高精密成像系统膜层引入的波像差

王庆国; 赵尚男; 张纪鹏; 吴庆; 史广维

doi:10.37188/CO.2025-0136

高精密成像系统膜层引入的波像差

doi: 10.37188/CO.2025-0136

cstr: 32171.14.CO.2025-0136

王庆国^{1, 2, 3,},
赵尚男^{1, 3, ,},
张纪鹏^{1, 2, 3},
吴庆^{1, 3},
史广维^{1, 3}

1.
中国科学院长春光学精密机械与物理研究所, 吉林长春 130033
2.
中国科学院大学, 北京100049
3.
光学系统先进制造全国重点实验室, 吉林长春 130033

基金项目: 中国科学院长春光学精密机械与物理研究所青年科学基金项目（No. 62005271）；国家自然科学基金（No. 62475122）

详细信息

作者简介:
王庆国（2001—），男，山东淄博人，硕士研究生，2023年于东北石油大学获得学士学位，主要从事光学系统设计研究。E-mail:1733641607@qq.com

赵尚男（1993—），女，吉林长春人，博士，副研究员，主要从事光学设计仿真、超构表面设计的研究。E-mail：18810575846@163.com

中图分类号: TP394.1;TH691.9
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出版历程
- 收稿日期: 2025-10-27
- 修回日期: 2025-12-10
- 录用日期: 2026-02-03
- 网络出版日期: 2026-04-24

Wavefront aberrations induced by coatings in high-precision imaging systems

WANG Qing-guo^{1, 2, 3
,},
ZHAO Shang-nan^{1, 3
, ,},
ZHANG Ji-peng^{1, 2, 3},
WU Qing^{1, 3},
SHI Guang-wei^{1, 3}

1.
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
State Key Laboratory of Advanced Manufacturing for Optical Systems, Changchun 130033, China

Funds: Supported by Youth Science Fund Project of Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences (No. 62005271); National Natural Science Foundation of China (NSFC) (No. 62475122)

More Information

Corresponding author: 18810575846@163.com

摘要

摘要:
为提高系统透过率，高精密成像光学系统表面常需镀制多层膜。然而在短波段光学系统中，多层膜不仅改变表面透过率，还会引入显著的相位效应和横向位移，从而导致系统产生额外的波像差。本文针对短波段小入射角系统，系统分析了多层膜对全视场成像质量的影响。首先，利用膜层断点追迹算法，将膜层效应与光线追迹过程相结合，比较了可见光、红外及极紫外（EUV）波段系统的膜层引起的波像差。然后，以数值孔径为0.25的六反EUV投影系统为例，分析了均匀的40层Mo/Si多层膜引入的波前变化。在此基础上，提出一种基于Gram–Schmidt正交化（GSO）的EUV系统波前全视场分析方法，对弧形视场下的Zernike像差分布进行分析。结果表明，膜层引起的波像差在长波段系统中确实可忽略，而在短波段系统中则十分显著；膜层对EUV引入明显的倾斜和离焦，使得波前RMS由0.016λ增至0.842λ；全视场分析表明，膜层引入了0.727λ全视场倾斜和0.034λ视场无关的离焦，倾斜主要引起平移、倍率和低阶畸变等视场相关波前变化。研究表明，膜层引起EUV系统剧烈的像面变形，应在设计阶段将膜层影响纳入考虑范围。
- 多层膜 /
- 波像差 /
- 横向位移 /
- 极紫外(EUV)光学系统 /
- Gram–Schmidt正交化(GSO) /
- 光学设计
Abstract:
Multilayer coatings are widely applied to high-precision imaging optics to improve throughput. In short-wavelength systems, however, coatings not only alter transmittance/reflectance but also introduce pronounced phase effects and coating-induced lateral shifts, which collectively manifest as additional wavefront aberrations at the system level. This work systematically investigates coating-induced full-field degradation in short-wavelength imaging systems operated at small angles of incidence. A multilayer-coating break-point ray-tracing algorithm is used to incorporate coating-induced phase and lateral-shift effects into the geometrical ray-tracing workflow, enabling a comparative evaluation of coating-induced wavefront aberrations in the visible, infrared, and extreme ultraviolet (EUV) bands. A six-mirror EUV projection system (NA = 0.25) is then analyzed to quantify the wavefront changes introduced by a uniform 40-bilayer Mo/Si multilayer coating. Furthermore, a full-field wavefront analysis method based on Gram–Schmidt orthogonalization (GSO) is developed to characterize the field dependence of Fringe-Zernike aberration coefficients over a curved image field. The results indicate that coating-induced wavefront aberrations are negligible for long-wavelength systems but become significant in the short-wavelength regime. In the EUV example, the coating introduces strong tilt and defocus, increasing the RMS wavefront error from 0.016λ to 0.842λ. Full-field analysis shows a 0.727λ field-dependent tilt component and a 0.034λ field-independent defocus component; the tilt terms primarily correspond to image translation, magnification variation, and low-order distortion. These results demonstrate that multilayer coatings can induce severe image-plane deformation in EUV systems and therefore must be accounted for during the optical design stage.
- multilayer coating /
- wavefront aberration /
- lateral displacement /
- extreme ultraviolet (EUV) projection optics /
- Gram–Schmidt orthogonalization (GSO) /
- optical system design

