Analysis and design of prisms using the derivatives of a ray. Part II: The derivatives of boundary variable vector with respect to system variable vector

To evaluate the merit function of an optical system, it is necessary to determine the first- and secondorder derivative matrices of the boundary variable vector with respect to the system variable vector. Accordingly, the present study proposes a computationally efficient method for determining both matrices for optical systems containing only flat boundary surfaces. The validity of the proposed method is demonstrated by means of two illustrative prism design problems. In general, the results show that the proposed method can provide efficient search directions in many gradient-based optical design optimization methods.