Diffraction and holography from a signal processing perspective

Date
2006
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Source Title
Proceedings of SPIE Vol. 6252, Holography 2005: International Conference on Holography, Optical Recording, and Processing of Information, SPIE 2005
Print ISSN
0277-786X
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Publisher
SPIE
Volume
6252
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Language
English
Type
Conference Paper
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Abstract

The fact that plane waves are solutions of the Helmholtz equation in free space allows us to write the exact solution to the diffraction problem as a superposition of plane waves. The solution of other related problems can also be expressed in similar forms. These forms are very well suited for directly importing various signal processing tools to diffraction related problems. Another signal processing-diffraction link is the application of novel sampling theorems and procedures in signal processing to diffraction for the purpose of more convenient and efficient discrete representation and the use of associated computational algorithms. Another noteworthy link between optics and signal processing is the fractional Fourier transform. Revisiting diffraction from a modern signal processing perspectiv is likely to yield both interesting viewpoints and improved techniques.

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Keywords
Diffraction, Fractional Fourier transform, Sampling, Signal processing, Helmholtz equations, Plane waves, Computational methods, Fourier transforms, Holography
Citation
Published Version (Please cite this version)