.59, 1.99	1.9939
$3 \times 4$	−77.72	−50.33	9.93, 2.41, 1.75, 1.52	4.79, 2.06, 1.62	1.9604
$4 \times 5$	−12.28	51.01	4.65, 1.52, 9.86, 2.14, 1.72	1.56, 6.41, 2.13, 1.92	1.9329

	Optimization Results of This Paper	Optimization Results of Reference [26]
$θ$ of ${L C V R}_{1}$ (°)	−17.31	27.4
$θ$ of ${L C V R}_{2}$ (°)	48.09	72.4
Voltages of ${L C V R}_{1}$ (V)	1.55, 2.09, 5.50	1.587, 2.113, 4.981
Voltages of ${L C V R}_{2}$ (V)	4.10, 1.98	1.588, 3.525
CN average	2.0000	2.0064

Parameter Settings	$θ$ of ${L C V R}_{1}$ (°)	$θ$ of ${L C V R}_{2}$ (°)	Voltages of ${L C V R}_{1}$ (V)	Voltages of ${L C V R}_{2}$ (V)
Optimization angle	−17.31	48.09	1.55, 2.09, 5.50	4.10, 1.98
Unoptimized angle	90	45	2,4,6	8,10

	RMS Error of Stokes Vector
SNR/dB	$S_{0}$	$S_{1}$	$S_{2}$	$S_{3}$
10	0.44968	0.7086	0.58089	0.56555
20	0.12564	0.39532	0.35717	0.33921
30	0.037685	0.15406	0.09503	0.098931
40	0.012247	0.043064	0.029134	0.039108
50	0.0024918	0.011565	0.011631	0.0062204

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Journal of the Optical Society of America A