Numerical approach for computing the Jacobian matrix between boundary variable vector and system variable vector for optical systems containing prisms

The design of optical systems containing prisms is comparatively difficult since each prism may contain multiple boundary surfaces. Many geometrical optical merit functions have been proposed based on first-order derivatives of the geometrical quantities of the system with respect to the boundary variable vector X(i). However, transferring the computed quantities into the system variable vector X(sys) is still highly challenging. Accordingly, this study proposes a new numerical method for determining the Jacobian matrix between X(i) and X(sys) directly. The proposed methodology can be easily implemented in computer code and provides a potential basis for the future development of a numerical technique for computing the second-order derivatives of the geometrical quantities of an optical system.