Three-dimensional spline-based computer-generated holography.

Electro-holography is a promising 3D display technology, as it can, in principle, account for all visual cues. Computing the interference patterns to drive them is highly calculation-intensive, requiring the design and development of efficient computer-generated holography (CGH) algorithms to facilitate real-time display. In this work, we propose a new algorithm for computing the CGH for arbitrary 3D curves using splines, as opposed to previous solutions, which could only draw planar curves. The solutions are analytically expressed; we conceived an efficiently computable approximation suitable for GPU implementations. We report over 55-fold speedups over the reference point-wise algorithm, resulting in real-time 4K holographic video generation of complex 3D curved objects. The proposed algorithm is validated numerically and optically on a holographic display setup.

Improving the imbalance of the light intensity of 3D wire-frame projection with electro-holography by superimposing a phase error.

The CG-line method is an algorithm for generating computer-generated holograms (CGHs), a digitally recording medium for three-dimensional images in electro-holography. Since the CG-line method is specialized for projecting three-dimensional wireframe objects, it can calculate CGH with a very low computational load. However, the reconstructed image of the conventional CG-line method suffers from unintended light imbalance depending on the object shape, which disturbs the understandability of the projecting image. Therefore, we propose a method for reducing light imbalance by imposing phase error that controls light according to the line shape. Consequently, we reduced light imbalance by maintaining the high computational speed.

Variable-intensity line 3D images drawn using kinoform-type electroholography superimposed with phase error.

Three-dimensional (3D) display using electroholography is a promising technology for next-generation television systems; however, its applicability is limited by the heavy computational load for obtaining computer-generated holograms (CGHs). The CG-line method is an algorithm that calculates CGHs to display 3D line-drawn objects at a very high computational speed but with limited expressiveness; for instance, the intensity along the line must be constant. Herein, we propose an extension for drawing gradated 3D lines using the CG-line method by superimposing phase noise. Consequently, we succeeded in drawing gradated 3D lines while maintaining the high computational speed of the original CG-line method.

Accelerating hologram generation using oriented-separable convolution and wavefront recording planes.

Recently, holographic displays have gained attention owing to their natural presentation of three-dimensional (3D) images; however, the enormous amount of computation has hindered their applicability. This study proposes an oriented-separable convolution accelerated using the wavefront-recording plane (WRP) method and recurrence formulas. We discuss the orientation of 3D objects that affects computational efficiency, which is overcome by reconsidering the orientation, and the suitability of the proposed method for hardware implementations.

GPU-accelerated calculation of computer-generated holograms for line-drawn objects.

The heavy computational burden of computer-generated holograms (CGHs) has been a significant issue for three-dimensional (3D) display systems using electro-holography. Recently, fast CGH calculation methods of line-drawn objects for electro-holography were proposed, which are targeted for holography-based augmented reality/virtual reality devices because of their ability to project object contours in space with a small computational load. However, these methods still face shortcomings, namely, they cannot draw arbitrary curves with graphics processing unit (GPU) acceleration, which is an obstacle for replaying highly expressive and complex 3D images. In this paper, we propose an effective algorithm for calculating arbitrary line-drawn objects at layers of different depths suitable for implementation of GPU. By combining the integral calculation of wave propagation with an algebraic solution, we successfully calculated CGHs of 1, 920 × 1, 080 pixels within 1.1 ms on an NVIDIA Geforce RTX 2080Ti GPU.

Analytic computation of line-drawn objects in computer generated holography.

Digital holography is a promising display technology that can account for all human visual cues, with many potential applications i.a. in AR and VR. However, one of the main challenges in computer generated holography (CGH) needed for driving these displays are the high computational requirements. In this work, we propose a new CGH technique for the efficient analytical computation of lines and arc primitives. We express the solutions analytically by means of incomplete cylindrical functions, and devise an efficiently computable approximation suitable for massively parallel computing architectures. We implement the algorithm on a GPU (with CUDA), provide an error analysis and report real-time frame rates for CGH of complex 3D scenes of line-drawn objects, and validate the algorithm in an optical setup.

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.

