Skew ray tracing and sensitivity analysis of hyperboloid optical boundary surfaces

详细信息    查看全文

• 作者：Chia-Hung Lu^a ; ^{rockylu@csu.edu.tw} ; Chi-Kuei Sung^b ; ^{cksongster@gmail.com}
• 关键词：Homogeneous transformation matrix ; Skew ray tracing ; Geometric optics
• 刊名：Optik - International Journal for Light and Electron Optics
• 出版年：2013
• 出版时间：June, 2013
• 年：2013
• 卷：124
• 期：12
• 页码：1159-1169
• 全文大小：639 K

文摘

One of the most popular mathematical tools in fields of robotics, mechanisms and computer graphics is the 4 ¡Á 4 homogeneous transformation matrix. Our group's previous application of the homogeneous transformation matrix to flat and spherical optical boundaries has been extended to hyperboloid surfaces for: (1) skew ray tracing to determine the paths of reflected/refracted skew rays; (2) sensitivity analysis for direct mathematical expression of differential changes of incident points and reflected/refracted vectors with respect to changes in incident light sources and boundary geometric parameters; (3) a sensitivity analysis-based merit function derived directly from mathematical expression of catadioptric imaging system components. The presented methodology is highly suited to digital implementation and offers direct and rapid analytical statement of ray path, chief ray, marginal rays and merit functions of optical systems.