## 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 |

Applied Optics, Vol. 52, Issue 18, pp. 4151-4162 (2013)

http://dx.doi.org/10.1364/AO.52.004151

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### Abstract

To evaluate the merit function of an optical system, it is necessary to determine the first- and second-order 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.

© 2013 Optical Society of America

**OCIS Codes**

(080.0080) Geometric optics : Geometric optics

(080.2720) Geometric optics : Mathematical methods (general)

(080.2740) Geometric optics : Geometric optical design

(080.3620) Geometric optics : Lens system design

(080.1753) Geometric optics : Computation methods

(080.2468) Geometric optics : First-order optics

**History**

Original Manuscript: February 26, 2013

Manuscript Accepted: April 17, 2013

Published: June 13, 2013

**Citation**

Psang Dain Lin, "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," Appl. Opt. **52**, 4151-4162 (2013)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-18-4151

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