Optimal configurations for different incident polarization states in linear polarization calibration

Xinkai Li; Xinkai Li; Bo Chen; Lingping He; Xingjun Gao; Xingjun Gao

doi:10.1364/AO.403647

Applied Optics
Vol. 59,
Issue 30,
pp. 9520-9531
(2020)
•https://doi.org/10.1364/AO.403647

Optimal configurations for different incident polarization states in linear polarization calibration

Xinkai Li, Bo Chen, Lingping He, and Xingjun Gao

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Xinkai Li, Bo Chen, Lingping He, and Xingjun Gao, "Optimal configurations for different incident polarization states in linear polarization calibration," Appl. Opt. 59, 9520-9531 (2020)

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Abstract

The purpose of polarization calibration is to measure the response matrix of an instrument and the deviation of noise to correct for subsequent flight measurements. The precision, however, is relative to the states of incident light. We investigate the influence of partially polarized light, in the presence of signal-independent additive noise or signal-dependent Poisson shot noise. We obtain the estimation precision for different numbers of the polarization state generators and analyzers in linear Stokes measurements. To reduce the influence of incident light, we suggest that the numbers of the polarization state generators and analyzers should be greater than or equal to 4. In particular, for an instrument including three polarizers oriented at 0°, 60°, and 120°, estimation precision is found to be dependent on the response matrix and incident polarization states.

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Equations (38)

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$N_{A} \times N_{B}$	$V A R [M]^{G a u} = 16 σ^{2} / (N_{A} N_{B}) \times$		$V A R [M]^{P o i} = 4 I / (N_{A} N_{B}) \times$
	$S_{1} = 0$	$S_{1} = - 0.1$	$S_{1} = 0$	$S_{1} = - 0.1$
$3 \times 3$	$(\begin{matrix} 1.00 & 2.01 & 2.00 \\ 1.95 & 4.01 & 4.00 \\ 2.00 & 4.01 & 4.00 \end{matrix})$	$(\begin{matrix} 1.00 & 2.19 & 1.82 \\ 2.00 & 4.37 & 3.63 \\ 1.99 & 4.42 & 3.59 \end{matrix})$	$(\begin{matrix} 1.00 & 1.99 & 1.98 \\ 1.97 & 4.96 & 3.00 \\ 1.99 & 2.97 & 4.92 \end{matrix})$	$(\begin{matrix} 1.00 & 2.17 & 1.89 \\ 2.09 & 5.43 & 2.79 \\ 1.93 & 3.11 & 4.75 \end{matrix})$
$4 \times 3$	$(\begin{matrix} 1.00 & 1.99 & 2.03 \\ 1.99 & 3.98 & 4.00 \\ 2.00 & 3.99 & 3.97 \end{matrix})$	1.02 $(\begin{matrix} 1.00 & 2.03 & 1.99 \\ 2.02 & 3.99 & 3.98 \\ 2.03 & 4.01 & 3.94 \end{matrix})$	$(\begin{matrix} 1.00 & 2.00 & 1.97 \\ 2.00 & 3.99 & 3.99 \\ 1.96 & 3.97 & 4.01 \end{matrix})$	1.01 $(\begin{matrix} 1.00 & 2.01 & 1.99 \\ 2.00 & 3.82 & 4.01 \\ 1.98 & 4.15 & 3.98 \end{matrix})$
$4 \times 4$	$(\begin{matrix} 1.01 & 1.99 & 1.99 \\ 2.01 & 4.01 & 3.99 \\ 1.99 & 4.02 & 4.00 \end{matrix})$	1.01 $(\begin{matrix} 1.00 & 1.98 & 1.99 \\ 2.02 & 4.01 & 4.00 \\ 2.01 & 3.97 & 4.01 \end{matrix})$	$(\begin{matrix} 1.00 & 2.01 & 1.98 \\ 1.96 & 4.01 & 4.00 \\ 1.99 & 3.98 & 3.99 \end{matrix})$	1.01 $(\begin{matrix} 1.00 & 2.01 & 2.00 \\ 2.03 & 3.98 & 4.01 \\ 1.99 & 3.99 & 4.01 \end{matrix})$

	A1	A2	A3
$V A R [M]_{3 \times 3} = I_{1 - 3} \times$	$(\begin{matrix} 1.00 & 1.82 & 1.97 \\ 1.83 & 4.96 & 2.91 \\ 1.89 & 2.98 & 4.84 \end{matrix})$	$(\begin{matrix} 1.00 & 1.97 & 1.82 \\ 1.93 & 5.20 & 2.81 \\ 1.90 & 3.06 & 4.81 \end{matrix})$	$(\begin{matrix} 1.00 & 1.89 & 2.01 \\ 1.84 & 4.97 & 2.91 \\ 1.87 & 2.89 & 4.84 \end{matrix})$
$I_{1 - 3}$	115	117	95
$V A R [M]_{4 \times 3} = I_{4 - 6} \times$	$(\begin{matrix} 1.00 & 2.03 & 1.98 \\ 2.0 4 & 3.96 & 4.02 \\ 1.94 & 4.03 & 3.93 \end{matrix})$	$(\begin{matrix} 1.00 & 2.02 & 1.99 \\ 2.08 & 3.88 & 4.08 \\ 1.98 & 4.13 & 3. 99 \end{matrix})$	$(\begin{matrix} 1.00 & 2.00 & 1.99 \\ 1.99 & 3.98 & 4.10 \\ 2.01 & 4.01 & 3.86 \end{matrix})$
$I_{4 - 6}$	71	73	68
$V A R [M]_{5 \times 5} = I_{7 - 9} \times$	$(\begin{matrix} 1.00 & 1.97 & 2.00 \\ 2.02 & 3.97 & 4.09 \\ 2.00 & 4.05 & 3.92 \end{matrix})$	$(\begin{matrix} 1.00 & 2.00 & 1.99 \\ 2.04 & 4.04 & 4.11 \\ 1.97 & 3.96 & 3.89 \end{matrix})$	$(\begin{matrix} 1.00 & 2.00 & 1.98 \\ 1.98 & 3.92 & 3.99 \\ 2.01 & 4.04 & 3.93 \end{matrix})$
$I_{7 - 9}$	35	35	32

