Skew ray tracing and sensitivity analysis of geometrical optics

In order to improve upon the inconvenient and complicated contemporary analytic techniques employed for optical systems, this paper investigates two important optical topics: (1) the determination of light ray paths and (2) sensitivity analysis of light path parameters with respect to the light source location for occasions when light rays cross medium boundary surfaces. To this end, the traditional laws of reflection and refraction are reformulated in terms of revolution geometry. This results in a set of laws much simpler than the original, suitable for use in mathematical modeling to determine light paths and system sensitivity from location of the light source, optical component location, the equation of the optical component’s surface curve, and the refractive index. Ray tracing and sensitivity analysis of the two most popular boundary surfaces, flat and spherical, are presented as examples. In order to illustrate experimentally the integration of these boundary surfaces into optical systems, an optical measurement system for measuring surface height and orientation, containing a beam splitter and a bi-convex lens, was built. Agreement between the experimental optical system’s performance and the theoretical predictions yielded by the proposed method are excellent.