Fast computer generated hologram calculation with a mini look-up table incorporated with radial symmetric interpolation

An ultrahigh-fidelity 3D holographic display using scattering to homogenize the angular spectrum

A three-dimensional (3D) holographic display (3DHD) can preserve all the volumetric information about an object. However, the poor fidelity of 3DHD constrains its applications. Here, we present an ultrahigh-fidelity 3D holographic display that uses scattering for homogenization of angular spectrum. A scattering medium randomizes the incident photons and homogenizes the angular spectrum distribution. The redistributed field is recorded by a photopolymer film with numerous modulation modes and a half-wavelength scale pixel size. We have experimentally improved the contrast of a focal spot to 6 × 106 and tightened its spatial resolution to 0.5 micrometers, respectively ~300 and 4.4 times better than digital approaches. By exploiting the spatial multiplexing ability of the photopolymer and the transmission channel selection capability of the scattering medium, we have realized a dynamic holographic display of 3D spirals consisting of 20 foci across 1 millimeter × 1 millimeter × 26 millimeters with uniform intensity.

Deep hologram converter from low-precision to middle-precision holograms

We propose a deep hologram converter based on deep learning to convert low-precision holograms into middle-precision holograms. The low-precision holograms were calculated using a shorter bit width. It can increase the amount of data packing for single instruction/multiple data in the software approach and the number of calculation circuits in the hardware approach. One small and one large deep neural network (DNN) are investigated. The large DNN exhibited better image quality, whereas the smaller DNN exhibited a faster inference time. Although the study demonstrated the effectiveness of point-cloud hologram calculations, this scheme could be extended to various other hologram calculation algorithms.

Real-time realistic computer-generated hologram with accurate depth precision and a large depth range

Holographic display is an ideal technology for near-eye display to realize virtual and augmented reality applications, because it can provide all depth perception cues. However, depth performance is sacrificed by exiting computer-generated hologram (CGH) methods for real-time calculation. In this paper, volume representation and improved ray tracing algorithm are proposed for real-time CGH generation with enhanced depth performance. Using the single fast Fourier transform (S-FFT) method, the volume representation enables a low calculation burden and is efficient for Graphics Processing Unit (GPU) to implement diffraction calculation. The improved ray tracing algorithm accounts for accurate depth cues in complex 3D scenes with reflection and refraction, which is represented by adding extra shapes in the volume. Numerical evaluation is used to verify the depth precision. And experiments show that the proposed method can provide a real-time interactive holographic display with accurate depth precision and a large depth range. CGH of a 3D scene with 256 depth values is calculated at 30fps, and the depth range can be hundreds of millimeters. Depth cues of reflection and refraction images can also be reconstructed correctly. The proposed method significantly outperforms existing fast methods by achieving a more realistic 3D holographic display with ideal depth performance and real-time calculation at the same time.

HoloKinect: Holographic 3D Video Conferencing

Recent world events have caused a dramatic rise in the use of video conferencing solutions such as Zoom and FaceTime. Although 3D capture and display technologies are becoming common in consumer products (e.g., Apple iPhone TrueDepth sensors, Microsoft Kinect devices, and Meta Quest VR headsets), 3D telecommunication has not yet seen any appreciable adoption. Researchers have made great progress in developing advanced 3D telepresence systems, but often with burdensome hardware and network requirements. In this work, we present HoloKinect, an open-source, user-friendly, and GPU-accelerated platform for enabling live, two-way 3D video conferencing on commodity hardware and a standard broadband internet connection. A Microsoft Azure Kinect serves as the capture device and a Looking Glass Portrait multiscopically displays the final reconstructed 3D mesh for a hologram-like effect. HoloKinect packs color and depth information into a single video stream, leveraging multiwavelength depth (MWD) encoding to store depth maps in standard RGB video frames. The video stream is compressed with highly optimized and hardware-accelerated video codecs such as H.264. A search of the depth and video encoding parameter space was performed to analyze the quantitative and qualitative losses resulting from HoloKinect's lossy compression scheme. Visual results were acceptable at all tested bitrates (3-30 Mbps), while the best results were achieved with higher video bitrates and full 4:4:4 chroma sampling. RMSE values of the recovered depth measurements were low across all settings permutations.

