OSA's Digital Library

Optics Letters

Optics Letters


  • 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)

View Full Text Article

Enhanced HTML    Acrobat PDF (69 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, 1979).
  2. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
  3. M. J. Bastiaans, J. Opt. Soc. Am. 69, 1710 (1979). [CrossRef]
  4. S. Abe and J. T. Sheridan, Opt. Lett. 19, 1801 (1994). [CrossRef] [PubMed]
  5. D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997). [CrossRef]
  6. D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, Opt. Commun. 164, 233 (1999). [CrossRef]
  7. L. Cohen, Time-Frequency Analysis (Prentice-Hall, 1995).
  8. H. M. Ozaktas and M. F. Erden, Opt. Commun. 143, 75 (1997). [CrossRef]
  9. H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 42, 2141 (1996). [CrossRef]
  10. B. M. Hennelly and J. T. Sheridan, J. Opt. Soc. Am. A 22, 917 (2005). [CrossRef]
  11. B. Barshan, M. A. Kutay, and H. M. Ozaktas, Opt. Commun. 135, 32 (1997). [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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited