Fractional Fourier Transform And Its Application

Fractional Fourier optics becomes a new branch of the modern optics after the introduction of Fractional Fourier Transform (FRT) from mathematics to optics. It is regarded as the development and extension of Fourier optics. It not only makes us look at optical propagation, optical imaging and information processing from a new point, but also provides us a new tool to treat these problems. Fractional Fourier optics has been widely used in many fields of information processing and will be used more widely in the future.During a few years the basic theoretical frame has been set up since Fractional Fourier Transform was successfully introduced into the optic field. However, the researches on its actual application are relatively sluggish and immature. This dissertation aims at the development of the actual application of Fractional Fourier Transform and involves the further research of Fractional Fourier Domain Filtering and chirp filtering in terms of fractional Fourier transform etc.In this paper, the basic theory and some applications are introduced. Two optical methods of fractional Fourier transform are represented. The definition and physical of Wigner distribution are presented, then the method of study on fractional Fourier transform by Wigner distribution is suggested. We also do further research on the relation between fractional Fourier transform and Fresnel diffraction.Aim at the limit of chirp filtering based on the conventional Fourier transform, the characteristics of fractional Fourier transform in spatial domain and frequency domain are discussed in terms of Wigner distribution. The principle of chirp filtering in fractional Fourier domain is proposed. Then, a method of chirp filtering is presented in image processing. The computer-simulation results of chirp filtering for 1D and 2D image are obtained satisfactorily, which have shown the availability of this method in image processing. So, we present a new method to improve the quality of images.There is few internal theory about chirp filtering in terms of fractional Fourier transform. In this paper, the principle of chirp filtering in terms of fractional Fourier transform is resolved. Then the computer-simulation results of chirp filtering for 1D and 2D image are presented. So, we can have suitable reference about this subject mentioned above.