Spherical crown diffraction model by occlusion utilizing for a curved holographic display

The information of occlusion culling in the spherical holography has been ignored or discarded for a long time. However, the information of the occlusion could be utilized, which has never been considered before. In this paper, a spherical crown diffraction model for a curved holographic display is proposed by occlusion utilizing. In the proposed spherical crown diffraction model, the method of occlusion utilizing is realized firstly, which is based on an optical-path-select function to remain the desired light information. Based on the method of occlusion utilizing, a spherical crown diffraction model for curve holographic display is proposed by further analyzing the optical propagation geometry relationship. This proposed diffraction model not only retains the advantage of a conventional diffraction model with a large view angle of 360°in the azimuth direction, but also improves the view angle in the latitude direction. Besides, the proposed model by occlusion utilizing has higher optical utilization than that model by occlusion culling. Furthermore, the effectiveness and feasibility of the proposed model are verified by numerical simulations. To our knowledge, it is the first time that a method and an application are proposed to utilize the occlusion.

Review of computer-generated hologram algorithms for color dynamic holographic three-dimensional display

Holographic three-dimensional display is an important display technique because it can provide all depth information of a real or virtual scene without any special eyewear. In recent years, with the development of computer and optoelectronic technology, computer-generated holograms have attracted extensive attention and developed as the most promising method to realize holographic display. However, some bottlenecks still restrict the development of computer-generated holograms, such as heavy computation burden, low image quality, and the complicated system of color holographic display. To overcome these problems, numerous algorithms have been investigated with the aim of color dynamic holographic three-dimensional display. In this review, we will explain the essence of various computer-generated hologram algorithms and provide some insights for future research.

Improved phase hologram generation of multiple 3D objects

We demonstrate the generation of phase holograms of multiple 3D objects at different axial positions without cross talk and significant improvements in performance over conventional methods. We first obtain the phase hologram of two 3D objects, each one comprising 50 layers, using the global Gerchberg-Saxton algorithm. Then, we discuss and demonstrate a propagation approach based on the singular value decomposition of the Fresnel impulse response function that enables fast computation of small distance propagations. Finally, we propose a new iterative hologram generation algorithm, to the best of our knowledge, that takes advantage of this propagation approach and use it to make the hologram of the same scene previously obtained with the global Gerchberg-Saxton algorithm. We perform numerical and experimental reconstructions to compare both methods, demonstrating that our proposal achieves 4 times faster computation, as well as improved reconstruction quality.

Faster generation of holographic video of 3-D scenes with a Fourier spectrum-based NLUT method

In this article, a new type of Fourier spectrum-based novel look-up table (FS-NLUT) method is proposed for the faster generation of holographic video of three-dimensional (3-D) scenes. This proposed FS-NLUT method consists of principal frequency spectrums (PFSs) which are much smaller in size than the principal fringe patterns (PFPs) found in the conventional NLUT-based methods. This difference in size allows for the number of basic algebraic operations in the hologram generation process to be reduced significantly. In addition, the fully one-dimensional (1-D) calculation framework of the proposed method also allows for a significant reduction of overall hologram calculation time. In the experiments, the total number of basic algebraic operations needed for the proposed FS-NLUT method were found to be reduced by 81.23% when compared with that of the conventional 1-D NLUT method. In addition, the hologram calculation times of the proposed method, when implemented in the CPU and the GPU, were also found to be 60% and 66% faster than that of the conventional 1-D NLUT method, respectively. It was also confirmed that the proposed method implemented with two GPUs can generate a holographic video of a test 3-D scene in real-time (>24f/s).

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.

Acceleration of polygon-based computer-generated holograms using look-up tables and reduction of the table size via principal component analysis

In this study, we first analyze the fully analytical frequency spectrum solving method based on three-dimensional affine transform. Thus, we establish a new method for combining look-up tables (LUTs) with polygon holography. The proposed method was implemented and proved to be accelerated about twice compared to the existing methods. In addition, principal component analysis was used to compress the LUTs, effectively reducing the required memory without artifacts. Finally, we calculated very complex objects on a graphics processing unit using the proposed method, and the calculation speed was higher than that of existing polygon-based methods.

