Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform |
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Authors: | Shi Peng Cao Guo-Wei and Li Yong-Ping |
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Affiliation: | Department of Optics and Optical Engineering, University of Science and Technology of China, Hefei 230026, China |
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Abstract: | Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional-order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase. |
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Keywords: | chirp transform Fresnel diffraction Wigner distribution function fractional Fourier transform |
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