$N_{A} \times N_{B}$	$V A R [M]^{G a u} = 16 σ^{2} / (N_{A} N_{B}) \times$		$V A R [M]^{P o i} = 4 I / (N_{A} N_{B}) \times$
	$S_{1} = 0$	$S_{1} = - 0.1$	$S_{1} = 0$	$S_{1} = - 0.1$
$3 \times 3$	$(\begin{matrix} 1.00 & 2.01 & 2.00 \\ 1.95 & 4.01 & 4.00 \\ 2.00 & 4.01 & 4.00 \end{matrix})$	$(\begin{matrix} 1.00 & 2.19 & 1.82 \\ 2.00 & 4.37 & 3.63 \\ 1.99 & 4.42 & 3.59 \end{matrix})$	$(\begin{matrix} 1.00 & 1.99 & 1.98 \\ 1.97 & 4.96 & 3.00 \\ 1.99 & 2.97 & 4.92 \end{matrix})$	$(\begin{matrix} 1.00 & 2.17 & 1.89 \\ 2.09 & 5.43 & 2.79 \\ 1.93 & 3.11 & 4.75 \end{matrix})$
$4 \times 3$	$(\begin{matrix} 1.00 & 1.99 & 2.03 \\ 1.99 & 3.98 & 4.00 \\ 2.00 & 3.99 & 3.97 \end{matrix})$	1.02 $(\begin{matrix} 1.00 & 2.03 & 1.99 \\ 2.02 & 3.99 & 3.98 \\ 2.03 & 4.01 & 3.94 \end{matrix})$	$(\begin{matrix} 1.00 & 2.00 & 1.97 \\ 2.00 & 3.99 & 3.99 \\ 1.96 & 3.97 & 4.01 \end{matrix})$	1.01 $(\begin{matrix} 1.00 & 2.01 & 1.99 \\ 2.00 & 3.82 & 4.01 \\ 1.98 & 4.15 & 3.98 \end{matrix})$
$4 \times 4$	$(\begin{matrix} 1.01 & 1.99 & 1.99 \\ 2.01 & 4.01 & 3.99 \\ 1.99 & 4.02 & 4.00 \end{matrix})$	1.01 $(\begin{matrix} 1.00 & 1.98 & 1.99 \\ 2.02 & 4.01 & 4.00 \\ 2.01 & 3.97 & 4.01 \end{matrix})$	$(\begin{matrix} 1.00 & 2.01 & 1.98 \\ 1.96 & 4.01 & 4.00 \\ 1.99 & 3.98 & 3.99 \end{matrix})$	1.01 $(\begin{matrix} 1.00 & 2.01 & 2.00 \\ 2.03 & 3.98 & 4.01 \\ 1.99 & 3.99 & 4.01 \end{matrix})$

	A1	A2	A3
$V A R [M]_{3 \times 3} = I_{1 - 3} \times$	$(\begin{matrix} 1.00 & 1.82 & 1.97 \\ 1.83 & 4.96 & 2.91 \\ 1.89 & 2.98 & 4.84 \end{matrix})$	$(\begin{matrix} 1.00 & 1.97 & 1.82 \\ 1.93 & 5.20 & 2.81 \\ 1.90 & 3.06 & 4.81 \end{matrix})$	$(\begin{matrix} 1.00 & 1.89 & 2.01 \\ 1.84 & 4.97 & 2.91 \\ 1.87 & 2.89 & 4.84 \end{matrix})$
$I_{1 - 3}$	115	117	95
$V A R [M]_{4 \times 3} = I_{4 - 6} \times$	$(\begin{matrix} 1.00 & 2.03 & 1.98 \\ 2.0 4 & 3.96 & 4.02 \\ 1.94 & 4.03 & 3.93 \end{matrix})$	$(\begin{matrix} 1.00 & 2.02 & 1.99 \\ 2.08 & 3.88 & 4.08 \\ 1.98 & 4.13 & 3. 99 \end{matrix})$	$(\begin{matrix} 1.00 & 2.00 & 1.99 \\ 1.99 & 3.98 & 4.10 \\ 2.01 & 4.01 & 3.86 \end{matrix})$
$I_{4 - 6}$	71	73	68
$V A R [M]_{5 \times 5} = I_{7 - 9} \times$	$(\begin{matrix} 1.00 & 1.97 & 2.00 \\ 2.02 & 3.97 & 4.09 \\ 2.00 & 4.05 & 3.92 \end{matrix})$	$(\begin{matrix} 1.00 & 2.00 & 1.99 \\ 2.04 & 4.04 & 4.11 \\ 1.97 & 3.96 & 3.89 \end{matrix})$	$(\begin{matrix} 1.00 & 2.00 & 1.98 \\ 1.98 & 3.92 & 3.99 \\ 2.01 & 4.04 & 3.93 \end{matrix})$
$I_{7 - 9}$	35	35	32

Abstract

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Equations (38)

Applied Optics