Method to construct the initial structure of optical systems based on full-field aberration correction

Xianxing Chen; Xianxing Chen; Xu Zhang; Xu Zhang; Zhiqiang Su; Jie Yu; Jie Yu; Liping Wang; Liping Wang

doi:10.1364/AO.488647

Applied Optics
Vol. 62,
Issue 17,
pp. 4571-4582
(2023)
•https://doi.org/10.1364/AO.488647

Method to construct the initial structure of optical systems based on full-field aberration correction

Xianxing Chen, Xu Zhang, Zhiqiang Su, Jie Yu, and Liping Wang

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Xianxing Chen, Xu Zhang, Zhiqiang Su, Jie Yu, and Liping Wang, "Method to construct the initial structure of optical systems based on full-field aberration correction," Appl. Opt. 62, 4571-4582 (2023)

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Abstract

To meet full-field image quality requirements for extremely low aberration optical systems, an initial structure construction method for reflective optical systems based on full-field aberration correction is proposed. The aberration of the full field is used as the main evaluation criterion in this method. A multi-field evaluation function is established using the aberration values of multiple characteristic field points to represent the full-field imaging quality, and spatial ray tracing is introduced to constrain the optical system structure. Multi-objective optimization of the evaluation function is performed using a combinatorial nondominated sorting and metaheuristics algorithm; an initial optical system with a reasonable structure and corrected third-order aberrations over the full field is subsequently obtained. After optimization, an extreme ultraviolet lithography objective with a numerical aperture of 0.33 and root-mean-square wavefront error of 0.128 nm ($1/105\lambda, \lambda = 13.5\;{\rm nm}$) is obtained.

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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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Field	$X/{\rm mm}$	$Y/{\rm mm}$
F1	0	140
F2	0	144
F3	0	136
F4	26	137.56
F5	26	141.56
F6	26	133.56
F7	52	129.98
F8	52	133.98
F9	52	125.98

Parameter	Value	Parameter	Value	Parameter	Value
$\alpha _1$	1.090	$\beta _3$	1.064	${k_4}$	0.049
$\alpha _2$	0.360	$\beta _4$	0.630	${k_5}$	6.975
$\alpha _3$	1.504	$\beta _5$	−0.303	${k_6}$	0.076
$\alpha _4$	−0.679	$\beta _6$	0.941	${l_1}$	750
$\alpha _5$	3.828	${k_1}$	−0.440	${u_1}$	−0.083
$\beta _1$	−5.526	${k_2}$	1.851	${u_z}$	0.101
$\beta _2$	0.265	${k_3}$	−0.089	$y$	140

Parameter	Specifications
Wavelength	13.5 nm
Object-side FOV	$8\;{\rm mm}\times 104\;{\rm mm}$
Magnification	0.25
Numerical aperture	0.33
${\rm MIN}_{\rm OBS}$ ^a	5 mm
Wavefront error RMS	0.128 nm
Max distortion	1 nm
Max telecentricity error	1.987 mrad
Back working distance	30 mm
Total track	1500 mm

Mirror	DLZ/µm	DLX/µm	DLY/µm	DLA/µrad	DLB/µrad
M1	$\pm 1$	$\pm 1$	± $\pm 1$	$\pm 2$	$\pm 2$
M2	$\pm 1$	$\pm 1$	$\pm 1$	$\pm 2$	$\pm 2$
M3	—	—	—	$\pm 5$	$\pm 5$
M4	Alignment datum
M5	$\pm 0.5$	$\pm 1$	$\pm 1$	$\pm 2$	$\pm 2$
M6	$\pm 0.5$	—	—	$\pm 1$	$\pm 1$

Field	$X/{\rm mm}$	$Y/{\rm mm}$
F1	0	140
F2	0	144
F3	0	136
F4	26	137.56
F5	26	141.56
F6	26	133.56
F7	52	129.98
F8	52	133.98
F9	52	125.98

Abstract

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Equations (14)

Applied Optics