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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 5 — May. 1, 2011
  • pp: 747–758

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

Wei Wu and Psang Dain Lin  »View Author Affiliations


JOSA A, Vol. 28, Issue 5, pp. 747-758 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000747


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Abstract

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.

© 2011 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: January 11, 2011
Manuscript Accepted: February 11, 2011
Published: April 7, 2011

Citation
Wei Wu and Psang Dain Lin, "Numerical approach for computing the Jacobian matrix between boundary variable vector and system variable vector for optical systems containing prisms," J. Opt. Soc. Am. A 28, 747-758 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-5-747

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