OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 14 — May. 10, 2014
  • pp: 3085–3100

Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design

Psang Dain Lin  »View Author Affiliations


Applied Optics, Vol. 53, Issue 14, pp. 3085-3100 (2014)
http://dx.doi.org/10.1364/AO.53.003085


View Full Text Article

Enhanced HTML    Acrobat PDF (751 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In a previous paper [Appl. Opt. 52, 4151 (2013)], we presented the first- and second-order derivatives of a ray for a flat boundary surface to design prisms. In this paper, that scheme is extended to determine the Jacobian and Hessian matrices of a skew ray as it is reflected/refracted at a spherical boundary surface. The validity of the proposed approach as an analysis and design tool is demonstrated using an axis-symmetrical system for illustration purpose. It is found that these two matrices can provide the search direction used by existing gradient-based schemes to minimize the merit function during the optimization stage of the optical system design process. It is also possible to make the optical system designs more automatic, if the image defects can be extracted from the Jacobian and Hessian matrices of a skew ray.

© 2014 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

ToC Category:
Geometric Optics

History
Original Manuscript: January 22, 2014
Revised Manuscript: April 7, 2014
Manuscript Accepted: April 8, 2014
Published: May 8, 2014

Citation
Psang Dain Lin, "Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design," Appl. Opt. 53, 3085-3100 (2014)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-53-14-3085


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Cox, A System of Optical Design (Focal, 1964).
  2. G. H. Spencer and M. V. R. K. Murty, “General ray-tracing procedure,” J. Opt. Soc. Am. 52, 672–676 (1962). [CrossRef]
  3. W. A. Allen and J. R. Snyder, “Ray tracing through uncentered and aspheric surfaces,” J. Opt. Soc. Am. 42, 243–249 (1952). [CrossRef]
  4. O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972).
  5. D. P. Feder, “Automatic optical design,” Appl. Opt. 2, 1209–1226 (1963). [CrossRef]
  6. D. C. Dilworth, “Pseudo-second-derivative matrix and its application to automatic lens design,” Appl. Opt. 17, 3372–3375 (1978). [CrossRef]
  7. B. D. Stone, “Determination of initial ray configurations for asymmetric systems,” J. Opt. Soc. Am. A 14, 3415–3429 (1997). [CrossRef]
  8. R. Shi and J. Kross, “Differential ray tracing for optical design,” Proc. SPIE 3737, 149–160 (1999). [CrossRef]
  9. T. B. Andersen, “Optical aberration functions: derivatives with respect to axial distances for symmetrical systems,” Appl. Opt. 21, 1817–1823 (1982). [CrossRef]
  10. T. B. Andersen, “Optical aberration functions: derivatives with respect to surface parameters for symmetrical systems,” Appl. Opt. 24, 1122–1129 (1985). [CrossRef]
  11. D. P. Feder, “Calculation of an optical merit function and its derivatives with respect to the system parameters,” J. Opt. Soc. Am. A 47, 913–925 (1957). [CrossRef]
  12. D. P. Feder, “Differentiation of ray-tracing equations with respect to constructional parameters of rotationally symmetric systems,” J. Opt. Soc. Am. 58, 1494–1505 (1968). [CrossRef]
  13. O. Stavroudis, “A simpler derivation of the formulas for generalized ray tracing,” J. Opt. Soc. Am. 66, 1330–1333 (1976). [CrossRef]
  14. J. Kross, “Differential ray tracing formulae for optical calculations: principles and applications,” Proc. SPIE 1013, 10–19 (1988). [CrossRef]
  15. W. Oertmann, “Differential ray tracing formulae; applications especially to aspheric optical systems,” Proc. SPIE 1013, 20–26 (1988). [CrossRef]
  16. B. D. Stone and G. W. Forbes, “Differential ray tracing in inhomogeneous media,” J. Opt. Soc. Am. A 14, 2824–2836 (1997). [CrossRef]
  17. A. A. Shekhonin, A. V. Ivanov, L. I. Przhevalinskii, and T. I. Zhukova, “An analytical method for estimating how the design parameters affect the characteristics of optical systems,” J. Opt. Technol. 79, 277–282 (2012). [CrossRef]
  18. S. H. Brewer, “Surface-contribution algorithms for analysis and optimization,” J. Opt. Soc. Am. 66, 8–13 (1976). [CrossRef]
  19. P. D. Lin, “Analysis and design of prisms using the derivatives of a ray, part I: the derivatives of a ray with respect to boundary variable vector,” Appl. Opt. 52, 4137–4150 (2013). [CrossRef]
  20. P. D. Lin, New Computation Methods for Geometrical Optics (Springer, 2013).
  21. P. D. 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). [CrossRef]
  22. M. Laikin, Lens Design (Marcel Dekker, 1995), pp 71–72.
  23. J. S. Arora, Introduction to Optimum Design, 3rd ed. (Elsevier, 2012), p. 482.

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited