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Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Alan E. Willner
  • Vol. 37, Iss. 1 — Jan. 1, 2012
  • pp: 103–105

Fundamental structure of Fresnel diffraction: longitudinal uniformity with respect to fractional Fourier order

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


Optics Letters, Vol. 37, Issue 1, pp. 103-105 (2012)
http://dx.doi.org/10.1364/OL.37.000103


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Abstract

Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with separation that increases with propagation distance. Here, we are concerned with the separation of the spherical reference surfaces along the longitudinal direction. We show that these surfaces should be equally spaced with respect to the fractional Fourier transform order, rather than being equally spaced with respect to the distance of propagation along the optical axis. The spacing should be of the order of the reciprocal of the space-bandwidth product of the signals. The space-dependent longitudinal and transverse spacings define a grid that reflects the structure of Fresnel diffraction.

© 2012 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
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms
(050.5082) Diffraction and gratings : Phase space in wave options
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: September 15, 2011
Revised Manuscript: November 17, 2011
Manuscript Accepted: November 18, 2011
Published: December 24, 2011

Citation
Haldun M. Ozaktas, Sercan Ö. Arık, and Türker Coşkun, "Fundamental structure of Fresnel diffraction: longitudinal uniformity with respect to fractional Fourier order," Opt. Lett. 37, 103-105 (2012)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-37-1-103

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