Optimization based on sensitivity for material birefringence in projection lens

Hongbo Shang; Luwei Zhang; Chunlai Liu; Ping Wang; Yongxin Sui; Huaijiang Yang

doi:10.3788/COL202018.062201

Chinese Optics Letters, Volume. 18, Issue 6, 062201(2020)

Optimization based on sensitivity for material birefringence in projection lens

Hongbo Shang^1,2, Luwei Zhang^1,2,3、*, Chunlai Liu¹, Ping Wang¹, Yongxin Sui^1,2, and Huaijiang Yang^1,2

Author Affiliations

¹Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China

²University of Chinese Academy of Sciences, Beijing 100049, China

³State Key Laboratory of Laser Interaction with Matter, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China

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Figures & Tables(12)

Fig. 1. Distribution of the first ±9 OZP terms.

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Fig. 2. Layout of the NA 0.93 optical system.

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Fig. 3. Birefringence map. (a) Element 1, RMS value is 0.54 nm/cm and PV value is 1.16 nm/cm; (b) element 11, RMS value is 0.52 nm/cm and PV value is 1.26 nm/cm; (c) element 17, RMS value is 0.61 nm/cm and PV value is 1.49 nm/cm.

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Fig. 4. OZP coefficients of elements 1, 11, and 17.

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Fig. 5. Retardation pupil before optimization. (a) Field 1, RMS value is 7.80 nm; (b) field 2, RMS value is 7.07 nm; (c) field 3, RMS value is 6.29 nm.

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Fig. 6. OZP coefficients of the retardation pupil before optimization.

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Fig. 7. Retardation pupil after optimization. (a) Field 1, RMS value is 2.25 nm; (b) field 2, RMS value is 2.45 nm; (c) field 3, RMS value is 2.77 nm.

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Fig. 8. OZP coefficients of the retardation pupil after optimization.

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Fig. 9. Comparison of convergence between the PSO and NLS methods.

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Table 1. First ±6 Terms of OZP

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Table 1. First ±6 Terms of OZP

$j$	$O Z_{j}$	$j$	$O Z_{j}$
1	$(\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix})$	4	$\sqrt{3} (2 ρ^{2} - 1) (\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix})$
$- 1$	$(\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix})$	$- 4$	$\sqrt{3} (2 ρ^{2} - 1) (\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix})$
2	$2 ρ (\begin{matrix} \cos θ & \sin θ \\ \sin θ & - \cos θ \end{matrix})$	5	$\sqrt{6} ρ^{2} (\begin{matrix} \cos 2 θ & \sin 2 θ \\ \sin 2 θ & - \cos 2 θ \end{matrix})$
$- 2$	$2 ρ (\begin{matrix} \cos θ & - \sin θ \\ - \sin θ & - \cos θ \end{matrix})$	$- 5$	$\sqrt{6} ρ^{2} (\begin{matrix} \cos 2 θ & - \sin 2 θ \\ - \sin 2 θ & - \cos 2 θ \end{matrix})$
3	$2 ρ (\begin{matrix} \sin θ & - \cos θ \\ - \cos θ & - \sin θ \end{matrix})$	6	$\sqrt{6} ρ^{2} (\begin{matrix} \sin 2 θ & - \cos 2 θ \\ - \cos 2 θ & - \sin 2 θ \end{matrix})$
$- 3$	$2 ρ (\begin{matrix} \sin θ & \cos θ \\ \cos θ & - \sin θ \end{matrix})$	$- 6$	$\sqrt{6} ρ^{2} (\begin{matrix} \sin 2 θ & \cos 2 θ \\ \cos 2 θ & - \sin 2 θ \end{matrix})$

Table 2. Projection Lens Parameters
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Table 2. Projection Lens Parameters
Parameter Specification
Central wavelength 193.368 nm
NA 0.93
Magnification $- 0.25$
Object height 56 mm
Resolution 65 nm
Element number 22

Table 3. Rotation Angles for Each Lens Element After Optimization

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Table 3. Rotation Angles for Each Lens Element After Optimization

Element number	Rotation angle (°)	Element number	Rotation angle (°)
1	−122.4877	12	−28.1719
2	151.9301	13	−130.8673
3	−18.5576	14	98.6486
4	−58.0564	15	163.6454
5	−166.2842	16	81.236
6	18.6296	17	53.6626
7	−40.8166	18	−41.0608
8	22.0181	19	139.3792
9	−26.4504	20	−102.1568
10	−8.5624	21	161.3852
11	163.3315	22	135.8173

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Hongbo Shang, Luwei Zhang, Chunlai Liu, Ping Wang, Yongxin Sui, Huaijiang Yang. Optimization based on sensitivity for material birefringence in projection lens[J]. Chinese Optics Letters, 2020, 18(6): 062201

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