Polarization Aberration Measurement Method Based on Principal Component Analysis of Differential Aerial Images

Zejiang Meng; Sikun Li; Xiangzhao Wang; Yang Bu; Chaoxing Yang; Fengzhao Dai

doi:10.3788/AOS201939.0712006

Acta Optica Sinica, Volume. 39, Issue 7, 0712006(2019)

Polarization Aberration Measurement Method Based on Principal Component Analysis of Differential Aerial Images

Zejiang Meng^1,2, Sikun Li^1,2、*, Xiangzhao Wang^1,2、**, Yang Bu^1,2, Chaoxing Yang^1,2, and Fengzhao Dai^1,2

¹ Laboratory of Information Optics and Opto-Electronic Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

² Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(6)

Fig. 1. Schematic of lithographic projection system[14]

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Fig. 2. Schematic of in-situ polarization aberration measurement system based on differential aerial images

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Fig. 3. Measurement errors of Zernike coefficients for real and imaginary parts of Pauli terms (standard deviation). (a) b1; (b) b2; (c) b3

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Table 1. Identity matrix, Pauli matrices and their eigen polarization states

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Table 1. Identity matrix, Pauli matrices and their eigen polarization states

Basis of Jones matrix	Eigen vector	Name of eigen polarization state
σ₀= $[\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array}]$	Any 2×1 vector	Unpolarized
σ₁= $[\begin{array}{l} 1 & 0 \\ 0 & - 1 \end{array}]$	$[\begin{array}{l} 1 \\ 0 \end{array}]$ , $[\begin{array}{l} 0 \\ 1 \end{array}]$	Linearly polarized (0°,90°)
σ₂= $[\begin{array}{l} 0 & 1 \\ 1 & 0 \end{array}]$	$\frac{1}{\sqrt[]{2}} [\begin{array}{l} 1 \\ 1 \end{array}]$ , $\frac{1}{\sqrt[]{2}} [\begin{array}{l} - 1 \\ 1 \end{array}]$	Linearly polarized (45°, 135°)
σ₃= $[\begin{array}{l} 0 & - i \\ i & 0 \end{array}]$	$\frac{1}{\sqrt[]{2}} [\begin{array}{l} 1 \\ i \end{array}]$ , $\frac{1}{\sqrt[]{2}} [\begin{array}{l} 1 \\ - i \end{array}]$	Circularly polarized (right, left)

Table 2. Simulation settings for the test of in-situ polarization aberration measurement

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Table 2. Simulation settings for the test of in-situ polarization aberration measurement

Part	Parameter	Value	Parameter	Value
Illuminator	Source type	Annular	Wavelength λ /nm	193
	Sigma inner	0.3	Sigma outer	0.6
	Polarization type	Constant	Polarization states /(°)	0/90, 45/135, right/left
Mask	Mask shape	Alt-PSM line	Line period l /nm	3000
	Line width w /nm	400	Line distance d /nm	500
	Phase shift /(°)	180	Orientations /(°)	0,90,30,120,60,150
Projector	Lens design	Catadioptric immersion	NA	1.35
	Immersion index	1.44	Scaling	4
	Polarization aberration	Pauli-Zernike	Re/Im amplitude	±0.02
Image	Image type	Vector aerial image	Polarizer angles /(°)	0, 90
	x (horizontal) range /nm	-1000-1000	x step /nm	50
	z (defocus) range /nm	-1200-1200	z step /nm	100

Table 3. Statistics of measurement errors of Pauli-Zernike coefficients for Pauli terms
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Table 3. Statistics of measurement errors of Pauli-Zernike coefficients for Pauli terms
Statistics b₁ error b₂ error b₃ error
Mean 2.81×10^-5 3.24×10^-5 2.43×10^-5
Std 1.01×10^-3 1.00×10^-3 1.01×10^-3

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Zejiang Meng, Sikun Li, Xiangzhao Wang, Yang Bu, Chaoxing Yang, Fengzhao Dai. Polarization Aberration Measurement Method Based on Principal Component Analysis of Differential Aerial Images[J]. Acta Optica Sinica, 2019, 39(7): 0712006

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Jan. 30, 2019

Accepted: Mar. 25, 2019

Published Online: Jul. 16, 2019

The Author Email: Li Sikun (lisikun@siom.ac.cn), Wang Xiangzhao (wxz26267@siom.ac.cn)

DOI:10.3788/AOS201939.0712006

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Identity matrix, Pauli matrices and their eigen polarization states

Table 1. Identity matrix, Pauli matrices and their eigen polarization states

Table 2. Simulation settings for the test of in-situ polarization aberration measurement

Table 2. Simulation settings for the test of in-situ polarization aberration measurement

Table 3. Statistics of measurement errors of Pauli-Zernike coefficients for Pauli terms

Table 3. Statistics of measurement errors of Pauli-Zernike coefficients for Pauli terms