OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 5, Iss. 8 — Aug. 1, 1988
  • pp: 1322–1327

Self-imaging with nonparabolic approximation of spherical wave fronts

Krzysztof Patorski and Sylwester Kozak  »View Author Affiliations

JOSA A, Vol. 5, Issue 8, pp. 1322-1327 (1988)

View Full Text Article

Enhanced HTML    Acrobat PDF (1132 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An analytical study of the influence of the diffraction process aberrations on the self-imaging phenomenon is presented. It is found that in a nonparabolic approximation of spherical waves there exists a range of self-imaging configurations of nonunity magnifications with a considerably reduced field of view that is free of image-line deformations and contrast variations. An experimental verification of the principles derived is given.

© 1988 Optical Society of America

Original Manuscript: February 4, 1988
Manuscript Accepted: March 28, 1988
Published: August 1, 1988

Krzysztof Patorski and Sylwester Kozak, "Self-imaging with nonparabolic approximation of spherical wave fronts," J. Opt. Soc. Am. A 5, 1322-1327 (1988)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Talbot, “Facts relating to optical science. IV,” Philos. Mag. 9, 401–407 (1836).
  2. W. D. Montgomery, “Self-imaging objects of infinite aperture,”J. Opt. Soc. Am. 57, 772–778 (1967). [CrossRef]
  3. J. M. Cowley, A. F. Moodie, “Fourier images. I. The point sources,” Proc. Phys. Soc. B 70, 486–496 (1956); “Fourier images. II. The out-of-focus patterns,” 70, 497–504 (1956); “Fourier images. III. Finite sources,” 70, 505–513 (1956). [CrossRef]
  4. 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]
  5. S. Szapiel, K. Patorski, “Fresnel diffraction images of periodic objects under Gaussian beam illumination,” Opt. Acta 26, 439–446 (1979). [CrossRef]
  6. S. Yokozeki, K. Patorski, K. Ohnishii, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975). [CrossRef]
  7. R. Jozwicki, “The Talbot effect as a sequence of quadratic phase corrections of the object Fourier transform,” Opt. Acta 30, 73–84 (1983). [CrossRef]
  8. J. Jahns, A. W. Lohmann, J. Ojeda-Castañeda, “Talbot and Lau effects, a parageometrical approach,” Opt. Acta 31, 313–324 (1984). [CrossRef]
  9. D. Joyeux, Y. Cohen-Sabban, “High magnification self-imaging,” Appl. Opt. 21, 625–627 (1982). [CrossRef] [PubMed]
  10. Y. Cohen-Sabban, D. Joyeux, “Aberration-free nonparaxial self-imaging,”J. Opt. Soc. Am. 73, 707–719 (1983). [CrossRef]
  11. J. E. Harvey, R. V. Shack, “Aberrations of diffracted wave fields,” Appl. Opt. 17, 3003–3009 (1978). [CrossRef] [PubMed]
  12. See, for example, D. Malacara, ed., Optical Shop Testing (Wiley, New York, 1979).
  13. K. Patorski, “Production of binary amplitude gratings with arbitrary opening ratio and variable period,” Opt. Laser Technol. 12, 267–270 (1980). [CrossRef]
  14. P. Szwaykowski, “Producing binary diffraction gratings in the double-diffraction system,” Opt. Laser Technol. 17, 255–260 (1985). [CrossRef]
  15. J. M. Cowley, A. F. Moodie, “Fourier images. IV. The phase grating,” Proc. Phys. Soc. London Ser. B 76, 378–384 (1960). [CrossRef]
  16. K. Patorski, G. Parfjanowicz, “Self-imaging phenomenon of a sinusoidal complex object,” Opt. Acta 28, 357–367 (1981). [CrossRef]
  17. K. Patorski, “Incoherent superposition of multiple self-imaging: Lau effect and moiré fringe explanation,” Opt. Acta 30, 745–758 (1983). [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.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited