提出了分数傅里叶变换计算全息图(FRTCGH).采用分数傅里叶变换的快速算法和罗曼Ⅲ型迂回位相编码方法设计并制作了一个物体不同分数阶的分数傅里叶变换计算全息图,用罗曼Ⅰ型分数傅里叶变换光学系统再现原物体,得到了物体清晰的像.分析了FRTCGH和再现图像随分数阶变化的规律,讨论了分数傅里叶变换计算全息图与菲涅耳计算全息图之间的关系.

Computer generated hologram of fractional Fourier transform is presented. With fast arithmetic of fractional Fourier transform and Lohmann Ⅲ detour phase coding method, fractional Fourier transform CGH in different fractional orders of one object are programmed and fabricated. These holograms are reconstructed with Lohmann Ⅰ fractional Fourier transform optical system and a clear images are obtained. The changing rule of FRTCGH and reconstructed images is analyzed as fractional orders change. The relationship between fractional Fourier transform CGH and Fresnel CGH is discussed.