OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 8 — Apr. 22, 2002
  • pp: 360–369

Self-imaging of three-dimensional images by pulsed wave fields

Kaido Reivelt  »View Author Affiliations

Optics Express, Vol. 10, Issue 8, pp. 360-369 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (588 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Recently, the classical Talbot effect (self-imaging of optical wave fields) has attracted a renewed interest, as the concept has been generalized to the domain of pulsed wave fields by several authors. In this paper we discuss the self-imaging of three-dimensional images. We construct pulsed wave fields that can be used as self-imaging “pixels” of a three-dimensional image and show that their superpositions reproduce the spatial separated copies of its initial three-dimensional intensity distribution at specific time intervals. The derived wave fields will be shown to be directly related to the fundamental localized wave solutions of the homogeneous scalar wave equation – focus wave modes. Our discussion is illustrated by some spectacular numerical simulations. We also propose a general idea for the optical generation of the derived wave fields. The results will be compared to the work, published so far on the subject.

© 2002 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.5540) Ultrafast optics : Pulse shaping

ToC Category:
Research Papers

Original Manuscript: March 14, 2002
Revised Manuscript: April 5, 2002
Published: April 22, 2002

Kaido Reivelt, "Self-imaging of three-dimensional images by pulsed wave fields," Opt. Express 10, 360-369 (2002)

Sort:  Journal  |  Reset  


  1. W. D. Montgomery, �Self-Imaging Objects of Infinite Aperture," J. Opt. Soc. Am. 57, 772-778 (1967). [CrossRef]
  2. J. Turunen and A. T. Friberg, �Self-imaging and propagation-invariance in electromagnetic fields,� Pure Appl. Opt. 2, 51-60 (1993). [CrossRef]
  3. Z. Bouchal and J. Wagner, �Self-reconstruction effect in free propagation of wavefield,� Opt. Commun. 176, 299-307 (2000). [CrossRef]
  4. J. Wagner and Z. Bouchal, �Experimental realization of self-reconstruction of the 2D aperiodic objects,� Opt.Commun. 176, 309-311 (2000). [CrossRef]
  5. R. Piestun, Y. Y. Schechner and J. Shamir, �Self-imaging with finite energy,� Opt. Lett. 22, 200-202 (1997). [CrossRef] [PubMed]
  6. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, �Diffraction-free beams,� Phys. Rev. Lett. 58, 1499�1501 (1987). [CrossRef] [PubMed]
  7. R. Piestun and J. Shamir, �Generalized propagation-invariant wave fields,� J. Opt. Soc. Am. A 15, 3039-3044 (1998). [CrossRef]
  8. Z. Bouchal and M. Bertolotti, �Self-reconstruction of wave packets due to spatio-temporal couplings,� J. Mod. Opt. 47, 1455 - 1467 (2000). [CrossRef]
  9. Z. Bouchal, �Self-reconstruction ability of wave field,� Proc. SPIE, vol. 4356, 217-224, (2001). [CrossRef]
  10. J. Salo and M. M. Salomaa, �Diffraction-free pulses at arbitrary speeds,� J. Opt. A: Pure Appl. Opt. 3, 366-373 (2001). [CrossRef]
  11. H. Wang, C. Zhou, L. Jianlang and L. Liu, �Talbot effect of a grating under ultrashort pulsed-laser illumination,� Microwave and Opt. Technol. Lett. 25, 184-187 (2000) [CrossRef]
  12. J. Aza�a and M. A. Muriel, �Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber grating,� Opt. Lett. 24, 1672-1674 (1999). [CrossRef]
  13. P. Saari, H. S�najalg, �Pulsed Bessel beams,� Laser Phys. 7, 32-39 (1997).
  14. A. A. Maznev, T. F. Crimmins and K.A. Nelson, �How to make femtosecond pulses overlap,� Opt. Lett. 23, 1378-1380 (1998). [CrossRef]
  15. Zs. Bor and B. R�cz, �Group velocity dispersion in prisms and its application to pulse compression and traveling-wave excitation,� Opt. Commun. 54, 165-170 (1985). [CrossRef]
  16. P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius and A. Piskarskas, �Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,� Phys. Rev. Lett. 81, 570-573 (1998). [CrossRef]
  17. P. Saari, J. Aaviksoo, A. Freiberg, K. Timpmann, �Elimination of excess pulse broadening at high spectral resolution of picosecond duration light emission,� Opt. Commun. 39, 94-98 (1981). [CrossRef]
  18. O. Svelto, Principles of Lasers (3rd ed. Plenum Press 1989).
  19. I. Besieris, M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, �Two fundamental representations of localized pulse solutions of the scalar wave equation,� Progr. In Electromagn. Research 19, 1 (1998). [CrossRef]
  20. P. Saari and K. Reivelt, �Evidence of X-shaped propagation-invariant localized light waves,� Phys. Rev. Lett. 79, 4135-4138 (1997). [CrossRef]
  21. K. Reivelt and P. Saari, �Optical generation of focus wave modes,� J. Opt. Soc. Am. A 17, 1785-1790 (2000). [CrossRef]
  22. K. Reivelt and P. Saari, �Optical generation of focus wave modes: errata,� J. Opt. Soc. Am. A 18, 2026-2026, (2001). [CrossRef]
  23. K. Reivelt and P. Saari, �Optically realizable localized wave solutions of homogeneous scalar wave equation,� Phys. Rev. E (to be published) [accepted for publication].

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.

Supplementary Material

» Media 1: MOV (853 KB)     
» Media 2: MOV (1223 KB)     
» Media 3: MOV (1387 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited