Fundamental structure of Fresnel diffraction: Longitudinal uniformity with respect to fractional Fourier order
Author
Haldun M. Özaktaş
Arik, S. O.
Coşkun, T.
Date
2011-12-24Source Title
Optics Letters
Print ISSN
0146-9592
Publisher
Optical Society of America
Volume
37
Issue
1
Pages
103 - 105
Language
English
Type
ArticleItem Usage Stats
127
views
views
91
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downloads
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.
Keywords
Fractional fourierFractional Fourier transformations
Fractional Fourier transforms
Fresnel diffraction
Fresnel integrals
Fundamental structures
Longitudinal direction
Optical axis
Propagation distances
Space-bandwidth product
Bandwidth
Diffraction
Fourier analysis
Fourier transforms
Permalink
http://hdl.handle.net/11693/21642Published Version (Please cite this version)
http://dx.doi.org/10.1364/OL.37.000103Collections
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