Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform

doi:10.1088/1674-1056/19/7/074201

中国物理B ›› 2010, Vol. 19 ›› Issue (7): 74201-074201.doi: 10.1088/1674-1056/19/7/074201

Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform

石鹏, 曹国威, 李永平

Department of Optics and Optical Engineering, University of Science and Technology of China, Hefei 230026, China

收稿日期:2009-08-31 修回日期:2009-12-14 出版日期:2010-07-15 发布日期:2010-07-15

Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform

Shi Peng(石鹏) , Cao Guo-Wei(曹国威), and Li Yong-Ping(李永平)^†

Department of Optics and Optical Engineering, University of Science and Technology of China, Hefei 230026, China

Received:2009-08-31 Revised:2009-12-14 Online:2010-07-15 Published:2010-07-15

摘要/Abstract

摘要： 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.

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.

Key words: chirp transform, Fresnel diffraction, Wigner distribution function , fractional Fourier transform

中图分类号: (Modulation, tuning, and mode locking)

42.60.Fc

02.50.Ng (Distribution theory and Monte Carlo studies) 02.30.Uu (Integral transforms) 02.60.Nm (Integral and integrodifferential equations)

石鹏, 曹国威, 李永平. Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform[J]. 中国物理B, 2010, 19(7): 74201-074201.

Shi Peng(石鹏) , Cao Guo-Wei(曹国威), and Li Yong-Ping(李永平). Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform[J]. Chin. Phys. B, 2010, 19(7): 74201-074201.

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Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform

Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform

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