OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 18 — Jun. 20, 2013
  • pp: 4137–4150

Analysis and design of prisms using the derivatives of a ray. Part I: derivatives of a ray with respect to boundary variable vector

Psang Dain Lin  »View Author Affiliations


Applied Optics, Vol. 52, Issue 18, pp. 4137-4150 (2013)
http://dx.doi.org/10.1364/AO.52.004137


View Full Text Article

Enhanced HTML    Acrobat PDF (804 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A computational scheme based on differential geometry is proposed for determining the first- and second-order derivative matrices of a skew ray as it is reflected/refracted at a flat boundary surface. In the proposed approach, the position and orientation of the boundary surface in 3D space are described using just four variables. As a result, the proposed method is more computationally efficient than existing schemes based on all six variables. The derivative matrices enable the cross-coupling effects of the system variables on the exit ray to be fully understood. Furthermore, the proposed method provides a convenient means of determining the search direction used by existing gradient-based schemes to minimize the merit function during the optimization stage of the optical system design process. The validity of the proposed approach as an analysis and design tool is demonstrated using a corner-cube mirror and laser tracking system for illustration purposes.

© 2013 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: February 26, 2013
Revised Manuscript: April 22, 2013
Manuscript Accepted: April 26, 2013
Published: June 13, 2013

Citation
Psang Dain Lin, "Analysis and design of prisms using the derivatives of a ray. Part I: derivatives of a ray with respect to boundary variable vector," Appl. Opt. 52, 4137-4150 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-18-4137


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. P. Feder, “Automatic optical design,” Appl. Opt. 2, 1209–1226 (1963). [CrossRef]
  2. D. C. Dilworth, “Pseudo-second-derivative matrix and its application to automatic lens design,” Appl. Opt. 17, 3372–3375 (1978). [CrossRef]
  3. B. D. Stone, “Determination of initial ray configurations for asymmetric systems,” J. Opt. Soc. Am. A 14, 3415–3429 (1997). [CrossRef]
  4. R. Shi and J. Kross, “Differential ray tracing for optical design,” Proc. SPIE 3737, 149–160 (1999). [CrossRef]
  5. T. B. Andersen, “Optical aberration functions: derivatives with respect to axial distances for symmetrical systems,” Appl. Opt. 21, 1817–1823 (1982). [CrossRef]
  6. T. B. Andersen, “Optical aberration functions: derivatives with respect to surface parameters for symmetrical systems,” Appl. Opt. 24, 1122–1129 (1985). [CrossRef]
  7. 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]
  8. 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]
  9. O. Stavroudis, “A simpler derivation of the formulas for generalized ray tracing,” J. Opt. Soc. Am. 66, 1330–1333 (1976). [CrossRef]
  10. J. Kross, “Differential ray tracing formulae for optical calculations: principles and applications,” Proc. SPIE 1013, 10–19 (1988). [CrossRef]
  11. W. Oertmann, “Differential ray tracing formulae; applications especially to aspheric optical systems,” Proc. SPIE 1013, 20–26 (1988). [CrossRef]
  12. B. D. Stone and G. W. Forbes, “Differential ray tracing in inhomogeneous media,” J. Opt. Soc. Am. A 14, 2824–2836 (1997). [CrossRef]
  13. W. Wu and P. D. Lin, “Numerical approach for computing the Jacobain matrix between boundary variable vector and system variable vector for optical systems containing prisms,” J. Opt. Soc. Am. A 28, 747–758 (2011). [CrossRef]
  14. P. D. Lin and W. 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). [CrossRef]
  15. 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]
  16. C. Olson and R. N. Youngworth, “Alignment analysis of optical systems using derivative information,” Proc. SPIE 7068, 70680A (2008). [CrossRef]
  17. J. S. Arora, Introduction to Optimum Design, 3rd ed. (Elsevier, 2012), p. 482.
  18. Leica Inc., Geodesy and Industrial Systems Center, Norcross, GA.
  19. 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]

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