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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 5 — Feb. 10, 2009
  • pp: 893–902

Computationally efficient gradient matrix of optical path length in axisymmetric optical systems

Chun-Che Hsueh and Psang-Dain Lin  »View Author Affiliations

Applied Optics, Vol. 48, Issue 5, pp. 893-902 (2009)

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We develop a mathematical method for determining the optical path length (OPL) gradient matrix relative to all the system variables such that the effects of variable changes can be evaluated in a single pass. The approach developed avoids the requirement for multiple ray-tracing operations and is, therefore, more computationally efficient. By contrast, the effects of variable changes on the OPL of an optical system are generally evaluated by utilizing a ray-tracing approach to determine the OPL before and after the variable change and then applying a finite-difference (FD) approximation method to estimate the OPL gradient with respect to each individual variable. Utilizing a Petzval lens system for verification purposes, it is shown that the approach developed reduces the computational time by around 90% compared to that of the FD method.

© 2009 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.2740) Geometric optics : Geometric optical design
(220.3620) Optical design and fabrication : Lens system design
(080.1753) Geometric optics : Computation methods

Original Manuscript: October 20, 2008
Revised Manuscript: January 5, 2009
Manuscript Accepted: January 5, 2009
Published: February 2, 2009

Chun-Che Hsueh and Psang-Dain Lin, "Computationally efficient gradient matrix of optical path length in axisymmetric optical systems," Appl. Opt. 48, 893-902 (2009)

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