Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform
Date
2011-06-29
Authors
Advisor
Instructor
Source Title
Optics Letters
Print ISSN
0146-9592
Electronic ISSN
Publisher
Optical Society of America
Volume
36
Issue
13
Pages
2524 - 2526
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. 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.
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Keywords
Efficient computation, Fresnel diffraction, Fresnel integrals, Fundamental structures, Sample point, Sampling grids, Diffraction, Fourier analysis, Fourier transforms