Computer-Aided Method for Off-axis Illumination Schwarzschild Projection Objectives Lin Qiang, Jin Chunshui, Xiang Peng, Cao Jianlin (The Center of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, National Center for Applied Optics, eccentric aperture diaphragm off-axis illumination StWschild projection objective. The projection objective is composed of two spherical mirrors with a numerical aperture of M=0.08 and a miniaturization ratio of 10:1. Each mirror is coated with a Mo/S reflective multilayer film with a center wavelength of 13.4 nm. The system design parameters are shown in Table 2. Table 2 System design parameters Miniaturization ratio Numerical aperture m Object distance (mm) Two mirror spacing (ran) Primary mirror 姊 蛟 蛟 Design residuals As mentioned above, the miniature projection objective requires extremely high optical precision; meanwhile, reflection The contribution of the mirrors to the optical system wavefront is complicated, and it is necessary to adopt the computer-aided adjustment technique. It is to detect the offset of the mirror by the detection of the positional wavefront of the miniature projection objective during the adjustment process. Guide the precise assembly of the system. The assembly process is as shown.
3 Computer-Aided Modulation Mathematical Model 3-1 The aberration of the system and the performance of the sensitive matrix optical system can be described by the wavefront aberration at the exit pupil position. Decomposing the wavefront aberration into the Zemike coefficient form constitutes the wavefront aberration. Vector Z. A mathematical model of wave aberrations is established by a functional relationship Z = Z(X) composed of optical system structural parameter vectors and wave aberration vectors.
Describe the best imaging quality of the system is to make the cross-correlation between the 丨|Z configuration parameters. There is an ill-posed problem when the least square method is used to solve |丨Z丨|minimum, that is, there are many approximate solutions. The nonlinearity of Z(X) and X needs to be iterated repeatedly in the solution process, which is not conducive to convergence of the assembly process as soon as possible; the cross-correlation between structural parameters increases the uncertainty of the assembly process. The Newton iteration method based on SVD can solve this problem well.
Suppose a small offset sx of the original structural parameters is found, so that the wave aberration of the system is zero, ie Zf+SX)=0, and is developed by the Tylor formula: where: J is the x-sensitive matrix a is the number of Zemike coefficients, ie The dimension of Z is the degree of freedom of structural adjustment. = 3 wide; = 1, 2, -, njj = 1, 2,. The Newton iteration method (ignoring the high-order term) is used to solve the above formula, that is, in equation (4), since the high-order nonlinear term is neglected, it is necessary to solve the SX. 3.2 matrix singular value and singular value decomposition multiple times. The parent matrix has a pseudo-order 酉 matrix U and an n-th order 酉 matrix V such that the diagonal matrix 2 =1, 2, for all non-zero singular values ​​of the matrix A, the VD is calculated. Optical Precision Engineering, 2000, 8 (1) You 70. Jin Chunshui, Wang Zhanshan, Zeng Jianlin. Soft X-ray projection lithography, strong laser and particle beam, 2000, 12 (3): 559-564. Jin Chunshui, Ma Yueying, Xi Shu, et al. Integration of EUV projection lithography experimental setup. Optical precision engineering r2l, 9 (5): 418423. Cheng Yunxuan matrix theory. Xi'an: Northwestern Polytechnical University Press, 20 (MK225-233. Shi, mainly engaged in optical instruments and testing technology research.
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