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.

Wide-viewing full-color depthmap computer-generated holograms

An efficient synthesis algorithm for wide-viewing full-color depthmap computer-generated holograms is proposed. We develop a precise computational algorithm integrating wave-optic geometry-mapping, color-matching, and noise-filtering to multiplex multiview elementary computer-generated holograms (CGHs) into a single high-definition CGH without three-dimensional perspective distortion or color dispersion. Computational parallelism is exploited to achieve significant computational efficiency improvement in the production throughput of full-color wide-viewing angle CGHs. The proposed algorithm is verified through the full-color binary hologram reconstruction experiments utilizing an off-axis R·G·B simultaneous illumination method, which suggests the feasibility of the full-color sub-wavelength binary spatial light modulator technology.

Conical holographic display to expand the vertical field of view

Recently, cylindrical holographic display technology as a 360-degree display technology has attracted much attention. However, all the studies are based on the field of view (FOV) in the azimuth direction, and the issue of FOV in the vertical direction has never been discussed. In this paper, a new holographic display is proposed to expand the vertical FOV by a conical holographic diffraction model, in which the object plane is the outer cylinder and the observation plane is a part of the cone. In this proposed method, the proposed diffraction model is firstly established by the Rayleigh-Sommerfeld diffraction formula, and then the convolution and FFT are used for a fast diffraction calculation. The correctness and effectiveness of our proposed method are verified by the simulation of Young's interference and the numerical reconstructions from the complex amplitude and encoded holograms, respectively. In addition, an accurate relationship between the conical inclination angle and the vertical FOV expansion is analyzed, and the simulation results show that our proposed method can significantly expand the vertical FOV by 0.4 of the original object. Therefore, the issue of the vertical FOV in cylindrical holography is deeply discussed and successfully addressed for the first time.

Low-complexity adaptive radius outlier removal filter based on PCA for lidar point cloud denoising

In autonomous driving, cars rely on light detection and ranging (lidar) to navigate the surroundings, but interference from the environment makes it difficult to retrieve useful information. To address this problem, this paper develops a noise reduction method to filter lidar point clouds (i.e., an adaptive radius outlier removal filter based on principal component analysis). We believe this method can outperform existing clustering algorithms when applied to point cloud images captured at a large distance from the lidar. Compared to traditional methods, the proposed method has higher precision and recall with an F-score up to 0.876 and complexity reduced by at least 50%.

Acceleration of fully computed hologram stereogram using lookup table and wavefront recording plane methods

Lookup table (LUT) and wavefront recording plane (WRP) methods are proposed to accelerate the computation of fully computed hologram stereograms (HSs). In the LUT method, we precalculate large and complete spherical wave phases with varying depths, and each complex amplitude distribution segment of the object point can be obtained quickly by cropping a specific and small part of the precalculated spherical wave phases. Then, each hologram element (hogel) can be calculated by superposing all the related segments. In addition, setting a WRP near the 3D scene can further accelerate computation and reduce storage space. Because the proposed methods only replace the complex calculation using referencing LUT, they are accurate and have no limitation on the size of hogel compared with some methods of paraxial approximation. Simulations and optical experiments verify that the proposed methods can reconstruct quality 3D images with reduced computational load.

Fast calculation of high-definition depth-added computer-generated holographic stereogram by spectrum-domain look-up table [Invited]

High-definition depth-added computer-generated holographic stereogram (DA-CGHS) is superior in its high quality, easy realization, and auto-shading effect. However, its computing cost is extremely high because numerous scenes together with depth information must be calculated. Here, we proposed a fast calculation scheme of DA-CGHS by the spectrum-domain look-up table (SDLUT) method. In SDLUT, diffraction fields on the hogel plane of selected reference points in the object space are calculated. Subsequently, the fields are Fourier transformed to the spectrum domain. Because the signal energy always concentrates in a small spectrum region, these regions are cropped as the elemental tables. In the computing of the hogels, the field superposition is conducted in the spectrum domain by using the elemental tables. In our demonstration, the table size of SDLUT is only 0.44% that of the look-up table (LUT). Because the table size is very small, the computing time of SDLUT method can be nearly 80 times faster than that of conventional LUTs in the spatial domain, while the image quality is comparable.

