OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.48.000893


View Full Text Article

Enhanced HTML    Acrobat PDF (530 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-5-893


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Sharma, “Computing optical path length in gradient-index media: a fast and accurate method,” Appl. Opt. 24, 4367-4370(1985). [CrossRef] [PubMed]
  2. M. Avendaño-Alejo and M. Rosete-Aguilar, “Optical path difference in a plane-parallel uniaxial plate,” J. Opt. Soc. Am. A 23, 926-932 (2006). [CrossRef]
  3. S. Purnet, B. Journet, and G. Fortunato, “Exact calculation of the optical path difference and description of a new birefringent interferometer,” Opt. Eng. 38, 983-990 (1999). [CrossRef]
  4. J. Meiron, “The use of merit functions on wavefront aberrations in automatic lens design,” Appl. Opt. 7, 667-672 (1968). [CrossRef] [PubMed]
  5. T. Suzuki and I. Uwoki, “Differential method for adjusting the wave-front aberrations of a lens system,” J. Opt. Soc. Am. 49, 402-404 (1959). [CrossRef]
  6. P. D. Lin and C. Y. Tsai, “First-order gradients of skew rays of axis- symmetrical optical systems,” J. Opt. Soc. Am. A 24, 776-784 (2007). [CrossRef]
  7. M. Laikin, Lens Design (Marcel Dekker, 1995).
  8. P. D. Lin and C. H. Lu, “Analysis and design of optical system by use of sensitivity analysis of skew ray tracing,” Appl. Opt. 43, 796-807 (2004). [CrossRef] [PubMed]
  9. P. D. Lin and C. K. Sung, “Camera calibration based on Snell's law,” J. Dyn. Syst. Meas. Control 128, 548-557 (2006). [CrossRef]
  10. P. D. Lin and C. Y. Tsai, “General method for determining the first order gradients of skew rays of optical systems with non-coplanar optical axes,” Appl. Phys. B 91, 621-628 (2008). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited