A skew ray tracing approach for error analysis of a light ray path for optical systems with asymmetrical optical axes

This 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 light path as it passes through a series of optical elements in an asymmetrical optical system. The proposed error analysis methodology considers two principal sources of a light path error, namely: i) the translational errors and the rotational errors which determine the deviation of the light path at each boundary surface, and ii) 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 a corner cube.