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Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 1 — Jan. 1, 2006
  • pp: 35–37

Efficient computation of quadratic-phase integrals in optics

Haldun M. Ozaktas, Aykut Koç, Ilkay Sari, and M. Alper Kutay  »View Author Affiliations


Optics Letters, Vol. 31, Issue 1, pp. 35-37 (2006)
http://dx.doi.org/10.1364/OL.31.000035


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Abstract

We present a fast N log N time algorithm for computing quadratic-phase integrals. This three-parameter class of integrals models propagation in free space in the Fresnel approximation, passage through thin lenses, and propagation in quadratic graded-index media as well as any combination of any number of these and is therefore of importance in optics. By carefully managing the sampling rate, one need not choose N much larger than the space–bandwidth product of the signals, despite the highly oscillatory integral kernel. The only deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus the algorithm computes quadratic-phase integrals with a performance similar to that of the fast-Fourier-transform algorithm in computing the Fourier transform, in terms of both speed and accuracy.

© 2006 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(350.6980) Other areas of optics : Transforms

ToC Category:
Fourier Optics and Optical Signal Processing

Citation
Haldun M. Ozaktas, Aykut Koç, Ilkay Sari, and M. Alper Kutay, "Efficient computation of quadratic-phase integrals in optics," Opt. Lett. 31, 35-37 (2006)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-1-35


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References

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  2. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
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