Compression scheme of electro-holography based on the vector quantization of point light sources.

Video holography has attracted attention after its invention in 1947; however, the enormous amount of data involved in recording and transmitting three-dimensional (3D) images remains a serious issue in electro-holography. Majority of the studies that have investigated holography transmission target the system that transmits the 3D images by compressing the holograms created on the distributor side using various compression techniques such as the conventional video compression techniques. However, the importance of the information in frequency space and characteristics, such as the correlation between adjacent pixels and frames, is different in natural images and holograms; therefore, these approaches are not always effective. In this study, we propose an effective electro-holography compression scheme based on the vector quantization of point light sources (PLSs). Instead of directly compressing a hologram, our method compresses and transmits PLSs from the distributor side and generates a hologram on the receiver side. To reduce the computational load that is required for creating a computer-generated hologram (CGH) on the receiver side, a fast CGH calculation technique has been developed for the vector-quantized PLS data based on the lookup tables (LUTs). This reduces the data rate by 76% when compared to that observed in case of uncompressed CGH transmission with 2K resolution and results in a calculation speed that is 1.34 times faster than that obtained using the conventional LUT method.

Dynamic-range compression scheme for digital hologram using a deep neural network.

This Letter aims to propose a dynamic-range compression and decompression scheme for digital holograms that uses a deep neural network (DNN). The proposed scheme uses simple thresholding to compress the dynamic range of holograms with 8-bit gradation to binary holograms. Although this can decrease the amount of data by one-eighth, the binarization strongly degrades the image quality of the reconstructed images. The proposed scheme uses a DNN to predict the original gradation holograms from the binary holograms, and the error-diffusion algorithm of the binarization process contributes significantly to training the DNN. The performance of the scheme exceeds that of modern compression techniques such as JPEG 2000 and high-efficiency video coding.

Digital holographic particle volume reconstruction using a deep neural network.

This paper proposes a particle volume reconstruction directly from an in-line hologram using a deep neural network (DNN). Digital holographic volume reconstruction conventionally uses multiple diffraction calculations to obtain sectional reconstructed images from an in-line hologram, followed by detection of the lateral and axial positions, and the sizes of particles by using focus metrics. However, the axial resolution is limited by the numerical aperture of the optical system, and the processes are time consuming. The method proposed here can simultaneously detect the lateral and axial positions, and the particle sizes via a DNN. We numerically investigated the performance of the DNN in terms of the errors in the detected positions and sizes. The calculation time is faster than conventional diffracted-based approaches.

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.

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.

Autoencoder-based holographic image restoration.

We propose a holographic image restoration method using an autoencoder, which is an artificial neural network. Because holographic reconstructed images are often contaminated by direct light, conjugate light, and speckle noise, the discrimination of reconstructed images may be difficult. In this paper, we demonstrate the restoration of reconstructed images from holograms that record page data in holographic memory and quick response codes by using the proposed method.

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

The cosine function is a heavy computational operation in computer-generated hologram (CGH) calculation; therefore, it is implemented by substitution methods such as a look-up table. However, the computational load and required memory space of such methods are still large. In this study, we propose a simple and fast cosine function approximation method for CGH calculation. As a result, we succeeded in creating CGH with sufficient quality and made the calculation time 1.6 times as fast at maximum compared to using the look-up table of the cosine function on CPU implementation.

Fast calculation of computer-generated hologram using run-length encoding based recurrence relation.

Computer-Generated Holograms (CGHs) can be generated by superimposing zoneplates. A zoneplate is a grating that can concentrate an incident light into a point. Since a zoneplate has a circular symmetry, we reported an algorithm that rapidly generates a zoneplate by drawing concentric circles using computer graphic techniques. However, random memory access was required in the algorithm and resulted in degradation of the computational efficiency. In this study, we propose a fast CGH generation algorithm without random memory access using run-length encoding (RLE) based recurrence relation. As a result, we succeeded in improving the calculation time by 88%, compared with that of the previous work.

Fast calculation of computer-generated hologram using the circular symmetry of zone plates.

