为了降低分数傅里叶全息图制作的复杂性,根据信号的分数傅里叶变换的定义式和菲涅耳衍射公式,通过求解它们的点扩展函数(PSF),推导出分数傅里叶变换与菲涅耳衍射公式的等价关系,从而把分数傅里叶变换转化为菲涅耳衍射。采用人眼分辨率极限尺寸和数字微镜器件(DMD)像素的尺寸分别对物体所在平面和全息图所在平面进行抽样,运用分块算法生成分数傅里叶全息图,使计算复杂度降低为O[N2lb(N2/M2)],提出了一种可行的动态全息显示方法,最后通过DMD全息显示系统对该算法生成的全息图进行实验验证。

In order to reduce complexity of generation of fractional Fourier hologram,according to signal′s fractional Fourier transform and Fresnel diffraction formula,the equivalence relation between them is derived by solving their point spread functions (PSF). So fractional Fourier transform can be transformed into Fresnel diffraction. The object and the hologram plane are sampled by limit of resolution of human eye and size of micromirror of digital micromirror device (DMD). Tiling algorithm is used to generate fractional Fourier hologram,its computation complexity is decreased to O[N2lb(N2/M2)],and a feasible dynamic holographic display is proposed. Finally,the algorithm is verified by DMD holographic display system.