Easily implemented approach for the calibration of alignment and retardation errors in a channeled spectropolarimeter

Xueping Ju; Bin Yang; Changxiang Yan; Junqiang Zhang; Wenhe Xing

doi:10.1364/AO.57.008600

Applied Optics
Vol. 57,
Issue 29,
pp. 8600-8613
(2018)
•https://doi.org/10.1364/AO.57.008600

Easily implemented approach for the calibration of alignment and retardation errors in a channeled spectropolarimeter

Xueping Ju, Bin Yang, Changxiang Yan, Junqiang Zhang, and Wenhe Xing

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Xueping Ju, Bin Yang, Changxiang Yan, Junqiang Zhang, and Wenhe Xing, "Easily implemented approach for the calibration of alignment and retardation errors in a channeled spectropolarimeter," Appl. Opt. 57, 8600-8613 (2018)

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Abstract

Calibration of the channeled spectropolarimeter is significant for the quantitative application of this instrument. In current calibration methods for a channeled spectropolarimeter, an absolute angle between the coordinate system of an auxiliary polarizer and the global coordinate system of the instrument is usually indispensable. The effectiveness of calibration depends on the precision of the absolute angle, while it is usually difficult to achieve in a practical calibration process. This paper presents an easily implemented method to simultaneously calibrate the alignment and retardation errors of high-order retarders for a channeled spectropolarimeter. In the presented method, the requirement of an absolute angle between the coordinate system of an auxiliary polarizer and the global coordinate system of the instrument is replaced by only rotating a relative angle in the coordinate system of the auxiliary polarizer itself. First, we theoretically derive the modified reconstruction model considering the alignment errors of high-order retarders. By analyzing and summarizing the modified reconstruction model, the calibration and compensation models of the alignment and retardation errors are further proposed. Then, two linearly polarized beams with a relative angle of 45° between them are utilized to determine the alignment and retardation errors. Based on these results, the alignment and retardation errors can be compensated by a software correction algorithm without any precise mechanical adjustments. The effectiveness and feasibility of the presented method are verified by numerical simulations and experiments. The advantage of easy implementation makes this calibration method more suitable to apply in the laboratory and to be on track for correcting the channeled spectropolarimeter.

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Situation	S1/S0 Error	S2/S0 Error	S3/S0 Error	DoP Error
0 deg	$9.97 \times 10^{- 7}$	$4.33 \times 10^{- 6}$	$- 3.16 \times 10^{- 6}$	$1.31 \times 10^{- 6}$
0.3 deg	$- 5.95 \times 10^{- 3}$	$6.15 \times 10^{- 3}$	$6.14 \times 10^{- 3}$	$3.71 \times 10^{- 3}$
0.6 deg	$- 1.17 \times 10^{- 2}$	$1.25 \times 10^{- 2}$	$1.25 \times 10^{- 2}$	$7.84 \times 10^{- 3}$
0.9 deg	$- 1.73 \times 10^{- 2}$	$1.90 \times 10^{- 2}$	$1.90 \times 10^{- 2}$	$1.24 \times 10^{- 2}$
1.2 deg	$- 2.27 \times 10^{- 2}$	$2.58 \times 10^{- 2}$	$2.58 \times 10^{- 2}$	$1.74 \times 10^{- 2}$

Parameter	Input Value	Calculated Value	Maximum Calculated Error	Average Calculated Error
$ϵ_{1}$	−0.5°	−0.512°	−0.056°	−0.012°
$ϵ_{2}$	0.5°	0.513°	0.027°	0.013°

Parameter	Nominal Value	Calibration Value	Actual Value
$ϕ_{2}$	636.64 rad	636.86 rad	636.86 rad
$ϕ_{1} + ϕ_{2}$	954.97 rad	955.38 rad	955.39 rad

Situation	S1/S0 Error	S2/S0 Error	S3/S0 Error	DoP Error
Without compensation	$- 2.62 \times 10^{- 2}$	$- 9.27 \times 10^{- 2}$	$- 3.41 \times 10^{- 1}$	$- 9.31 \times 10^{- 2}$
With compensation	$- 4.41 \times 10^{- 5}$	$- 7.85 \times 10^{- 4}$	$6.83 \times 10^{- 4}$	$- 7.24 \times 10^{- 4}$

Situation	Deviation Type	S1/S0 Error	S2/S0 Error	S3/S0 Error	DoP Error
Without compensation	Maximum	$- 2.96 \times 10^{- 2}$	$- 1.40 \times 10^{- 1}$	$4.73 \times 10^{- 1}$	$1.31 \times 10^{- 1}$
Without compensation	Average	$- 1.02 \times 10^{- 2}$	$- 3.06 \times 10^{- 2}$	$1.10 \times 10^{- 1}$	$3.15 \times 10^{- 2}$
With compensation	Maximum	$- 7.93 \times 10^{- 3}$	$5.38 \times 10^{- 3}$	$5.15 \times 10^{- 2}$	$- 4.63 \times 10^{- 3}$
With compensation	Average	$- 6.62 \times 10^{- 3}$	$2.37 \times 10^{- 3}$	$4.85 \times 10^{- 2}$	$- 1.25 \times 10^{- 3}$

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Applied Optics