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

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.

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.

Wavefront recording plane-like method for polygon-based holograms

The wavefront recording plane (WRP) method is an algorithm for computer-generated holograms, which has significantly promoted the accelerated computation of point-based holograms. Similarly, in this paper, we propose a WRP-like method for polygon-based holograms. A WRP is placed near the object, and the diffracted fields of all polygons are aggregated in the WRP so that the fields propagating from the polygonal mesh affect only a small region of the plane rather than the full region. Unlike the conventional WRP method used in point-based holograms, the proposed WRP-like method utilizes sparse sampling in the frequency domain to significantly reduce the practical computational kernel size. The proposed WRP-like method and the analytical shading model are used to generate polygon-based holograms of multiple three-dimensional (3D) objects, which are then reproduced to confirm 3D perception. The results indicate that the proposed WRP-like method based on an analytical algorithm is hundreds of times faster than the reference full region sampling case; a hologram with tens of thousands of triangles can be computed in seconds even on a CPU, whereas previous methods required a graphics processing unit to achieve these speeds.

Real-Time CGH Generation by CUDA-OpenGL Interoperability for Adaptive Beam Steering with a MEMS Phase SLM

Real-time, simultaneous, and adaptive beam steering into multiple regions of interest replaces conventional raster scanning with a less time-consuming and flexible beam steering framework, where only regions of interest are scanned by a laser beam. CUDA-OpenGL interoperability with a computationally time-efficient computer-generated hologram (CGH) calculation algorithm enables such beam steering by employing a MEMS-based phase light modulator (PLM) and a Texas Instruments Phase Light Modulator (TI-PLM). The real-time CGH generation and display algorithm is incorporated into the beam steering system with variable power and scan resolution, which are adaptively controlled by camera-based object recognition. With a mid-range laptop GPU and the current version of the MEMS-PLM, the demonstrated scanning speed can exceed 1000 points/s (number of beams > 5) and potentially exceeds 4000 points/s with state-of-the-art GPUs.

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.

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.

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.