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图 1 EUV投影系统结构。物方离轴视场高度为134～142 mm

Figure 1. Optical layout of the EUV projection system. The object-side off-axis field height ranges from 134 mm to 142 mm

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图 2 修正均匀膜层的反射相位和反射率随入射角的变化。实线、虚线和点划线分别表示表面1、3、5膜层反射特性

Figure 2. Reflection phase and reflectivity of the corrected uniform multilayer coating versus angle of incidence. The solid, dashed, and dash-dotted curves correspond to surfaces 1, 3, and 5, respectively

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图 3 横向位移和额外相移随入射角的变化，入射角范围0~28°

Figure 3. Coating-induced lateral shift and the associated additional phase versus angle of incidence (AOI = 0–28°)

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图 4 膜层断点追迹算法与有效反射深度算法计算的横向位移比较。二者在小角度下具有良好的一致性

Figure 4. Comparison of the lateral shift computed by the multilayer break-point ray-tracing method and the effective reflection-depth method. The two approaches agree well at small angles of incidence

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图 5 FFTM与HFTM计算的反射场振幅与相位随入射角分布情况。振幅、相位曲线对应左y轴，差值曲线对应右y轴

Figure 5. Reflected-field amplitude and phase versus angle of incidence calculated using FFTM and the HFTM. The amplitude/phase curves correspond to the left y-axis, and the difference curves correspond to the right y-axis

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图 6 比较不同波段膜层影响的反射系统

Figure 6. Test reflective system used to compare coating-induced effects at different wavelength bands

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图 7 弧形视场形状及视场采样数

Figure 7. Curved scanning field and the corresponding field-sampling grid

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图 8 裸系统、镀膜系统及膜层引入波像差的前16项Zernike系数全视场分布。（a）、（b）、（c）中相同Zernike项绘制范围一致

Figure 8. Full-field maps of the first 16 Fringe-Zernike coefficients for (a) the uncoated system, (b) the coated system, and (c) the coating-induced aberration (coated minus uncoated). For each Zernike term, the color scale limits are kept identical in (a)–(c)

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图 9 Z₂～Z₄拟合系数及拟合误差

Figure 9. Fitting coefficients and fitting errors of Z₂–Z₄

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表 1 EUV系统各表面平均入射角和膜层厚度

Table 1. Average incidence angle and coating thickness of each surface in the EUV system

表面序号	平均入射角/°	Si/nm	Mo/nm
1	6.5034	4.2272	2.8181
2	6.5397	4.2275	2.8183
3	17.6011	4.4063	2.9375
4	8.3387	4.2449	2.8299
5	10.6555	4.2737	2.8491
6	3.7275	4.2089	2.8059

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表 2 倾斜平面镜镀膜前后波前RMS。对600 nm和1100 nm采取2种膜层形式，括号中数据是镀有膜系一的波前RMS

Table 2. Wavefront RMS of a tilted plane mirror before and after coating. Two alternative multilayer designs are used for the 600-nm and 1100-nm cases. The data in parentheses corresponding to the wavefront RMS with coating type I applied

波长/nm	镀膜前RMS(λ)	镀膜后RMS(λ)
13.4	0.0000	0.1691
600	0.0000	0.0440(0.0069)
1100	0.0000	0.0203(0.0038)

