| Summary: | 碩士 === 國立成功大學 === 機械工程學系專班 === 91 === The majority of optical systems are based on spherical components because they are easy to manufacture and low in costs. But the aberration form a spherical boundary is inevitable and may degrade the quality of image. Aspherical boundary surfaces are more difficult and expensive to make. However, there are cases where components with aspherical boundary surfaces (one example is paraboloids) have a significant advantage over spherical ones. Thus the aspherical boundary surfaces are worthful for study.
One of the most popular mathematical tools in fields of robotics, mechanisms and computer graphics is the 4x4 homogeneous transformation matrix. In previous work we applied this matrix to the optical domains of planar and spherical surfaces for: (1) skew ray tracing to determine the paths of skew rays being reflected/refracted; (2) sensitivity analysis to determine by direct mathematical analysis the differential change of incident point and reflected/refracted vector with respect to change in incident light source or orientation of optical boundary; 3) a sensitivity analysis-based merit function derived directly from mathematical expression of system components. The present work extends our previous work to include the cases of parabaloidal, eliiptical, and hyperbolical boundary surfaces.
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