Reconstructed quality improvement with a stochastic gradient descent optimization algorithm for a spherical hologram

Abstract

The spherical holography is a promising technology to realize a true three-dimensional (3D) display. Compared to plane holography and cylindrical holography, it has an unlimited field of view, which can be observed from all perspectives. However, so far, the reconstructed images from computer-generated spherical holograms (CGSHs) are not of high quality, especially phase-only holograms, which will seriously affect its application. In this paper, an optimization algorithm for a CGSH based on stochastic gradient descent (SGD) is proposed to improve the quality of the reconstructed image. First, a new, to the best of our knowledge, diffraction model used in the process of optimization is proposed by considering the obliquity factor and occlusion culling. Based on our proposed diffraction model, the optimization process includes diffracting the initial random phase to another sphere, calculating the loss between the reconstructed image and the original image, and optimizing the initial phase through the SGD optimization algorithm. Both the correctness of the proposed diffraction model and the effectiveness of the SGD optimization for spherical holograms are verified well by numerical simulations. Through SGD, a high-quality reconstructed image can be achieved, which is 18 dB higher in the PSNR than that of spherical self-diffraction iteration. Meaningfully, our method has broad application prospects in 3D and omnidirectional displays. The SGD optimization algorithm is brought into the CGSH, and remarkable results have been achieved.