Fast hologram generation method based on the optimal segmentation of a sub-CGH

In this paper, a fast hologram generation method is proposed based on the optimal segmentation of a sub-computer-generated-hologram (sub-CGH). The relationship between the pixels on the hologram and the corresponding reconstructed image is calculated firstly. Secondly, the sub-CGH corresponding to the object point from the recorded object is optimized and divided into the optimized diffraction area and the invalid diffraction area. Then, the optimized diffraction area of the sub-CGH for each object point is pre-calculated and saved. Finally, the final hologram can be generated by superimposing all the sub-CGHs. With the proposed method, the calculation time for the final hologram can be significantly reduced and the quality of the reconstructed image is not affected. Moreover, the proposed method has the advantages of perspective enlargement compared with the traditional method, and the experiment results verify its feasibility.

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.

Occlusion culling for computer-generated cylindrical holograms based on a horizontal optical-path-limit function

Recently, great progress has been made in the research of cylindrical holography as a promising technique of 360° display. However, there is an unsolved issue of occlusion culling, which is critical to cylindrical holography and degrades the reconstructed images due to overlapping. To our knowledge, the occlusion issue in cylindrical holography has never been deeply discussed. In this paper, a method of occlusion culling is proposed for computer-generated cylindrical holograms based on a horizontal optical-path-limit function. In cylindrical diffraction, the propagation characteristics of light waves can be described by the point spread function, which is mainly obtained by analyzing the meaning of the obliquity factor in the concentric cylinder model. Different from the planar diffraction, the diffraction area of each source point is limited within the tangents in cylindrical diffraction. Therefore, a horizontal optical path limit function that acts directly on the point spread function for occlusion culling is established. Besides, the proposed method can be applied to the three-dimensional object by using the layer-oriented method. Moreover, the effectiveness of the proposed occlusion culling method is verified by the numerical simulation results and error analysis of the reconstructed images.

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.

Fast calculation method with saccade suppression for a computer-generated hologram based on Fresnel zone plate limitation

The computer-generated hologram (CGH) is an ideal 3D technology that can satisfy all the physiological factors of the human eye (such as binocular parallax, focus adjustment and convergence etc.) by simulating the recording part of traditional optical holography with a computer. CGH has a lot of advantages such as being able to be used for animation. However, it also has many disadvantages, and one of them is the large amount of calculation. A saccade is one of a very rapid movement of human eye, and also, it is an ability of the eye to quickly and accurately move from one target to another. This is very critical for reading and involves very precise and specific eye movements. Saccades normally happen at a frequency of 2 - 8 times per second in daily life without our being conscious, and their peak angular speed can reach 900 degrees/second. However, saccades can also be initiated by an expected stimulus such as looking from one object to another, and they last from 20 - 200 ms depending on their amplitude. In addition, our visual information is suppressed while saccade occurs. In this paper, to realize the fast calculation of CGHs, a new method is proposed that uses saccades to reduce the amount of CGH calculation without any negative effects on observers viewing CGH reconstruction images. We increased high-speed calculation by at least 4 times through Fresnel zone plate limitation and 4.64 times through saccade suppression.

Max-depth-range technique for faster full-color hologram generation

In this paper, a max-depth-range method is proposed to determine the optimum length of depth range for faster generation of full-color holograms. For each color channel, objects are divided by a fixed length to create a temporary depth range, and the wavefront recording plane (WRP) is placed in the middle of all layers within the temporary depth range. The proposed method is used to calculate full-color holograms significantly faster than a conventional multiple-WRP method but with almost the same reconstructed image quality. The feasibility of the proposed method was confirmed using numerical and optical experiments for various scenes containing multiple real objects.

