Concise formula for the Zernike coefficients of scaled pupils

被引:26
作者
Janssen, Augustus J. E. M. [1 ]
Dirksen, Peter [1 ]
机构
[1] Philips Res Europe, NL-5656 AE Eindhoven, Netherlands
来源
JOURNAL OF MICROLITHOGRAPHY MICROFABRICATION AND MICROSYSTEMS | 2006年 / 5卷 / 03期
关键词
optical lithography; NA scaling; Zernike coefficients; Strehl ratio;
D O I
10.1117/1.2345672
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Modern steppers and scanners have a projection lens whose numerical aperture (NA) can be varied so as to optimize the image performance for certain lithographic features. Thus a variable fraction of the aberrations is actually involved in the imaging process. In this letter, we present a concise formula for the NA scaling of the Zernike coefficients. In addition, we apply our results to the Strehl ratio. (C) 2006 Society of Photo-Optical Instrumentation Engineers.
引用
收藏
页数:3
相关论文
共 7 条
[1]  
Abramowitz M, 1970, HDB MATH FUNCTIONS F, V9th, P361
[2]  
Born M., 2001, PRINCIPLES OPTICS
[3]   Scalino Zernike expansion coefficients to smaller pupil sizes: a simpler formula [J].
Dai, GM .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 2006, 23 (03) :539-543
[4]   Implementation of pattern specific illumination pupil optimization on Step & Scan systems [J].
Engelen, A ;
Socha, R ;
Hendrickx, E ;
Scheepers, W ;
Nowak, F ;
van Dam, M ;
Liebchen, A ;
Faas, D .
OPTICAL MICROLITHOGRAPHY XVII, PTS 1-3, 2004, 5377 :1323-1333
[5]   Signamization of resist images [J].
Lin, BJ .
OPTICAL MICROLITHOGRAPHY X, 1997, 3051 :620-628
[6]   ZERNIKE POLYNOMIALS AND ATMOSPHERIC-TURBULENCE [J].
NOLL, RJ .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, 1976, 66 (03) :207-211
[7]  
*SIGMA C GMBH, SOLID C REL 6 3 0