Optical systems are currently evaluated by use of ray-tracing techniques to extract performance quantities such as aberration and spot size. To improve on the use of optical equations, we formulate various important optical functions using a 4×4 homogeneous transformation matrix to design and analyze skew rays that cross flat optical boundary surfaces. We address three important topics: (1) the direction of a reflected or refracted ray is determined according to Snell's law, (2) sensitivity analysis expresses differential changes of reflected or refracted rays in terms of differential changes of incident rays, and (3) aberration of polychromatic light is presented analytically. A solid-glass corner cube and a Pechan prism are used to demonstrate the validity of the developed methodology.
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