Application of derivative matrices of skew rays to design of compound dispersion prisms

Numerous optimization methods have been developed in recent decades for optical system design. However, these methods rely heavily on ray tracing and finite difference techniques to estimate the derivative matrices of the rays. Consequently, the accuracy of the results obtained from these methods is critically dependent on the incremental step size used in the tuning stage. To overcome this limitation, the present study proposes a comprehensive methodology for the design of compound dispersion prisms based on the first- and second-order derivative matrices of skew rays. The proposed method facilitates the analysis and design of prisms with respect to arbitrary system variables and provides an ideal basis for automatic prism design applications. Four illustrative examples are given. It is shown that the optical quantities required to evaluate the prism performance can be extracted directly from the proposed derivative matrices. In addition, it is shown in this study that the single-element 3D prism can have the same deviation angle and spectral dispersion as the 2D compound prism.