Gerchberg-Saxton algorithm and angular-spectrum layer-oriented method for true color three-dimensional display
Authors: Fan Shuang  , Zhang Ya-Ping  , Wang Fan  , Gao Yun-Long  , Qian Xiao-Fan  , Zhang Yong-An  , Xu Wei  , Cao Liang-Cai  ,   Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China;,   Architectural Engineering Institute, Kunming University of Science and Technology, Kunming 650500, China;,   State Key Laboratory of Precision Measurement Technology and Instruments, Tsinghua University, Beijing 100084, China
Published: December 2020

Computer-generated hologram (CGH) makes possible the three-dimensional (3D) display of true stereo. It has characteristics of strong flexibility, small noise, easy replication, and computable virtual object. However, there are still some difficulties with the CGH 3D display presently, such as slow computation speed of complex object hologram, small size and small field angle of 3D scene, much noise of reconstruction image, and true color display. In this paper, the problem of reconstruction image noise and true color display of the CGH are studied, and the hologram of true color 3D object with complex morphologies is calculated. First of all, the angular-spectrum layer-oriented method can avoid error caused by the paraxial approximation and be used to accurately generate and calculate 3D object hologram. And it also has advantages of efficient computation, reduced complexity, and less storage memory. We achieve the true color display of a 3D object by using the angular-spectrum method based on intensity and depth maps. We also analyze the problem of multi-wavelength sampling, and mitigate the phenomenon of frequency mixing effectively. Then, we propose to use the Gerchberg-Saxton (GS) algorithm along with the angular-spectrum layer oriented method to reduce the speckle noise in the reconstruction image. The root mean-square error (RMSE) and peak signal-to-noise ratio (PSNR) of the reconstruction image by angular-spectrum layer-oriented method with the GS algorithm are compared with those obtained in the case without using the GS algorithm. The RMSE and PSNR are the main methods of evaluating the image quality. Smaller RMSE and bigger PSNR correspond to higher quality of the image. The hologram and reconstruction image of the true color locomotive with complex morphologies are calculated using the method proposed in this paper and the locomotive is divided into three parts:head, middle and tail. The RMSE and the PSNR of reconstruction image of the head are approximately 0.77 and 65.7, respectively. The RMSE and the PSNR of reconstruction image of the middle are approximately 0.68 and 70.0, respectively, and so are those of the tail. Comparing with the traditional angular-spectrum layer-oriented method, the RMSE of the reconstruction images of the head, middle and tail are reduced approximately by 0.11, 0.40, 0.41, and the PSNR are increased approximately by 1.15, 5.70, 4.13, respectively. The simulation results show that the speckle noise is suppressed effectively and the quality of the reconstruction image is improved when the GS algorithm along with the angular-spectrum layer oriented method is used. The proposed method is more suitable for the calculation of complex 3D objects with true color.