Gradient matrix of optical path length for evaluating the effects of design variable changes in a prism

The effects of variable changes on the optical path length (OPL) of optical elements such as a prism are generally evaluated by utilizing a ray tracing approach to determine the OPL before and after the variable change, respectively, and then applying a finite difference (FD) method to estimate the OPL gradient with respect to each individual variable. By contrast, this study constructs the gradient matrix of OPL of a prism which permits the effects of multiple variable changes to be determined in a single pass. The developed approach not only resolves the error inherent in the FD method as a result of the denominator being far smaller than the numerator, but also avoids the requirement for multiple ray tracing operations and therefore yields a substantial improvement in the computational efficiency. The validity of the proposed approach is demonstrated utilizing a Pechan prism for illustration purposes.