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

Levent Onural

doi:10.1117/1.1802232

1 November 2004 Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations

Levent Onural

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Optical Engineering, Vol. 43, Issue 11, (November 2004). https://doi.org/10.1117/1.1802232

Abstract

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 (SPIE)

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Levent Onural "Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations," Optical Engineering 43(11), (1 November 2004). https://doi.org/10.1117/1.1802232

Published: 1 November 2004

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