Acceleration of computer-generated hologram using wavefront-recording plane and look-up table in three-dimensional holographic display

In this paper, we propose a fast calculation method using look-up table and wavefront-recording plane. Wavefront-recording plane method consists of two steps: the first step is the calculation of a wavefront-recording plane which is placed between the object and the hologram. In the second step, we obtain the hologram by executing diffraction calculation from the wavefront-recording plane to the hologram plane. The first step of the previous wavefront-recording plane method is time consuming. In order to obtain further acceleration to the first step, we propose high compressed look-up table method based on wavefront-recording plane. We perform numerical simulations and optical experiments to verify the proposed method. Numerical simulation results show that the calculation time reduces dramatically in comparison with previous wavefront-recording plane method and the memory usage is very small. The optical experimental results are in accord with the numerical simulation results. It is expected that proposed method can greatly reduce the computational complexity and could be widely applied in the holographic field in the future.

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.

Divide and conquer: high-accuracy and real-time 3D reconstruction of static objects using multiple-phase-shifted structured light illumination

Multiple-phase-shifted structured light illumination achieves high-accuracy 3D reconstructions of static objects, while typically it can't achieve real-time phase computation. In this paper, we propose to compute modulations and phases of multiple scans in real time by using divide-and-conquer solutions. First, we categorize total N = KM images into M groups and each group contains K phase equally shifted images; second, we compute the phase of each group; and finally, we obtain the final phase by averaging all the separately computed phases. When K = 3, 4 or 6, we can use integer-valued intensities of images as inputs and build one or M look-up tables storing real-valued phases computed by using arctangent function. Thus, with addition and/or subtraction operations computing indices of the tables, we can directly access the pre-computed phases and avoid time-consuming arctangent computation. Compared with K-step phase measuring profilometry repeated for M times, the proposed is robust to nonlinear distortion of structured light systems. Experiments show that, first, the proposed is of the same accuracy level as the traditional algorithm, and secondly, with employing one core of a central processing unit, compared with the classical 12-step phase measuring profilometry algorithm, for K = 4 and M = 3, the proposed improves phase computation by a factor of 6 ×.

Reconstruction of a three-dimensional color-video of a point-cloud object using the projection-type holographic display with a holographic optical element

Here, we managed to reconstruct a three-dimensional color video of a point-cloud object using a projection-type holographic display with a holographic optical element as an optical screen. The holographic optical element has the function of an off-axis concave mirror and has been created by the wavefront printer digitally. We defined and implemented an algorithm to reconstruct a three-dimensional image at a chosen position considering the specification of the holographic optical element designed digitally. We successfully demonstrated a reconstruction of the color video in question, composed of three-dimensional images through the holographic optical element.

Simple and effective calculation method for computer-generated hologram based on non-uniform sampling using look-up-table

Heavy computational complexity and imprecise reconstruction of objects are crucial problems in computer-generated holograms. In this paper, we propose a non-uniform sampling based on novel compressed look up table method to generate holograms. The method consists of two steps: in the first step, the non-uniform basic modulation factors are precalculated and stored in look-up-table. Secondly, fringe patterns for other points are obtained by simply shifting and multiplying the pre-calculated non-uniform basic modulation factors, and the final computer-generated hologram is obtained by adding them all together. The proposed method eliminates the redundant information properly and modulates the reconstructed images precisely. Numerical simulation results show proposed method reduces the memory usage, speeds up computation time and the quality of reconstructed images do not degrade evidently compared with uniform sampling method. Optical experiments results are in good agreement with numerical simulation results. The proposed method is simple, effective and could be applied in the holographic field in the future.

Reconstructing 3D point clouds in real time with look-up tables for structured light scanning along both horizontal and vertical directions

By scanning static, not moving, objects along both the horizontal and vertical axes instead of one, structured light illumination achieves more accurate and robust 3D surface reconstructions but with greater latency on computing 3D point clouds. If scanning is performed along only one axis, it has been reported that look-up tables, manually derived from the calibration matrices of a camera and a projector, can significantly help to speed up computation; however, it has been nearly impossible to manually derive similar look-up tables for phases scanned along two axes. In this Letter, we bridge this divide by introducing the constraint of epipolar geometry to automatically compute look-up tables and thus, significantly speed up computing 3D point clouds with only basic arithmetic operations rather than time-consuming matrix computations. Experimental results show that the proposed method, using only single-thread CPU computing, reduces process latency by an order of magnitude.

