Zhang Zhen, Chen Siqing, Zheng Huadong, Zeng Zhenxiang, Gao Hongyue, Yu Yingjie, Asundi Anand K
Appl Opt. 2017 Jul 10;56(20):5668-5675. doi: 10.1364/AO.56.005668.
The fractional Fourier transform (FRT) has been used for computing holograms in holographic displays due to its continuity of describing wave diffraction in the near field and far field. In this study, we propose a method to realize a full-color holographic 3D display with combined use of the FRT and the free-space Fresnel diffraction. A slice-based optical configuration and the calculation algorithm of the FRT are proposed for generating phase-only holograms of full-color 3D objects. Sequential phase-only holograms are generated for reducing the speckle noise of reconstructed images by the time-averaging effect. Free-space Fresnel diffraction is used for 3D image reconstruction from the generated holograms. The relationship between the fractional orders of different color channels and the free-space Fresnel diffraction distance is analyzed. Chromatic aberrations caused by different wavelengths of RGB lasers are also compensated. A full-color holographic display system using a reflective phase-only spatial light modulator (SLM) is established. Both the numerical and optical reconstruction results demonstrate the feasibility of the proposed method.
分数傅里叶变换（FRT）由于其在描述近场和远场波衍射方面的连续性，已被用于全息显示中计算全息图。在本研究中，我们提出了一种结合使用FRT和自由空间菲涅耳衍射来实现全彩色全息3D显示的方法。提出了一种基于切片的光学配置和FRT的计算算法，用于生成全彩色3D物体的纯相位全息图。通过时间平均效应生成顺序纯相位全息图，以减少重建图像的散斑噪声。自由空间菲涅耳衍射用于从生成的全息图进行3D图像重建。分析了不同颜色通道的分数阶与自由空间菲涅耳衍射距离之间的关系。还补偿了由RGB激光不同波长引起的色差。建立了使用反射型纯相位空间光调制器（SLM）的全彩色全息显示系统。数值和光学重建结果均证明了该方法的可行性。
