Simple and fast cosine approximation method for computer-generated hologram calculation

Fast calculation of computer-generated hologram of line-drawn objects without FFT

Although holographic display technology is one of the most promising three-dimensional (3D) display technologies for virtual and augmented reality, the enormous computational effort required to produce computer-generated holograms (CGHs) to digitally record and display 3D images presents a significant roadblock to the implementation of this technology. One of the most effective methods to implement fast CGH calculations is a diffraction calculation (e.g., angular spectrum diffraction) based on the fast-Fourier transform (FFT). Unfortunately, the computational complexity increases with increasing CGH resolution, which is what determines the size of a 3D image. Therefore, enormous calculations are still required to display a reasonably sized 3D image, even for a simple 3D image. To address this issue, we propose herein a fast CGH algorithm for 3D objects comprised of line-drawn objects at layers of different depths. An aperture formed from a continuous line at a single depth can be regarded as a series of aligned point sources of light, and the wavefront converges for a sufficiently long line. Thus, a CGH of a line-drawn object can be calculated by synthesizing converged wavefronts along the line. Numerical experiments indicate that, compared with the FFT-based method, the proposed method offers a factor-56 gain in speed for calculating 16-k-resolution CGHs from 3D objects composed of twelve line-drawn objects at different depths.

Large-scale electroholography by HORN-8 from a point-cloud model with 400,000 points

We developed a HORN-8 system that generates computer-generated holograms at a high speed. The cluster system employed eight HORN-8 boards and achieved a level of performance that was 1,000 times faster than that of a PC. From a point-cloud model comprising 65,536 (2¹⁶) points, the proposed cluster system can update a 2-million-pixel (1,920 × 1,080) hologram at 60 frames per second. 65,536 (2¹⁶) is the internal memory size of the HORN-8 hardware. However, the HORN-8 system can calculate a hologram at a high speed even if the number of point-cloud sources exceeds 65,536 (2¹⁶). Herein, we spatiotemporally divided a point-cloud model comprising ~400,000 points and succeeded in reproducing the video-holography. We demonstrated the performance of the special-purpose computer for electroholography using HORN-8 hardware that does not require a large internal memory when the calculation speed is high.

Special-purpose computer HORN-8 for phase-type electro-holography

Electro-holography is a promising display technology that can reconstruct a photorealistic three-dimensional (3D) movie; however, it is yet to be realized practically owing to the need for enormous calculation power. A special-purpose computer for electro-holography, namely HORN, has been studied for over 20 years as a means to solve this problem. The latest version of HORN, HORN-8, was developed using field programmable gate array (FPGA) technology. Initially, a circuit for amplitude-type electro-holography was implemented in HORN-8; however, implementation of phase-type electro-holography has remained an issue. In this paper, the development of new version of HORN-8 and its cluster system, which achieved a real-time reconstruction of a 3D movie with point clouds comprised of 32,000 points for phase-type electro-holography, was reported.

Fast two-step layer-based method for computer generated hologram using sub-sparse 2D fast Fourier transform

Fast two-step layer-based and sub-sparse two-dimensional Fast Fourier transform (SS-2DFFT) algorithms are proposed to speed up the calculation of computer-generated holograms. In a layer-based method, each layer image may contain large areas in which the pixel values are zero considering the occlusion effect among the different depth layers. By taking advantage of this feature, the two-step layer-based algorithm only calculates the non-zero image areas of each layer. In addition, the SS-2DFFT method implements two one-dimensional fast Fourier transforms (1DFFT) to compute a 2DFFT without calculating the rows or columns in which the image pixels are all zero. Since the size of the active calculation is reduced, the computational speed is considerably improved. Numerical simulations and optical experiments are performed to confirm these methods. The results show that the total computational time can be reduced by 5 times for a three-dimensional (3D) object of a train, 3.4 times for a 3D object of a castle and 10 times for a 3D object of a statue head when compared with a conventional layer-based method if combining the two proposed methods together.

Decomposition method for fast computation of gigapixel-sized Fresnel holograms on a graphics processing unit cluster

A parallel computation method for large-size Fresnel computer-generated hologram (CGH) is reported. The method was introduced by us in an earlier report as a technique for calculating Fourier CGH from 2D object data. In this paper we extend the method to compute Fresnel CGH from 3D object data. The scale of the computation problem is also expanded to 2 gigapixels, making it closer to real application requirements. The significant feature of the reported method is its ability to avoid communication overhead and thereby fully utilize the computing power of parallel devices. The method exhibits three layers of parallelism that favor small to large scale parallel computing machines. Simulation and optical experiments were conducted to demonstrate the workability and to evaluate the efficiency of the proposed technique. A two-times improvement in computation speed has been achieved compared to the conventional method, on a 16-node cluster (one GPU per node) utilizing only one layer of parallelism. A 20-times improvement in computation speed has been estimated utilizing two layers of parallelism on a very large-scale parallel machine with 16 nodes, where each node has 16 GPUs.

Rendering of specular curved objects in polygon-based computer holography

A realistic rendering technique is presented for creating large-scale computer-generated holograms. The technique is based on the polygon-based method, but allows specular curved surfaces to be reconstructed without increasing the number of polygons. In this technique, specular flat surfaces are transformed into curved surfaces. This is achieved by controlling the direction of reflected light, using fragmentary plane waves. An actual large-scale computer-generated hologram is created, and is used to verify the validity and practicality of the technique.

Acceleration of the calculation speed of computer-generated holograms using the sparsity of the holographic fringe pattern for a 3D object

In computer-generated hologram (CGH) calculations, a diffraction pattern needs to be calculated from all points of a 3-D object, which requires a heavy computational cost. In this paper, we propose a novel fast computer-generated hologram calculation method using sparse fast Fourier transform. The proposed method consists of two steps. First, the sparse dominant signals of CGHs are measured by calculating a wavefront on a virtual plane between the object and the CGH plane. Second, the wavefront on CGH plane is calculated by using the measured sparsity with sparse Fresnel diffraction. Experimental results proved that the proposed method is much faster than existing works while it preserving the visual quality.

Practical system for generating digital mixed reality video holograms

We propose a practical system that can effectively mix the depth data of real and virtual objects by using a Z buffer and can quickly generate digital mixed reality video holograms by using multiple graphic processing units (GPUs). In an experiment, we verify that real objects and virtual objects can be merged naturally in free viewing angles, and the occlusion problem is well handled. Furthermore, we demonstrate that the proposed system can generate mixed reality video holograms at 7.6 frames per second. Finally, the system performance is objectively verified by users' subjective evaluations.

Fast generation of a high-quality computer-generated hologram using a scalable and flexible PC cluster

In order to efficiently generate a high-quality computer-generated hologram (HQ-CGH), which requires that both a three-dimensional object image and its computer-generated hologram (CGH) are in high-definition resolution, we implement a fast CGH generation system using a scalable and flexible personal computer (PC) cluster. From experimental results obtained in generating a HQ-CGH with a CGH resolution of 1536×1536 and 2,155,898 light sources using a PC cluster comprising a server PC and nine client PCs, it is verified that the proposed system is approximately 4.7 times faster than a single PC with two high-performance GPUs.