Computer-Generated Holograms (CGHs) can be generated from three-dimensional objects composed of point light sources by overlapping zone plates. A zone plate is a grating that can focus an incident wave and it has circular symmetry shape. In this study, we propose a fast CGH generating algorithm using the circular symmetry of zone plates and computer graphics techniques. We evaluated the proposed method by numerical simulation.

Real-Time Computation of 3D Wireframes in Computer-Generated Holography.

Computer-Generated Holography (CGH) algorithms simulate numerical diffraction, being applied in particular for holographic display technology. Due to the wave-based nature of diffraction, CGH is highly computationally intensive, making it especially challenging for driving high-resolution displays in real-time. To this end, we propose a technique for efficiently calculating holograms of 3D line segments. We express the solutions analytically and devise an efficiently computable approximation suitable for massively parallel computing architectures. The algorithms are implemented on a GPU (with CUDA), and we obtain a 70-fold speedup over the reference point-wise algorithm with almost imperceptible quality loss. We report real-time frame rates for CGH of complex 3D line-drawn objects, and validate the algorithm in both a simulation environment as well as on a holographic display setup.

An interactive holographic projection system that uses a hand-drawn interface with a consumer CPU.

Holography is a promising technology for photo-realistic three-dimensional (3D) displays because of its ability to replay the light reflected from an object using a spatial light modulator (SLM). However, the enormous computational requirements for calculating computer-generated holograms (CGHs)-which are displayed on an SLM as a diffraction pattern-are a significant problem for practical uses (e.g., for interactive 3D displays for remote navigation systems). Here, we demonstrate an interactive 3D display system using electro-holography that can operate with a consumer's CPU. The proposed system integrates an efficient and fast CGH computation algorithm for line-drawn 3D objects with inter-frame differencing, so that the trajectory of a line-drawn object that is handwritten on a drawing tablet can be played back interactively using only the CPU. In this system, we used an SLM with 1,920 [Formula: see text] 1,080 pixels and a pixel pitch of 8 µm × 8 µm, a drawing tablet as an interface, and an Intel Core i9-9900K 3.60 GHz CPU. Numerical and optical experiments using a dataset of handwritten inputs show that the proposed system is capable of reproducing handwritten 3D images in real time with sufficient interactivity and image quality.

Digital holographic high-speed 3D imaging for the vibrometry of fast-occurring phenomena.

Digital holography allows production of high-speed three-dimensional images at rates over 100,000 frames per second; however, simultaneously obtaining suitable performance and levels of accuracy using digital holography is difficult. This problem prevents high-speed three-dimensional imaging from being used for vibrometry. In this paper, we propose and test a digital holography method that can produce vibration measurements. The method is based on single-shot phase-shifting interferometry. Herein, we imaged the surface of a loudspeaker diaphragm and measured its displacement due to the vibrations produced by a frequency sweep signal. We then analyzed the frequency of the experimental data and confirmed that the frequency spectra inferred from the reconstructed images agreed well with the spectra produced by the sound recorded by a microphone. This method can be used for measuring vibrations with three-dimensional imaging for loudspeakers, microelectromechanical systems, surface acoustic wave filters, and biological tissues and organs.

Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors.

We demonstrate an aerial projection system for reconstructing 3D motion pictures based on holography. The system consists of an optical source, a spatial light modulator corresponding to a display and two parabolic mirrors. The spatial light modulator displays holograms calculated by computer and can reconstruct holographic motion pictures near the surface of the modulator. The two parabolic mirrors can project floating 3D images of the motion pictures formed by the spatial light modulator without mechanical scanning or rotating. In this demonstration, we used a phase-modulation-type spatial light modulator. The number of pixels and the pixel pitch of the modulator were 1,080 × 1,920 and 8.0 µm × 8.0 µm, respectively. The diameter, the height and the focal length of each parabolic mirror were 288 mm, 55 mm and 100 mm, respectively. We succeeded in aerially projecting 3D motion pictures of size ~2.5 mm(3) by this system constructed by the modulator and mirrors. In addition, by applying a fast computational algorithm for holograms, we achieved hologram calculations at ~12 ms per hologram with 4 CPU cores.