Fresnel diffraction and the fractional-order Fourier transform.
Fractional-order Fourier transforms are adapted to the mathematical expression of Fresnel diffraction, just as the standard Fourier transform is adapted to Fraunhofer diffraction. The continuity of fractional Fourier transforms with respect to their orders corresponds to the continuity of wave propagation, and their composition is in accordance with the Huygens principle.
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Pellat-Finet