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Special Section On Diffractive Optics

Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations

[+] Author Affiliations
Levent Onural

Bilkent University, Electrical and Electronics Engineering Department, TR-06533?Ankara, Turkey E-mail: onural@ee.bilkent.edu.tr

Opt. Eng. 43(11), 2557-2563 (Nov 01, 2004). doi:10.1117/1.1802232
History: Received Dec. 1, 2003; Revised Apr. 21, 2004; Accepted Apr. 28, 2004; Online November 03, 2004
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The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms. This function has interesting properties and Fourier transform relations. For example, the Fourier transform of the sampled chirp is also a sampled chirp for some sampling rates. These properties are essential in interpreting the aliasing and its effects as a consequence of sampling of the quadratic phase function, and lead to interesting and efficient algorithms to simulate Fresnel diffraction. For example, it is possible to construct discrete Fourier transform (DFT)-based algorithms to compute exact continuous Fresnel diffraction patterns of continuous, not necessarily bandlimited, periodic masks at some specific distances. © 2004 Society of Photo-Optical Instrumentation Engineers.

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© 2004 Society of Photo-Optical Instrumentation Engineers

Citation

Levent Onural
"Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations", Opt. Eng. 43(11), 2557-2563 (Nov 01, 2004). ; http://dx.doi.org/10.1117/1.1802232


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