Abstract: Conventional Computer-generated hologram was obtained by Fresnel diffraction, there were not an uniformly numerical method to describe the whole Fresnel diffraction. For better research Computer-generated hologram, This paper introduce fractional fourier transform and propose a new method to synthesize computer-generated hologram of three-dimensional object based on fast algorithm of fractional Fourier transform, experimemt realize the computer simulation holographic generation and digital reconstruction. The result shows: for introduce of the order of Fractional fourier, a new uniform method to calculate optical diffraction. It is an ideal tool to make it.

Key words: Computer-generated hologram, synthesized fractional Fourier transform hologram, Double fractional Fourier transform, Fresnel diffraction.

摘要： 传统的计算全息图大多采用菲涅耳衍射积分得到，但菲涅耳衍射积分在描述整个衍射光场中，没有一个统一的采样方法来对积分进行数值计算，从而给计算带来不便。为了更好的研究计算全息图问题，文章引入了分数傅里叶变换，通过利用分数傅里叶变换的一种快速数值模拟算法，提出了一种基于分数傅里叶变换的合成空间三维物体全息图的新方法，并用计算机模拟了合成的全息图及其数字重构的结果。实验结果表明：由于分数阶的引入，得到一种处理处理光场衍射问题的统一算法，因此用分数傅里叶变换来处理光场衍射问题是十分理想的。

关键词: 计算全息图, 分数傅里叶变换合成全息图, 双次分数傅里叶变换, 菲涅耳衍射