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. 19, Iss. 3 — Mar. 1, 2002
  • pp: 481–484

Finite-mode analysis by means of intensity information in fractional optical systems

Tatiana Alieva and Martin J. Bastiaans  »View Author Affiliations


JOSA A, Vol. 19, Issue 3, pp. 481-484 (2002)
http://dx.doi.org/10.1364/JOSAA.19.000481


View Full Text Article

Enhanced HTML    Acrobat PDF (127 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

It is shown how a coherent optical signal that contains only a finite number of Hermite–Gauss modes can be reconstructed from the knowledge of its Radon–Wigner transform—associated with the intensity distribution in a fractional-Fourier-transform optical system—at only two transversal points. The proposed method can be generalized to any fractional system whose generator transform has a complete orthogonal set of eigenfunctions.

© 2002 Optical Society of America

OCIS Codes
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(100.5070) Image processing : Phase retrieval
(200.1130) Optics in computing : Algebraic optical processing

History
Original Manuscript: April 12, 2001
Revised Manuscript: July 11, 2001
Manuscript Accepted: July 26, 2001
Published: March 1, 2002

Citation
Tatiana Alieva and Martin J. Bastiaans, "Finite-mode analysis by means of intensity information in fractional optical systems," J. Opt. Soc. Am. A 19, 481-484 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-3-481


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  2. M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994). [CrossRef] [PubMed]
  3. J. Tu, S. Tamura, “Analytic relation for recovering the mutual intensity by means of intensity information,” J. Opt. Soc. Am. A 15, 202–206 (1998). [CrossRef]
  4. Z. Zalevsky, R. G. Dorsch, “Gerchberg–Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996). [CrossRef] [PubMed]
  5. W. X. Cong, N. X. Chen, B. Y. Gu, “Recursive algorithm for phase retrieval in the fractional Fourier transform domain,” Appl. Opt. 37, 6906–6910 (1998). [CrossRef]
  6. T. Alieva, M. J. Bastiaans, “Mode analysis through the fractional transforms in optics,” Opt. Lett. 24, 1206–1208 (1999). [CrossRef]
  7. T. Alieva, K. B. Wolf, “Finite mode analysis through harmonic waveguides,” J. Opt. Soc. Am. A 17, 1482–1484 (2000). [CrossRef]
  8. A. W. Lohmann, D. Mendlovic, Z. Zalevsky, “Fractional transformation in optics,” in Progress in Optics XXXVIII, E. Wolf, ed. (Elsevier, Amsterdam, 1998), pp. 263–342.
  9. H. M. Ozaktas, M. A. Kutay, D. Mendlovic, “Introduction to the fractional Fourier transform and its applications,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic Press, San Diego, Calif., 1999), Vol. 106, pp. 239–291.
  10. T. Alieva, M. L. Calvo, “Fractionalization of the cyclic transforms,” J. Opt. Soc. Am. A 17, 2330–2338 (2000). [CrossRef]
  11. L. B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42, 3084–3091 (1994). [CrossRef]
  12. L. Yu, W. D. Huang, M. C. Huang, Z. Z. Zhu, X. M. Zeng, W. Ji, “The Laguerre–Gaussian series representation of 2-dimensional fractional Fourier transform,” J. Phys. A Math. Gen. 31, 9353–9357 (1998). [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
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited