分数傅里叶变换计算全息

Computer generated hologram of fractional Fourier transform

在计算全息和分数傅里叶变换的基础上提出了不对称分数傅里叶变换计算全息和双随机相位不对称分数傅里叶变换计算全息。在这种方法中,首先用一随机相位函数乘以输入图像信息,然后沿x方向实施α级次的一维分数傅里叶变换,再乘以第二个随机相位函数,最后,沿y方向实施β级次的一维分数傅里叶变换。采用迂回位相编码法对变换后的结果编码,绘出计算全息图。为了恢复原始图像,需要知道变换级次和随机相位函数。利用这种方法进行图像加密,使加密图像的密钥由原来两重增加到四重,从而提高了系统的保密性能。

Asymmetry fractional Fourier transform computer-generated hologram（AFRTCGH） and double random phase AFRTCGH are presented based on computer-generated hologram（CGH） and fractional Fourier transform（FRT） is presented.The fractional Fourier transform of the input image is performed by two single one-dimensional FRT with different orders in the x and y directions in cascade.With Lohmann Ⅲ detour phase encoding method and computer plotting program,the transformed image is fabricated into CGH on the computer.Then a piece of asymmetry fractional Fourier transform CGH（AFRTCGH） of original input image is obtained.In order to reconstruct the encoded image,only when the transform order in each direction is respectively matched with that of the asymmetry fractional Fourier transform CGH,the encoded image can be reconstructed exactly.Because of its particularity of image reconstruction,it is regarded as a new optical security system and can be used in anti-counterfeiting.When it is used to encrypt image or to anti-counterfeit,anti-counterfeiting intensity can be improved greatly.So it has very high applying value.