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 ${\mathbf{X}}_i$ . However, transferring the computed quantities into the system variable vector ${\mathbf{X}}_{\mathrm{sys}}$ is still highly challenging. Accordingly, this study proposes a new numerical method for determining the Jacobian matrix between ${\mathbf{X}}_i$ and ${\mathbf{X}}_{\mathrm{sys}}$ 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.

© 2011 Optical Society of America

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