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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 8 — Aug. 1, 1999
  • pp: 1986–1991

Random fractional Fourier transform: stochastic perturbations along the axis of propagation

Sumiyoshi Abe and John T. Sheridan  »View Author Affiliations


JOSA A, Vol. 16, Issue 8, pp. 1986-1991 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001986


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Abstract

The fractional Fourier transform (FRT) is known to be optically implementable with use of a medium with a perfect radial quadratic-index profile. Using the quantum-mechanical operator formalism, we examine the effects on the FRT action of such a medium that are due to small random inhomogeneities in the longitudinal direction, the direction of propagation, and we formulate the random fractional Fourier transform (RFRT). Applying the RFRT to a self-fractional Fourier function, a Gaussian function, we discuss both the total power and the variance. The random Fourier transform is examined as a special limiting case.

© 1999 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(030.4280) Coherence and statistical optics : Noise in imaging systems
(070.2590) Fourier optics and signal processing : ABCD transforms
(270.2500) Quantum optics : Fluctuations, relaxations, and noise

History
Original Manuscript: August 25, 1998
Revised Manuscript: March 23, 1999
Manuscript Accepted: March 23, 1999
Published: August 1, 1999

Citation
Sumiyoshi Abe and John T. Sheridan, "Random fractional Fourier transform: stochastic perturbations along the axis of propagation," J. Opt. Soc. Am. A 16, 1986-1991 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-8-1986


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References

  1. V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980). [CrossRef]
  2. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995). [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. M. I. Charnotskii, J. Gozani, V. I. Tatarskii, V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” in Progress in Optics XXXII, E. Wolf, ed. (North-Holland, Amsterdam, The Netherlands, 1993), Chap. IV, pp. 203–266.
  5. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980).
  6. M. Imai, S. Kikuchi, T. Matsumoto, Y. Kinoshita, “Mode conversion due to fluctuations in a lens-like medium,” J. Opt. Soc. Am. 59, 904–913 (1969).
  7. T. Asakura, Y. Kinoshita, M. Suzuki, “Further correlation studies of Gaussian-beam fluctuations caused by a random medium,” J. Opt. Soc. Am. 59, 913–920 (1969).
  8. G. C. Papanicolaou, D. McLaughlin, R. Burridge, “A stochastic Gaussian beam,” J. Math. Phys. 14, 84–89 (1973). [CrossRef]
  9. M. Eve, J. H. Hannay, “Ray theory and random mode coupling in an optical fibre wave guide,” Opt. Quantum Electron. 8, “Part I,” 503–508; “Part II,” 509–512 (1976).
  10. A. Sharma, I. C. Goyal, N. K. Bansal, A. K. Ghatak, “Propagation of Gaussian beams through parabolic index optical waveguides with random dielectric constant gradient,” Fiber Integr. Opt. 2, 299–314 (1979). [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  12. S. Abe, J. T. Sheridan, “Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: an operator approach,” J. Phys. A Math. Gen. 27, 4179–4187 (1994);Corrigenda 27, 7937 (1994). [CrossRef]
  13. S. Abe, J. T. Sheridan, “Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation,” Opt. Lett. 19, 1801–1803 (1994). [CrossRef] [PubMed]
  14. M. O. Scully, M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997).
  15. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  16. Information is available from Sumiyoshi Abe, College of Science and Technology, Nihon University, 7-24-1 Narashinodai, Funabashi Chiba 274-8501, Japan, or John T. Sheridan, Physics Department, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland.
  17. L.-Y. Chen, N. Goldenfeld, Y. Oono, “Renormalization group and singular perturbations: multiple scales, boundary layers, and reductive perturbation theory,” Phys. Rev. E 54, 376–394 (1996). [CrossRef]

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