面向真彩色三维显示的分层角谱算法和Gerchberg-Saxton算法研究

Gerchberg-Saxton algorithm and angular-spectrum layer-oriented method for true color three-dimensional display

分层角谱算法可用于三维物体全息图的生成计算,在计算时间、占用内存和算法复杂度方面占有优势.本文基于强度图和深度图的分层角谱算法,对多波长采样进行分析,有效抑制混频现象,实现了真彩色物体的计算全息图生成.针对分层角谱算法重建时产生的散斑噪声问题,引入Gerchberg-Saxton(GS)算法,提出基于分层角谱算法的GS算法.通过计算比较引入GS算法前后再现像的均方根误差和峰值信噪比,证明该算法可有效地抑制散斑噪声,提高全息图的再现像质量,更适用于复杂形貌三维物体的计算.

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.