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

Date
2011-12-24
Advisor
Instructor
Source Title
Optics Letters
Print ISSN
0146-9592
Electronic ISSN
Publisher
Optical Society of America
Volume
37
Issue
1
Pages
103 - 105
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
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.

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Keywords
Fractional fourier, Fractional 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
Citation
Published Version (Please cite this version)