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

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 1 — Jan. 1, 2008
  • pp: 203–210

Reciprocal vector theory for diffractive self-imaging

Lin-Wei Zhu, Xia Yin, Zhengping Hong, and Cheng-Shan Guo  »View Author Affiliations


JOSA A, Vol. 25, Issue 1, pp. 203-210 (2008)
http://dx.doi.org/10.1364/JOSAA.25.000203


View Full Text Article

Enhanced HTML    Acrobat PDF (523 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A reciprocal vector theory for analysis of the Talbot effect of periodic objects is proposed. Using this method we deduce a general condition for determining the Talbot distance. Talbot distances of some typical arrays (a rectangular array, a centered-square array, and a hexagonal array) are derived from this condition. Further, the fractional Talbot effect of a one-dimensional grating, a square array, a centered-square array, and a hexagonal array is analyzed and some simple analytical expressions for calculation of the complex amplitude distribution at any fractional Talbot plane are deduced. Based on these formulas, we design some Talbot array illuminators with a high compression ratio. Finally, some computer-simulated results consistent with the theoretical analysis are given.

© 2008 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(230.1360) Optical devices : Beam splitters

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: July 25, 2007
Revised Manuscript: October 25, 2007
Manuscript Accepted: October 28, 2007
Published: December 19, 2007

Citation
Lin-Wei Zhu, Xia Yin, Zhengping Hong, and Cheng-Shan Guo, "Reciprocal vector theory for diffractive self-imaging," J. Opt. Soc. Am. A 25, 203-210 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-1-203


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. F. Talbot, "Facts relating to optical science. No. IV," Philos. Mag. 9, 401-407 (1836). [CrossRef]
  2. J. T. Winthrop and C. R. Worthington, "Theory of Fresnel images. I. Plane periodic objects in monochromatic light," J. Opt. Soc. Am. 55, 373-381 (1965). [CrossRef]
  3. A. W. Lohmann and J. A. Thomas, "Making an array illuminator based on the Talbot effect," Appl. Opt. 29, 4337-4340 (1990). [CrossRef] [PubMed]
  4. C. Zhou and L. Liu, "Simple equations for the calculation of a multilevel phase grating for Talbot array illumination," Opt. Commun. 115, 40-44 (1995). [CrossRef]
  5. C. Zhou, L. Wang, and T. Tschudi, "Solutions and analyses of fractional-Talbot array illuminations," Opt. Commun. 147, 224-228 (1998). [CrossRef]
  6. C. Zhou, H. Wang, S. Zhao, P. Xi, and L. Liu, "Number of phase levels of a Talbot array illuminator," Appl. Opt. 40, 607-613 (2001). [CrossRef]
  7. Y. Lu, C. Zhou, S. Wang, and B. Wang, "Polarization-dependent Talbot effect," J. Opt. Soc. Am. A 23, 2154-2160 (2006). [CrossRef]
  8. J. R. Leger and G. J. Swanson, "Efficient array illuminator using binary-optics phase at fractional-Talbot planes," Opt. Lett. 15, 288-290 (1990). [CrossRef] [PubMed]
  9. P. Szwaykowski and V. Arrizon, "Talbot array illuminator with multilevel phase grating," Appl. Opt. 32, 1109-1114 (1993). [CrossRef] [PubMed]
  10. C. Zhou, S. Stankovic, and T. Tschudi, "Analytic phase-factor equations for Talbot array illuminations," Appl. Opt. 38, 284-290 (1999). [CrossRef]
  11. C.-S. Guo, X. Yin, L.-W. Zhu, and Z.-P. Hong, "Analytical expression for phase distribution of a hexagonal array at fractional Talbot planes," Opt. Lett. 32, 2079-2081 (2007). [CrossRef] [PubMed]
  12. C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, 1996).
  13. P. Xi, C. Zhou, E. Dai, and L. Liu, "Generation of near-field hexagonal array illumination with a phase grating," Opt. Lett. 27, 228-230 (2002). [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
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited