Direct calculation of computer-generated holograms in sparse bases

Computer holography using deep neural network with Fourier basis

The use of a deep neural network is a promising technique for rapid hologram generation, where a suitable training dataset is vital for the reconstruct quality as well as the generalization of the model. In this Letter, we propose a deep neural network for phase hologram generation with a physics-informed training strategy based on Fourier basis functions, leading to orthonormal representations of the spatial signals. The spatial frequency characteristics of the reconstructed diffraction fields can be regulated by recombining the Fourier basis functions in the frequency domain. Numerical and optical results demonstrate that the proposed method can effectively improve the generalization of the model with high-quality reconstructions.

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.

Hologram computation using the radial point spread function

Holograms are computed by superimposing point spread functions (PSFs), which represent the distribution of light on the hologram plane. The computational cost and the spatial bandwidth product required to generate holograms are significant; therefore, it is challenging to compute high-resolution holograms at the rates required for videos. Among the possible displays, fixed-eye-position holographic displays, such as holographic head-mounted displays, reduce the spatial bandwidth product by fixing eye positions while satisfying almost all human depth cues. In eye-fixed holograms, by calculating a part distribution of the entire PSF, we observe reconstructed images that maintain the image quality and the depth of focus almost as high as those generated by the entire PSF. In this study, we accelerate the calculation of eye-fixed holograms by engineering the PSFs. We propose cross and radial PSFs, and we determine that, out of the two, the radial PSFs have a better image quality. By combining the look-up table method and the wavefront-recording plane method with radial PSFs, we show that the proposed method can rapidly compute holograms.

Photorealistic computer generated holography with global illumination and path tracing

Computer generated holography (CGH) algorithms come in many forms, with different trade-offs in terms of visual quality and calculation speed. However, no CGH algorithm to date can accurately account for all 3D visual cues simultaneously, such as occlusion, shadows, continuous parallax, and precise focal cues, without view discretization. The aim is to create photorealistic CGH content, not only for display purposes but also to create reference data for comparing and testing CGH and compression algorithms. We propose a novel algorithm combining the precision of point-based CGH with the accurate shading and flexibility of ray-tracing algorithms. We demonstrate this by creating a scene with global illumination, soft shadows, and precise occlusion cues, implemented with OptiX and CUDA.

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.

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document}× 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.

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.

Dedicated processor for hologram calculation using sparse Fourier bases

Recently, a calculation method involving sparse point spread functions in the short-time Fourier transform (STFT) domain was proposed. In this paper, a dedicated processor using the STFT algorithm is described, which is implemented on a field-programmable gate array. All the operations in this algorithm are implemented using fixed-point arithmetic. Since this algorithm includes a trigonometric function and an error function, lookup tables (LUTs) are utilized to reduce the calculation costs. We have devised a dedicated circuit architecture that allows parallel operations. In addition, a central processing unit could generate holograms using the STFT-based algorithm with fixed-point arithmetic and LUTs at a higher speed than the generation using floating-point arithmetic.

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.

Phase added sub-stereograms for accelerating computer generated holography

Phase-added stereograms are a form of sparse computer generated holograms, subdividing the hologram in small Fourier transformed blocks and updating a single coefficient per block and per point-spread function. Unfortunately, these algorithms' computational performance is often bottlenecked by the relatively high memory requirements. We propose a technique to partition the 3D point cloud into cells using time-frequency analysis, grouping the affected coefficients into subsets that improve caching and minimize memory requirements. This results in significant acceleration of phase added stereogram algorithms without affecting render quality, enabling real-time CGH for driving holographic displays for more complex and detailed scenes than previously possible. We report a 30-fold speedup over the base implementation, achieving real-time speeds of 80ms per million points per megapixel on a single GPU.

Comparison of wavefront recording plane-based hologram calculations: ray-tracing method versus look-up table method

In this study, we compare the ray-tracing method with the look-up table (LUT) method in order to optimize computer-generated hologram (CGH) calculation based on the wavefront recording plane (WRP) method. The speed of the WRP-based CGH calculation largely depends on implementation factors, such as calculation methods, hardware, and parallelization method. Therefore, we evaluated the calculation time and image quality of the reconstructed three-dimensional (3D) image by using the ray-tracing and LUT methods in the central processing unit (CPU) and graphics processing unit (GPU) implementations. Thereafter, we performed several implementations by changing the number of object points and the distance from 3D objects to the WRP. Furthermore, we confirmed different characteristics between CPU and GPU implementations.

Efficient algorithms for the accurate propagation of extreme-resolution holograms

Display-sized full-parallax holograms with large viewing angles require resolutions surpassing tens of Gigapixels. Unfortunately, computer-generated holography is computationally intensive, particularly for these huge display resolutions. Existing algorithms designed for diffraction of typical Megapixel-sized holograms do not scale well for these large resolutions. Furthermore, since the holograms will not fit in the RAM of most of today's computers, the algorithms should be modified to minimize disk access. We propose two novel algorithms respectively for short-distance and long-distance propagation, and accurately compute the diffraction of a 17.2 Gigapixel hologram on a standard desktop machine. We report a 500-fold speedup over the reference rectangular tiling algorithm for the short-distance version, and a 50-fold speedup for the long-distance version.