A skew ray tracing approach for the error analysis of optical elements with spherical boundary surfaces

This study applies a skew ray tracing approach based on a 44 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 with spherical boundary surfaces. The proposed error analysis methodology considers two principal sources of light path error, namely: (1) the translational errors Xi, Yi and Zi and the rotational errors Delta X(i), Delta Y(i) and Delta Z(i) and the rotational errrors Delta Gamma(i), Delta Psi(i) and Delta Phi(i), 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 a solid glass cat's eye.