Fast calculation method for viewpoint movements in computer-generated holograms using a Fourier transform optical system

Augmented reality (AR) using a holographic head-mounted display has been attracting a great deal of attention. In the AR system, computer-generated holograms (CGHs) are calculated and displayed on an electronic display. However, the time required for making CGHs is very long. Here, we propose a fast calculation method for arbitrary viewpoint movements in holographic AR systems. The calculation uses a Fourier transform optical system to enlarge the visual field of electroholography. In experiments, the generation time of the proposed method was approximately twice as fast as that of the conventional method. Furthermore, the quality of the CGHs generated by our method was sufficiently high.

Optimized random phase tiles for non-iterative hologram generation

In this work, we introduce a technique for fast, high-quality, non-iterative generation of phase-only holograms from both 2D and 3D scenes. In this technique, we generate an optimized random phase tile which behaves like a small diffuser, spreading the amplitude of a section of the scene throughout the hologram plane. Each section of the scene is multiplied by this tile and then propagated to the hologram plane by means of the Fresnel transform. The contribution from each tile is added, resulting in a phase-only hologram of the scene. The optimized random phase tiles can be generated for any distance between the hologram plane and the object using an iterative Fresnel algorithm. Afterwards, this tile can be used to generate holograms from any number of objects without the need for further iterative algorithms. These holograms present increased quality after reconstruction compared to similar non-iterative hologram generation techniques. Both numerical and optical experiments are carried out, demonstrating the effectiveness of our proposal.

Reducing the memory usage of computer-generated hologram calculation using accurate high-compressed look-up-table method in color 3D holographic display

In this paper, we propose an accurate high-compressed look-up-table method that uses less memory to generate the hologram. In precomputation, we separate the longitudinal modulation factors and only calculate the basic horizontal and vertical factors. Therefore, we obtain other horizontal and vertical modulation factors of object points by simply shifting the basic horizontal and vertical modulation factors while computing holograms. We perform numerical simulations and optical experiments to verify the proposed method. Numerical simulation results show that the proposed method has the least memory usage, the fastest computation time and no distortion. The optical experimental results are in accord with the numerical simulation results. The proposed method is simple and effective to calculate computer-generated holograms for color dynamic holographic display with high speed, less memory usage and high accuracy that could be applied in the holographic field in the future.

Direct calculation of computer-generated holograms in sparse bases

Computer-generated holography is computationally intensive, making it especially challenging for holographic displays where high-resolutions and video rates are needed. To this end, we propose a technique for directly calculating short-time Fourier transform coefficients without the need for a look-up table. Because point spread functions are sparse in this transform domain, only a small fraction of the coefficients need to be updated, enabling significant speed gains. Twenty-fold accelerations are reported over the reference implementation. This approach generalizes the notion of the phase-added stereogram, allowing for the calculatiion of an arbitrary number of Fourier coefficients per block, enabling high calculation speed with holograms of good visual quality, targeting minimal memory requirements.

Error diffusion method with optimized weighting coefficients for binary hologram generation

The error diffusion method can effectively reduce quality degradation by propagating thresholding errors to neighboring pixels in the conversion of a gray-scale hologram to a binary hologram. In previous works, the four weighting coefficients in error diffusion are mostly set as the Floyd-Steinberg coefficient, which was determined empirically and originally proposed for photograph processing. In this work, we point out that the Floyd-Steinberg coefficients can be suboptimal for hologram error diffusion binarization. Furthermore, the weighting coefficients are optimized for each different hologram adaptively. Compared with conventional coefficients, our optimized coefficients can better preserve the fidelity of a reconstructed image after a hologram is binarized.

