Optical system assessment for design: numerical ray tracing in the Gaussian pupil

The continuing rapid increase in available computing power has not reduced the importance of efficient methods of optical system assessment for automatic lens design. On the contrary, the new capabilities simply show that truly automatic optical design will eventually be accomplished. It is proposed that the merit of a system-assessment scheme be measured in terms of the accuracy of its estimation of the overall performance of a proposed system as a function of the amount of work done (e.g., number of rays traced). By using this criterion, a number of schemes based on ray tracing are compared, and some highly efficient assessment procedures are developed. As a simplifying approximation, the effects of vignetting and pupil distortion are ignored here. The key to the most-effective methods lies in coupling appropriate coordinates to Gaussian quadrature schemes. Appropriate coordinate systems are those for which the relevant integrands (either wave-front errors or transverse intercept errors) take the form of smooth functions. The resulting methods for system assessment are typically at least an order of magnitude more efficient than comparatively simple schemes.