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