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表 3 裸系统和镀膜系统的各Zernike项沿视场变化的RMS（单位：λ@13.4 nm）

Table 3. Field-dependent RMS of each Fringe-Zernike term for the uncoated and coated systems (unit: λ@13.4 nm)

Zernike项	未镀膜	镀膜
Z₂	0.00121	0.31954
Z₃	0.00537	1.41882
Z₄	0.01855	0.05474
Z₅	0.01623	0.01565
Z₆	0.00752	0.00727
Z₇	0.00242	0.00223
Z₈	0.01071	0.00995
Z₉	0.00323	0.00387
Z₁₀	0.00165	0.00213
Z₁₁	0.00225	0.00296
Z₁₂	0.00605	0.00660
Z₁₃	0.00278	0.00304
Z₁₄	0.00184	0.00181
Z₁₅	0.00806	0.00790
Z₁₆	0.00143	0.00111

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表 4 对x^2myⁿ正交化的前8项系数矩阵

Table 4. Coefficient matrix of the first eight terms in the orthogonalization of x^2myⁿ

1	y	y²	y³	y⁴	x²	x²y	x²y²
1.000	0	0	0	0	0	0	0
−34.910	36.832	0	0	0	0	0	0
1.015E3	−2.153E3	1.142E3	0	0	0	0	0
−2.993E4	9.555E5	−1.016E5	3.600E4	0	0	0	0
4.701E3	−1.531E4	1.654E4	−5.934E3	5.5765	0	0	0
6.466E3	−1.799E4	1.646E4	−4.941E3	−301.235	319.7468	0	0
−8.479E4	2.652E5	−2.763E5	9.594E4	1.101E4	−2.341E4	1.244E4	0
4.543E4	−1.434E5	1.509E5	−5.291E4	−1.167E5	3.743E5	−4.001E5	1.425E5

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表 5 正交多项式拟合的Zernike系数的视场分布（单位:λ@13.4 nm）

Table 5. Field dependence of Zernike coefficients described by the orthogonal polynomial fitting (unit: λ@13.4 nm)

m	n	Z₂	Z₃	Z₄	Z₅	Z₆	Z₇	Z₈	Z₉
0	0	−0.278	−1.419	0.059	0.012	−0.005	−0.001	−0.004	0.001
0	1	0.118	−0.053	−0.001	0.002	0.002	0.000	0.000	0.000
0	2	0.000	−0.005	0.000	0.000	0.000	0.000	0.000	0.000
0	3	−0.014	−0.003	0.000	0.000	0.000	0.000	0.000	0.000
1	0	−0.099	−0.016	0.000	0.000	−0.002	0.000	0.001	0.000
1	1	−0.027	−0.004	0.000	0.000	0.000	0.000	0.000	0.000
1	2	−0.005	0.001	0.000	0.000	0.000	0.000	0.000	0.000
1	3	−0.005	0.001	0.000	0.000	0.000	0.000	0.000	0.000
2	0	0.014	−0.004	0.000	0.000	0.000	0.000	0.000	0.000
2	1	0.011	0.003	0.000	0.000	0.000	0.000	0.000	0.000
2	2	0.005	0.000	0.000	0.000	0.000	0.000	0.000	0.000
2	3	0.002	0.000	0.000	0.000	0.000	0.000	0.000	0.000
3	0	−0.005	0.003	0.000	0.000	0.000	0.000	0.000	0.000
3	1	−0.006	0.000	0.000	0.000	0.000	0.000	0.000	0.000
3	2	−0.003	0.000	0.000	0.000	0.000	0.000	0.000	0.000
3	3	−0.001	0.000	0.000	0.000	0.000	0.000	0.000	0.000
RMS		0.320	1.420	0.059	0.013	0.006	0.001	0.004	0.001
RMSE		0.0086	0.0015	0.0001	0.0000	0.0000	0.0000	0.0000	0.0000

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表 6 EUV裸系统和镀膜后的波前RMS（单位：λ@13.4 nm）

Table 6. Full-field RMS wavefront error of the EUV system before and after coating (unit: λ at 13.4 nm)

	RMS	RMS（去除倾斜）
裸系统	0.01619	0.01588
镀膜	0.8422	0.04486
镀膜后离焦	0.6576	0.01707

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