Estimation precision for a normalized response matrix in linear polarization calibration

Xinkai Li; Pengfei Miao; Lingping He; Heng Shen; Xiaodong Wang; Bowen Gong; Bowen Gong; Xingjun Gao; Bo Chen

doi:10.1364/AO.465538

Applied Optics
Vol. 61,
Issue 23,
pp. 6736-6743
(2022)
•https://doi.org/10.1364/AO.465538

Estimation precision for a normalized response matrix in linear polarization calibration

Xinkai Li, Pengfei Miao, Lingping He, Heng Shen, Xiaodong Wang, Bowen Gong, Xingjun Gao, and Bo Chen

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Xinkai Li, Pengfei Miao, Lingping He, Heng Shen, Xiaodong Wang, Bowen Gong, Xingjun Gao, and Bo Chen, "Estimation precision for a normalized response matrix in linear polarization calibration," Appl. Opt. 61, 6736-6743 (2022)

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Abstract

The purpose of polarization calibration is to obtain the response matrix of an instrument such that the subsequent observation data can be corrected. The calibration precision, however, is partially restricted by the noise of the detector. We investigate the precision of the normalized response matrix in the presence of signal-independent additive noise or signal-dependent Poisson shot noise. The influences of the source intensity, type of noise, and calibration configuration on the precision are analyzed. We compare the theoretical model and the experimental measurements of the polarization calibration to show that the relative difference between the two is less than 16%. From this result, we can use the model to determine the minimum source intensity and choose the optimal configurations that provide the required precision.

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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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	Experimental Matrix	Theoretical Matrix	Experimental Matrix	Theoretical Matrix	Experimental Matrix	Theoretical Matrix
$VAR [M] = V_{1 - 3} \times V_{1 - 3}$	$(\begin{matrix} 0 & 2.03 & 1.98 \\ 2.03 & 3.89 & 3.93 \\ 1.96 & 3.82 & 3.58 \end{matrix})$	$(\begin{matrix} 0 & 2.00 & 2.00 \\ 2.00 & 3.78 & 4.00 \\ 2.00 & 4.00 & 3.78 \end{matrix})$	$(\begin{matrix} 0 & 2.02 & 1.99 \\ 2.03 & 3.85 & 3.87 \\ 1.97 & 3.89 & 3.71 \end{matrix})$	$(\begin{matrix} 0 & 2.00 & 2.00 \\ 2.00 & 3.59 & 4.00 \\ 2.00 & 4.00 & 3.59 \end{matrix})$	$(\begin{matrix} 0 & 2.02 & 1.99 \\ 2.02 & 3.52 & 3.97 \\ 1.97 & 3.84 & 3.47 \end{matrix})$	$(\begin{matrix} 0 & 2.00 & 2.00 \\ 2.00 & 3.48 & 4.00 \\ 2.00 & 4.00 & 3.48 \end{matrix})$
	$1.15 \times 10^{- 4}$	$1.12 \times 10^{- 4}$	$6.83 \times 10^{- 5}$	$6.25 \times 10^{- 5}$	$4.83 \times 10^{- 5}$	$4.27 \times 10^{- 5}$
$VAR [M] = V_{4 - 6} \times V_{4 - 6}$	$(\begin{matrix} 0 & 2.02 & 1.99 \\ 2.04 & 3.58 & 4.03 \\ 1.96 & 3.82 & 3.39 \end{matrix})$	$(\begin{matrix} 0 & 2.00 & 2.00 \\ 2.00 & 3.40 & 4.00 \\ 2.00 & 4.00 & 3.40 \end{matrix})$	$(\begin{matrix} 0 & 2.01 & 1.99 \\ 2.03 & 3.45 & 4.09 \\ 1.97 & 3.91 & 3.34 \end{matrix})$	$(\begin{matrix} 0 & 2.00 & 2.00 \\ 2.00 & 3.34 & 4.00 \\ 2.00 & 4.00 & 3.34 \end{matrix})$	$(\begin{matrix} 0 & 2.01 & 2.00 \\ 2.02 & 3.35 & 4.16 \\ 1.97 & 3.99 & 3.30 \end{matrix})$	$(\begin{matrix} 0 & 2.00 & 2.00 \\ 2.00 & 3.30 & 4.00 \\ 2.00 & 4.00 & 3.30 \end{matrix})$
	$3.75 \times 10^{- 5}$	$3.27 \times 10^{- 5}$	$2.95 \times 10^{- 5}$	$2.56 \times 10^{- 5}$	$2.44 \times 10^{- 5}$	$2.12 \times 10^{- 5}$
$VAR [M] = V_{7 - 9} \times V_{7 - 9}$	$(\begin{matrix} 0 & 2.01 & 2.00 \\ 2.01 & 3.24 & 4.03 \\ 1.98 & 4.12 & 3.23 \end{matrix})$	$(\begin{matrix} 0 & 2.00 & 2.00 \\ 2.00 & 3.26 & 4.00 \\ 2.00 & 4.00 & 3.26 \end{matrix})$	$(\begin{matrix} 0 & 1.99 & 2.02 \\ 2.01 & 3.16 & 4.15 \\ 1.99 & 4.16 & 3.22 \end{matrix})$	$(\begin{matrix} 0 & 2.00 & 2.00 \\ 2.00 & 3.25 & 4.00 \\ 2.00 & 4.00 & 3.25 \end{matrix})$	$(\begin{matrix} 0 & 1.98 & 2.03 \\ 2.00 & 3.05 & 4.06 \\ 2.00 & 4.09 & 3.11 \end{matrix})$	$(\begin{matrix} 0 & 2.00 & 2.00 \\ 2.00 & 3.23 & 4.00 \\ 2.00 & 4.00 & 3.23 \end{matrix})$
	$2.01 \times 10^{- 5}$	$1.80 \times 10^{- 5}$	$1.92 \times 10^{- 5}$	$1.72 \times 10^{- 5}$	$1.65 \times 10^{- 5}$	$1.56 \times 10^{- 5}$

Abstract

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Equations (26)

Applied Optics