为了快速获取更好的全息图显示效果，在研究了分数傅里叶变换与菲涅耳衍射光场的紧密联系的基础上，首先给出了一种分数傅里叶变换的快速数值算法，并将分数傅里叶变换应用到计算全息图中提出了一种用于计算全息图的分数傅里叶变换方法；然后分析了用这种记录全息的方法得到的全息图优越于传统的傅里叶变换获得的全息图，同时给出了计算机的模拟实验结果；最后利用拆卸的投影装置搭建出了以空间光调制器——DMD (数字微镜装置)为核心的全息显示光学系统,并在该系统下获得了用分数傅里叶变换计算得到的全息图的全息显示结果。

The relation of Fresnel diffraction and factional Fourier transform are analyzed, a fast simulated algorithm of fractional Fourier transform based on FFT is proposed By making use of fractional Fourier transform as the center tool, the new computing methods of holograms are obtained and the computer simulation holographic generation and digital reconstruction are realized By introducing the spatial light modulators DMD, a holography imaging system to complement the holography display is set up