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Optics Letters

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  • Editor: Alan E. Willner
  • Vol. 36, Iss. 13 — Jul. 1, 2011
  • pp: 2524–2526

Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform

Haldun M. Ozaktas, Sercan Ö Arık, and Türker Coşkun  »View Author Affiliations


Optics Letters, Vol. 36, Issue 13, pp. 2524-2526 (2011)
http://dx.doi.org/10.1364/OL.36.002524


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Abstract

Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. We show that by judiciously choosing sample points on these curved reference surfaces, it is possible to represent the diffracted signals in a nonredundant manner. The change in sample spacing with distance reflects the structure of Fresnel diffraction. This sampling grid also provides a simple and robust basis for accurate and efficient computation, which naturally handles the challenges of sampling chirplike kernels.

© 2011 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2025) Fourier optics and signal processing : Discrete optical signal processing
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms
(050.5082) Diffraction and gratings : Phase space in wave options

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: February 15, 2011
Revised Manuscript: May 6, 2011
Manuscript Accepted: May 20, 2011
Published: June 29, 2011

Citation
Haldun M. Ozaktas, Sercan Ö Arık, and Türker Coşkun, "Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform," Opt. Lett. 36, 2524-2526 (2011)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-13-2524


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References

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