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. 16, Iss. 1 — Jan. 1, 1999
  • pp: 97–105

Numerical optimization of phase-only elements based on the fractional Talbot effect

Markus Testorf, Victor Arrizón, and Jorge Ojeda-Castañeda  »View Author Affiliations


JOSA A, Vol. 16, Issue 1, pp. 97-105 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000097


View Full Text Article

Enhanced HTML    Acrobat PDF (433 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Based on the matrix description of the fractional Talbot effect, a new and effective method to numerically optimize diffractive optical elements that work in the Fresnel diffraction regime is described. When the investigation is restricted to spatially quantized phase-only gratings, diffraction can be described in terms of the fractional Talbot effect and the diffraction amplitude is efficiently evaluated from a finite set of sampling points. As an illustrating example we numerically optimize Talbot array illuminators. Our results show that a limited number of discrete phase levels does not imply a limited compression ratio but does lead to a reduced diffraction efficiency. Experimental results obtained from lithographically fabricated surface-relief gratings are compared with our theoretical designs.

© 1999 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1380) Diffraction and gratings : Binary optics
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(090.0090) Holography : Holography
(090.1970) Holography : Diffractive optics

History
Original Manuscript: May 1, 1998
Revised Manuscript: September 4, 1998
Manuscript Accepted: September 14, 1998
Published: January 1, 1999

Citation
Markus Testorf, Victor Arrizón, and Jorge Ojeda-Castañeda, "Numerical optimization of phase-only elements based on the fractional Talbot effect," J. Opt. Soc. Am. A 16, 97-105 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-1-97


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms generated by computer,” Appl. Opt. 6, 1739–1743 (1967). [CrossRef] [PubMed]
  2. H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971). [CrossRef]
  3. J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. (Bellingham) 19, 297–305 (1980). [CrossRef]
  4. O. Bryngdahl, F. Wyrowski, “Digital holography—computer generated holograms,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. XXVIII.
  5. J. N. Mait, “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A 12, 2145–2158 (1995). [CrossRef]
  6. R. Piestun, B. Spektor, J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996). [CrossRef]
  7. R. G. Dorsch, A. W. Lohmann, S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated hologram display,” Appl. Opt. 33, 869–875 (1994). [CrossRef] [PubMed]
  8. P. Pellat-Finet, “Fresnel diffraction and fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994). [CrossRef] [PubMed]
  9. G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. (Bellingham) 28, 605–608 (1989). [CrossRef]
  10. J. T. Winthrop, C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373–381 (1965). [CrossRef]
  11. V. Arrizón, J. Ojeda-Castañeda, “Fresnel diffraction of substructured gratings: matrix description,” Opt. Lett. 20, 118–120 (1995). [CrossRef] [PubMed]
  12. H. Hamam, J. L. de Bougrenet de la Tocnaye, “Efficient Fresnel-transform algorithm based on fractional Fresnel diffraction,” J. Opt. Soc. Am. A 12, 1920–1931 (1995). [CrossRef]
  13. M. Testorf, J. Jahns, “Planar-integrated Talbot array illuminators,” Appl. Opt. 37, 5399–5407 (1998). [CrossRef]
  14. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, pp. 57–76.
  15. V. Arrizón, J. G. Ibarra, J. Ojeda-Castañeda, “Matrix formulation of the Fresnel transform of complex transmittance gratings,” J. Opt. Soc. Am. A 13, 2414–2422 (1996). [CrossRef]
  16. V. Arrizón, J. Ojeda-Castañeda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 33, 5925–5931 (1994). [CrossRef] [PubMed]
  17. M. Testorf, J. Ojeda-Castañeda, “Fractional Talbot effect: analysis in phase space,” J. Opt. Soc. Am. A 13, 119–125 (1996). [CrossRef]
  18. H. Hamam, “Design of Talbot array illuminators,” Opt. Commun. 131, 359–370 (1996). [CrossRef]
  19. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).
  20. A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttgart) 79, 41–45 (1988).
  21. W. Klaus, Y. Arimoto, K. Kodate, “High performance Talbot array illuminators,” Appl. Opt. 37, 4357–4365 (1998). [CrossRef]
  22. V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994). [CrossRef]
  23. J. R. Leger, G. J. Swanson, “Efficient array illuminator using binary-optics phase plates at fractional Talbot planes,” Opt. Lett. 15, 288–290 (1990). [CrossRef] [PubMed]
  24. V. Arrizón, E. López-Olazagasti, A. Serrano-Heredia, “Talbot array illuminators with optimum compression ratio,” Opt. Lett. 21, 233–235 (1996). [CrossRef] [PubMed]
  25. V. Arrizón, J. G. Ibarra, A. Serrano-Heredia, “Split Talbot array illuminators,” Opt. Commun. 123, 63–70 (1996). [CrossRef]
  26. T. J. Suleski, “Generation of Lohmann images from binary-phase Talbot array illuminators,” Appl. Opt. 36, 4686–4691 (1997). [CrossRef] [PubMed]
  27. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990). [CrossRef]
  28. M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996). [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