Random Error Estimation and Configuration Optimization of Dual-Rotating Compensator-Mueller Matrix Ellipsometer Calibration Experiments

Zhengwei Miao; Yuanyuan Tang; Kai Wei; Yudong Zhang

doi:10.3788/AOS202141.2412003

Acta Optica Sinica, Volume. 41, Issue 24, 2412003(2021)

Random Error Estimation and Configuration Optimization of Dual-Rotating Compensator-Mueller Matrix Ellipsometer Calibration Experiments

Zhengwei Miao^1,2,3, Yuanyuan Tang^1,2、*, Kai Wei^1,2, and Yudong Zhang^1,2

Author Affiliations

¹Key Laboratory of Adaptive Optics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China

²Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China

³University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(10)

Fig. 1. Optics path of DRC-MME calibration experiment

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Fig. 2. Random error of measurement results on zero-order noise-limited system. (a) Relationship between random error and five calibration parameters; (b) relationship between random error and phase delay of two compensators; (c) results on the symmetry axis (δ₂=δ₃)

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Fig. 3. Random error of measurement results on one-order noise-limited system. (a) Relationship between random error and five calibration parameters; (b) relationship between random error and phase delay of two compensators (δ₂=δ₃)

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Fig. 4. Random error of measurement results on two-order noise-limited system. (a) Relationship between random error and five calibration parameters; (b) result of genetic algorithm; (c) relationship between random error and phase delay of two compensators (δ₂=δ₃)

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Fig. 5. Simulation results and numerical prediction results of measured random errors. (a) Zero-order noise-limited system; (b) one-order noise-limited system; (c) two-order noise-limited system

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Fig. 6. Prototype of home-made DRC-MME structure

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Fig. 7. Distribution of three types of noise

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Fig. 8. Results of 30 repeat calibration experiments. (a) Mean; (b) variance

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Table 1. Relationship between nonzero Fourier coefficients and calibration parameters in the calibration experiment

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Table 1. Relationship between nonzero Fourier coefficients and calibration parameters in the calibration experiment

Nonzero Fourier coefficient	Corresponding equation
A₀	I₀ $[\frac{1}{4} + \frac{1}{16} \cos (2 α_{4}) (1 + \cos δ_{2}) (1 + \cos δ_{3})]$
A₄	- $\frac{I_{0}}{8}$ cos(2α₂-2α₃+2α₄)sin δ₂sin δ₃
A₈	$\frac{I_{0}}{16}$ cos(4α₂-4α₃+2α₄)(1-cos δ₂)(1-cos δ₃)
A₁₂	$\frac{I_{0}}{16}$ cos(4α₃-2α₄)(1+cos δ₂)(1-cos δ₃)
A₁₆	$\frac{I_{0}}{8}$ cos(2α₂+2α₃-2α₄)sin δ₂sin δ₃
A₂₀	$\frac{I_{0}}{16}$ cos(4α₂-2α₄)(1-cos δ₂)(1+cos δ₃)
B₄	$\frac{I_{0}}{8}$ sin(2α₂-2α₃+2α₄)sin δ₂sin δ₃
B₈	- $\frac{I_{0}}{16}$ sin(4α₂-4α₃+2α₄)(1-cos δ₂)(1-cos δ₃)
B₁₂	- $\frac{I_{0}}{16}$ sin(4α₃-2α₄)(1+cos δ₂)(1-cos δ₃)
B₁₆	- $\frac{I_{0}}{8}$ sin(2α₂+2α₃-2α₄)sin δ₂sin δ₃
B₂₀	- $\frac{I_{0}}{16}$ sin(4α₂-2α₄)(1-cos δ₂)(1+cos δ₃)

Table 2. Random errors of calibration experiment with different configurations
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Table 2. Random errors of calibration experiment with different configurations
Group α₄ /(°) α₁ /(°) ${δ_{2}}_{}$ /(°) ${δ_{3}}_{}$ /(°) $σ_{}^{2}$ /10⁶
1 90 90 90 90 2.34
2 0 90 90 90 1.92
3 90 90 127 127 0.471
4 0 90 127 127 0.436

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Zhengwei Miao, Yuanyuan Tang, Kai Wei, Yudong Zhang. Random Error Estimation and Configuration Optimization of Dual-Rotating Compensator-Mueller Matrix Ellipsometer Calibration Experiments[J]. Acta Optica Sinica, 2021, 41(24): 2412003

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