A skew ray tracing-based approach to the error analysis of optical elements with flat boundary surfaces

This study applies skew ray tracing based on a 4×4 homogeneous coordinate transformation matrix and Snell's law to develop a detailed methodology for analyzing the errors of a ray's light path as it passes through optical elements with flat boundary surfaces. The error analysis methodology considers two fundamental sources of light path error, namely (1) the translational errors (ΔXi, ΔYi and ΔZi) and rotational errors (ΔΓi, ΔΨi and ΔΦi) which determine the deviation of the light path at each boundary surface in terms of the coordinate frame attached to that surface, and (2) the differential changes induced in the incident point and unit directional vector of the refracted/reflected ray by differential changes in the position and unit directional vector of the light source. The validity of the proposed methodology is verified using a solid glass corner-cube.