OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 35, Iss. 20 — Jul. 10, 1996
  • pp: 3925–3929

Optical illustration of a varied fractional Fourier-transform order and the Radon–Wigner display

David Mendlovic, Rainer G. Dorsch, Adolf W. Lohmann, Zeev Zalevsky, and Carlos Ferreira  »View Author Affiliations


Applied Optics, Vol. 35, Issue 20, pp. 3925-3929 (1996)
http://dx.doi.org/10.1364/AO.35.003925


View Full Text Article

Enhanced HTML    Acrobat PDF (341 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 an all-optical system, a display of a fractional Fourier transform with many fractional orders is proposed. Because digital image-processing terminology is used, this display is known as the Radon–Wigner transform. It enables new aspects for signal analysis that are related to time- and spatial-frequency analyses. The given approach for producing this display starts with a one-dimensional input signal although the output signal contains two dimensions. The optical setup for obtaining the fractional Fourier transform was adapted to include only fixed free-space propagation distances and variable lenses. With a set of two multifacet composite holograms, the Radon–Wigner display has been demonstrated experimentally.

© 1996 Optical Society of America

History
Original Manuscript: March 20, 1995
Revised Manuscript: February 21, 1996
Published: July 10, 1996

Citation
David Mendlovic, Rainer G. Dorsch, Adolf W. Lohmann, Zeev Zalevsky, and Carlos Ferreira, "Optical illustration of a varied fractional Fourier-transform order and the Radon–Wigner display," Appl. Opt. 35, 3925-3929 (1996)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-35-20-3925


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transformations and their optical implementation: Part I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993). [CrossRef]
  2. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transformations and their optical implementation: Part II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993). [CrossRef]
  3. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
  4. D. Mendlovic, H. M. Ozaktas, A. W. Lohmann, “Graded index fibers, Wigner distribution functions and the fractional Fourier transform,” Appl. Opt. 33, 6188–6193 (1994). [CrossRef] [PubMed]
  5. J. C. Wood, D. T. Barry, “Radon transform of the Wigner spectrum,” in Advanced Signal Processing Algorithms, Architectures, and Implementations III, F. T. Luk, ed., Proc. SPIE1770, 358–375 (1992). [CrossRef]
  6. J. C. Wood, D. T. Barry, “Linear signal synthesis using the Radon–Wigner transform,” IEEE Trans. Signal Process. 42, 2105–2111 (1994). [CrossRef]
  7. J. C. Wood, D. T. Barry, “Tomographic time-frequency analysis and its application toward time-varying filtering and adaptive kernel design for multicomponent linear-FM signals,” IEEE Trans. Signal Process. 42, 2094–2104 (1994). [CrossRef]
  8. A. W. Lohmann, B. H. Soffer, “Relationships between the Radon–Wigner and fractional Fourier transforms,” J. Opt. Soc. Am. A 11, 1798–1801 (1994). [CrossRef]
  9. D. Mendlovic, Z. Zalevsky, R. G. Dorsch, Y. Bitran, A. W. Lohmann, H. Ozaktas, “New signal representation based on the fractional Fourier transform: definitions,” J. Opt. Soc. Am. A 12, 2424–2431 (1995). [CrossRef]
  10. A. W. Lohmann, “A fake zoom lens for fractional Fourier experiments,” Opt. Commun. (to be published).
  11. H. M. Ozaktas, D. Mendlovic, “Multistage optical implementation architecture with least possible growth of system size,” Opt. Lett. 18, 296–298 (1993). [CrossRef] [PubMed]
  12. W. H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974). [CrossRef] [PubMed]

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 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited