Error Analysis of Ray’s Light Path for Axis-Symmetrical Optical System by Using Skew Ray Tracing

Abstract

ωThis study applies a skew ray tracing approach based on a 4×4 homogeneous coordinate transformation matrix and Snell’s law to analyze the errors of a ray’s light path as it passes through a series of optical elements for axis-symmetrical optical system. The proposed error analysis methodology considers two principal sources of light path error, namely: (1) the translational errors Δxi, Δyi and Δzi and the rotational errors Δωix, Δωiy and Δωiz, which determine the deviation of the light path at each boundary surface, and (2) the differential changes induced in the incident point position and unit directional vector of the refracted / reflected ray as a result of differential changes in the position and unit directional vector of the light source. The validity of the proposed methodology is verified by analyzing the effects of optical errors in Petzval lens.