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 ($2^{16}$) points, the proposed cluster system can update a 2-million-pixel (1,920 × 1,080) hologram at 60 frames per second. 65,536 ($2^{16}$) 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 ($2^{16}$). 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.

Holography is a technology that uses light interference and diffraction to record and reproduce three-dimensional (3D) information. Using computers, holographic 3D scenes (electroholography) have been widely studied. Nevertheless, its practical application requires enormous computing power, and current computers have limitations in real-time processing. In this study, we show that holographic reconstruction (HORN)-9, a special-purpose computer for electroholography with the Hilbert transform, can compute a 1, 920 × 1, 080-pixel computer-generated hologram from a point cloud of 65,000 points in 0.030 s (33 fps) on a single card. This performance is 8, 7, and 170 times more efficient than a previously developed HORN-8, a graphics processing unit, and a central processing unit (CPU), respectively. We also demonstrated the real-time processing and display of 400,000 points on multiple HORN-9s, achieving an acceleration of 600 times with four HORN-9 units compared with a single CPU.

Electroholography is attracting attention as an ideal 3D image presentation method. Developing such methods involves significant computational complexity; thus, they are difficult to realize. Typically, large cluster systems with a control PC and a field-programmable gate array (FPGA) acceleration board are used to reduce hologram calculation time. However such systems cannot be used for embedded 3D systems, such as a head-mounted display. In this study, we developed a compact holographic computer using a Xilinx Zynq UltraScale+ MPSoC with an ARM CPU and an FPGA on a single chip. The proposed system can reproduce a 3D video at 15 frames per second for a spatial light modulator of 1,920 $\times$ 1,080 pixels from an object represented by 6,500 point cloud sources. The proposed system can be embedded in various systems, e.g., head-mounted displays and 3D televisions.

We propose an indirect method for generating a complex hologram and phase-only hologram from an amplitude hologram using the Hilbert transform. The Hilbert transform generates an imaginary part of complex amplitude from only an amplitude hologram, resulting in the reduction of the total computational complexity of complex and phase-only holograms. More importantly, the proposed method can reduce the hardware resources of dedicated hologram processors.

The digital holography field began with electronic recording of holograms in the 1960s.^1,2 Digital holography can dynamically capture information about the amplitude and phase of light. In addition, it is possible to record an instantaneous three-dimensional (3D) velocity field,^{3 – 7} which is attracting attention. Hologram resolution and image quality have also improved significantly. Gigapixel digital holography^8,9 and large-scale holograms^10,11 have been manufactured. Large-scale holograms enable deep 3D measurement and simultaneous imaging of a large number of particle images. However, a huge amount of time is required to calculate the reconstructed image. Research about optical methods is also important; however, computation time remains a problem, but algorithm improvements and hardware approaches are very effective.

A complex amplitude hologram can reconstruct perfect light waves. However, as there are no spatial light modulators that are able to display complex amplitudes, we need to use amplitude, binary, or phase-only holograms. The images reconstructed from such holograms will deteriorate; to address this problem, iterative hologram optimization algorithms have been proposed. One of the iterative algorithms utilizes a blank area to help converge the optimization; however, the calculation time and memory usage involved increases. In this study, we propose to reduce the computational complexity and memory usage of the iterative optimization using scaled diffraction, which can calculate light propagation with different sampling pitches on a hologram plane and object plane. Scaled diffraction can introduce a virtual blank area without using physical memory. We further propose a combination of scaled diffraction-based optimization and conventional methods. The combination algorithm improves the quality of a reconstructed complex amplitude while accelerating optimization.