## Abstract

A computational scheme based on differential geometry is proposed for determining the first- and second-order derivative matrices of a skew ray as it is reflected/refracted at a flat boundary surface. In the proposed approach, the position and orientation of the boundary surface in 3D space are described using just four variables. As a result, the proposed method is more computationally efficient than existing schemes based on all six variables. The derivative matrices enable the cross-coupling effects of the system variables on the exit ray to be fully understood. Furthermore, the proposed method provides a convenient means of determining the search direction used by existing gradient-based schemes to minimize the merit function during the optimization stage of the optical system design process. The validity of the proposed approach as an analysis and design tool is demonstrated using a corner-cube mirror and laser tracking system for illustration purposes.

© 2013 Optical Society of America

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