Full-scale one-dimensional NLUT method for accelerated generation of holographic videos with the least memory capacity

A full-scale one-dimensional novel-look-up-table (1-D NLUT) method enabling faster generation of holographic videos with the minimum memory capacity is proposed. Only a pair of half-sized 1-D baseline and depth-compensating principal-fringe-patterns (PFPs) is pre-calculated and stored based on the concentric-symmetry property of the PFP, and from which a set of half-sized 1-D PFPs for all depth planes are generated based on its thin-lens property, which enables minimization of the required memory size down to a few KB regardless of the number of depth planes. Moreover, all those hologram calculations are fully one-dimensionally performed with a set of half-sized 1-D PFPs based on its shift invariance property, which also allows minimization of its overall hologram calculation time. From experiments with test videos, the proposed method has been found to have the shortest hologram calculation time even with the least memory in comparison with several modified versions of the conventional NLUT and LUT methods, which confirms its feasibility.

Progress in virtual reality and augmented reality based on holographic display

The past, present, and future industry prospects of virtual reality (VR) and augmented reality (AR) are presented. The future of VR/AR technology based on holographic display is predicted by analogy with the VR/AR based on binocular vision display and light field display. The investigations on holographic display that can be used in VR/AR are reviewed. The breakthroughs of holographic display are promising in VR/AR with high resolution. The challenges faced by VR/AR based on holographic display are analyzed.

Highly efficient calculation method for computer-generated holographic stereogram using a lookup table

A highly efficient calculation method to synthesize a computer-generated holographic stereogram using a lookup table (LUT) is proposed. The complete phase distribution (CPD) of a spherical wave that is larger than the hologram is precalculated and stored as a LUT. The wavefront converging to each viewpoint can be directly obtained by adding a specific part of the precalculated CPD to the parallax image, instead of computing the wavefronts pixel by pixel in the conventional method. The computation amount and calculation time are effectively reduced to one-third of the conventional method. The working memory size is reduced effectively using the symmetry of the phase distributions of different viewpoints. A simulation and an optical experiment are performed to verify the proposed method.

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.

Compression of Phase-Only Holograms with JPEG Standard and Deep Learning

It is a critical issue to reduce the enormous amount of data in the processing, storage and transmission of a hologram in digital format. In photograph compression, the JPEG standard is commonly supported by almost every system and device. It will be favorable if JPEG standard is applicable to hologram compression, with advantages of universal compatibility. However, the reconstructed image from a JPEG compressed hologram suffers from severe quality degradation since some high frequency features in the hologram will be lost during the compression process. In this work, we employ a deep convolutional neural network to reduce the artifacts in a JPEG compressed hologram. Simulation and experimental results reveal that our proposed “JPEG + deep learning” hologram compression scheme can achieve satisfactory reconstruction results for a computer-generated phase-only hologram after compression.

Accelerating computation of CGH using symmetric compressed look-up-table in color holographic display

The huge computational complexity is a challenge for computer-generated hologram (CGH) calculation in a holographic display. In this paper, we propose a symmetric compressed look-up-table algorithm to accelerate CGH computation based on the Fresnel diffraction theory and compressed look-up-table algorithm. In offline computation, the memory usage of horizontal and vertical modulation factors is reduced to the order of Kilobytes by using translational symmetric compression and wavelength separation. In online computation, we develop a one-time generation of color holograms method which is accelerated by matrix convolution operation. Numerical simulation results show at least 13 times faster than existing algorithms without sacrificing the computation precision. The optical experiments are performed to demonstrate its feasibility. It is believed that the proposed method is an effective algorithm to accelerate the computation of CGH in color holographic display.

Accelerated synthesis of wide-viewing angle polygon computer-generated holograms using the interocular affine similarity of three-dimensional scenes

The interocular affine similarity of three-dimensional scenes is investigated and a novel accelerated reconfiguration algorithm for intermediate-view polygon computer-generated holograms based on interocular affine similarity is proposed. We demonstrate by using the numerical simulations of full-color polygon computer-generation holograms that the proposed intermediate view reconfiguration algorithm is particularly useful for the computation of wide-viewing angle polygon computer-generated holograms.