Research Of The Fractional Fourier Transform Applied In Optical Image Processing

The fractional Fourier Transform (FRFT) is a generalization of the conv-entional Fourier transform (FT), which is one of the most important mathematical tools used in information processing, optic systems, optical image processing and some other areas. As a generalization of FT, FRFT inherits the excellent characte-ristics of FT, and it also owns some special features. So FRFT can be directly applied in the areas where FT has been used. And FRFT can be used in some other areas where FT has not been used.This thesis is the research about FRFT applied in optical image processing areas.We find out the relationship of the defocus distance and the fractional order of FRFT based on the relationship of the optical image system, FRFT and the Fresnel Diffraction, according to which we can restore the defocus image by adjust the fractional order of FRFT. This new method has been simulated by computer under two different conditions. One is that the defocus distance is already known. In this condition it can restore the degrade image by adjusting the fractional order. The other is that the defocus distance is unknown. In this condition, we have to adjusting the fractional order more than one time. The results of simulation show the feasibility of this new manner.The variety of FRFT can be used to encrypt the optical images, because the secret keys are infinite, which ensure the security of the image encryption. This method can continually do the image encryption. From the physical view, the continual encryption is that an optical image can be seen as the combination of many different fractional order FRFTs. Encryption is adding random phase in the fractional Fourier domains. The image can only be decrypted by knowing bath the phase distribution and the fractional orders. This encryption manner has infinite keys which makes the result safer. The simulation is done. The results of the simulation verify the validity of this encryption method.A new method based on FRFT is proposed to detect the optical image edge. And two kinds of optical setups for this method have been given in this paper. The simulation of this method is done, the results is ideal. Then experiment is...