OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 7, Iss. 6 — Jun. 1, 1990
  • pp: 977–981

Coordinate transformations realizable with multiple holographic optical elements

M. A. Stuff and J. N. Cederquist  »View Author Affiliations


JOSA A, Vol. 7, Issue 6, pp. 977-981 (1990)
http://dx.doi.org/10.1364/JOSAA.7.000977


View Full Text Article

Enhanced HTML    Acrobat PDF (550 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Holographic optical elements that perform one-to-one coordinate transformations can be designed by using the stationary phase approximation. All coordinate transformations that are sufficiently differentiable can be decomposed into two transformations in series and therefore performed by using two holographic elements. Although the method presented here for designing the two required holographic elements is not explicit for the general case, a useful necessary condition for the decomposition is given. A simple explicit solution is given for an example for which the necessary equations for the first of the two serial transformations are separable.

© 1990 Optical Society of America

History
Original Manuscript: May 15, 1989
Manuscript Accepted: January 29, 1990
Published: June 1, 1990

Citation
M. A. Stuff and J. N. Cederquist, "Coordinate transformations realizable with multiple holographic optical elements," J. Opt. Soc. Am. A 7, 977-981 (1990)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-7-6-977


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. N. Cederquist, A. M. Tai, “Computer-generated holograms for geometric transformations,” Appl. Opt. 23, 3099–3104 (1984). [CrossRef] [PubMed]
  2. J. N. Cederquist, M. T. Eismann, A. M. Tai, “Holographic polar formatting and real-time optical processing of synthetic aperture radar data,” Appl. Opt. 28, 4182–4189 (1989). [CrossRef] [PubMed]
  3. O. Bryngdahl, “Optical map transformations,” Opt. Commun 10, 164–168 (1974). [CrossRef]
  4. O. Bryngdahl, “Geometrical transformations in optics,” J. Opt Soc. Am. 64, 1092–1099 (1974). [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), pp. 749–750.
  6. W. Kaplan, Advanced Calculus (Addison-Wesley, Reading Mass., 1959), pp. 243–249.
  7. W. Kaplan, Advanced Calculus (Addison-Wesley, Reading Mass., 1959), pp. 90–97.
  8. M. Spivak, Calculus on Manifolds (Benjamin, Menlo Park Calif., 1965), pp. 34–39.
  9. I. G. Petrovsky, Lectures on Partial Differential Equations (Interscience, New York, 1954), pp. 67–72.
  10. E. C. Zachmanoglou, D. W. Thoe, Introduction to Partia Differential Equations with Applications (Dover, New York1986), pp. 361–362.
  11. A. E. Taylor, Advanced Calculus (Ginn, Boston, 1955), pp. 267–271, 428–431.

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
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited