## Determination of second-order derivatives of a skew ray with respect to the variables of its source ray in optical prism systems |

JOSA A, Vol. 28, Issue 8, pp. 1600-1609 (2011)

http://dx.doi.org/10.1364/JOSAA.28.001600

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### Abstract

The second-order derivative of a scalar function with respect to a variable vector is known as the Hessian matrix. We present a computational scheme based on the principles of differential geometry for determining the Hessian matrix of a skew ray as it travels through a prism system. A comparison of the proposed method and the conventional finite difference (FD) method is made at last. It is shown that the proposed method has a greater inherent accuracy than FD methods based on ray-tracing data. The proposed method not only provides a convenient means of investigating the wavefront shape within complex prism systems, but it also provides a potential basis for determining the higher order derivatives of a ray by further taking higher order differentiations.

© 2011 Optical Society of America

**OCIS Codes**

(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: May 20, 2011

Manuscript Accepted: June 13, 2011

Published: July 12, 2011

**Citation**

Psang Dain Lin and Wei Wu, "Determination of second-order derivatives of a skew ray with respect to the variables of its source ray in optical prism systems," J. Opt. Soc. Am. A **28**, 1600-1609 (2011)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-8-1600

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