Optical Image Encryption Based On Complex-Order Fourier Transform

The fractional Fourier transform attracts much attention as a new mathematic transform in recent years. Its advantage in optics and signal processing is found and widely used. Especially, its application in image encryption is one of the most popular domains.The fractional Fourier transform is the generalized form of common Fourier transform, and the complex fractional Fourier transform expands the exponent number to complex. The process of the Fourier transform changing to the fractional Fourier transform and the complex fractional Fourier transform is depicted briefly in this thesis as well as their applications in image encryption. The author analyzes some different types of the definition of the fractional Fourier transform and its essential characters. The optical implementation of the fractional Fourier transform is presented also. The numerical simulation is achieved by FFT in Matlab and its integral definition.In this thesis, the author clarifies the definition of the complex exponent and indicates that the definition of Shih is correct. By using of Gaussian apertures, it is demonstrated that a bulk lens system can be related to complex-order Fourier transforms. The numerical simulation is based on the state-function definition of Shih.The random complex Fourier transform based on double-phase encoding technology and random fractional Fourier transform is presented to encrypting an optical image. The optical implementation is consisted of the bulk lens system, three Gaussian apertures and two random phase planes. Finally, the encryption as well as the recover of the optical image is achieved. The author do some analysis of the characters of the exponent and the random phase planes as the code through the mean-squared error curves between the decrypted images and the original image.