Analysis of errors in polarimetry using a rotating waveplate

Yu Liang; Zhongquan Qu; Yue Zhong; Zhiming Song; Shaoying Li

doi:10.1364/AO.58.009883

Applied Optics
Vol. 58,
Issue 36,
pp. 9883-9895
(2019)
•https://doi.org/10.1364/AO.58.009883

Analysis of errors in polarimetry using a rotating waveplate

Yu Liang, Zhongquan Qu, Yue Zhong, Zhiming Song, and Shaoying Li

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Yu Liang, Zhongquan Qu, Yue Zhong, Zhiming Song, and Shaoying Li, "Analysis of errors in polarimetry using a rotating waveplate," Appl. Opt. 58, 9883-9895 (2019)

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Table of Contents Category
- Instrumentation and Measurements
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About this Article
History
- Original Manuscript: September 16, 2019
- Revised Manuscript: November 6, 2019
- Manuscript Accepted: November 6, 2019
- Published: December 11, 2019

Abstract

Modulation using a rotating waveplate is the most popular way in astronomy to obtain radiation polarization states and thus the physical condition of celestial bodies. Modulation error analysis of the rotating quarter-waveplate polarimeter is presented in this paper. In terms of geometric dimensions, three modulation error sources are analyzed: the waveplate axial error, waveplate rotation axis tip–tilt error (zenithal error), and position error of the waveplate fast axis (azimuthal error). The dispersion deviation, as another dimension of modulator error, is also studied in this paper. In theory, two factors affect the accuracy of polarization measurement using waveplate polarimetry: retardance $ \delta $and fast axis position $ \theta $. The temperature property of the waveplate, which represents the axial error, the waveplate mounting tip–tilt error, which represents the zenithal error, and the wavelength-based retardance characteristic, which represents the dispersion property of the waveplate, belong to the retardance error. The motorized rotary stage home position error and the random sample rotating position error, representing the azimuthal error, belong to the fast axis position error. These factors will be analyzed in detail here. Based on these analyses, the maximum allowable upper limits for each error source under $ 1 \times {10^{ - 4}} $ polarization measurement accuracy are presented. Also, feasible solutions are proposed to address these errors.

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				Modulation
		Coefficient of		Frequency
Signal	Phase	Amplitude	Offset	( $ω$ )
Q	0	$A Q = \frac{1}{2} (1 - \cos δ)$	$\frac{1}{2} (1 + \cos δ)$	4
U	$- \frac{π}{2}$	$A U = \frac{1}{2} (1 - \cos δ)$	0	4
V	$+ \frac{π}{2}$	$A V = \sin δ$	0	2

Items	Ideal	Simulation
Initialization parameters	$α_{1} = α_{2} = 0$	$α_{1} = 0.3$ , $α_{2} = 0.1$
Initialization parameters	$β_{1} = β_{2} = 0$	$β_{1} = 0.1$ , $β_{2} = 0.4$
Zenithal error	$d_{0} = 2 m m$	$d^{'}$ , see Eq. (17)
	$E_{z e n, 0} = 0$	$E_{z e n}$ , see Figs. 6 and 9
	$δ = 1 / 4 λ$	$δ^{'}$ , see Fig. 9
Fourier demodulation	$Q = R e (F F T (I) [4]) / A Q$	$Q = R e (F F T (I^{'}) [4]) / A Q^{'}$
	$U = I m (F F T (I) [4]) / A U$	$U = I m (F F T (I^{'}) [4]) / A U^{'}$
	$V = I m (F F T (I) [2]) / A V$	$V = I m (F F T (I^{'}) [2]) / A V^{'}$
Mueller matrix demodulation	$M = M (θ, δ)$	$M = M (θ, δ^{'})$

$λ$ nm	$γ^{\circ} C^{- 1}$	$\frac{1}{n} \frac{d n}{d λ} {n m}^{- 1}$
633	$- 1.3 \times 10^{- 4}$	$- 1.2 \times 10^{- 4}$
850	$- 1.4 \times 10^{- 4}$	$- 7.1 \times 10^{- 5}$

Items	Parameter	Maximum Permissible Value
Axis error	$Δ h$	14 nm
Zenithal error (Fourier demodulation)	$α_{1}$	0.306°
	$α_{2}$	0.306°
	$β_{1}$	0.306°
	$β_{2}$	0.306°
Azimuthal error (Fourier demodulation)	$θ_{h}$	$\pm {0.0025}^{\circ}$
Azimuthal error (Fourier demodulation)	$θ_{b r}$	$\pm {0.09}^{\circ}$

				Modulation
		Coefficient of		Frequency
Signal	Phase	Amplitude	Offset	( $ω$ )
Q	0	$A Q = \frac{1}{2} (1 - \cos δ)$	$\frac{1}{2} (1 + \cos δ)$	4
U	$- \frac{π}{2}$	$A U = \frac{1}{2} (1 - \cos δ)$	0	4
V	$+ \frac{π}{2}$	$A V = \sin δ$	0	2

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Applied Optics