Computer-generated Hologram Calculation Research Articles

CGH calculation algorithm for expressing reflection on a curved mirror surface

Rendering techniques are important in computer-generated holograms (CGHs) for expressing various types of holo-realistic 3D images. Rendering techniques such as hidden surface removal and reflection by a planar mirror have been proposed thus far, but reflection on a curved mirror surface has yet to be achieved. In this study, we propose a calculation algorithm that can express the reflection of the surrounding environment on a mirror surface defined as a Bézier surface. The results of optical experiments demonstrate that the proposed algorithm enables reflection on such a mirror surface and that the calculation can be accelerated by using a graphics processing unit (GPU).

Rapid calculation of computer-generated holograms for line-drawn 3D objects with varying thicknesses

Accelerating the calculation of computer-generated holograms (CGHs) is an important requirement for three-dimensional (3D) electro-holography display systems. Among the several sophisticated algorithms for CGH acceleration, the CG-line method for projecting 3D wire-frame objects is highly promising due to its high acceleration capability. However, conventional algorithms cannot account for line thickness, and only lines with a constant thickness corresponding to the pixel pitch of the spatial light modulator can be drawn. This restricts the expressiveness and visibility of 3D images, particularly for high-resolution holograms. Therefore, we propose a method for widening the line thickness of the CG-line method. We successfully generated a 3D object comprising bold lines of different thicknesses without sacrificing speed.

Calculation of Computer-Generated Hologram Over 100K Resolution Range for Realistic 3D Meta-Space Reproduction

Calculation of Computer-Generated Hologram Over 100K Resolution Range for Realistic 3D Meta-Space Reproduction

Unifying fast computer-generated hologram calculation and prepress for new and existing production techniques.

Directed by successfully manufacturing the computer-generated hologram (CGH) using the computer-to-film (CtF) process, we present, to the best of our knowledge, a new method for low-cost and fast hologram manufacturing. This new method allows for advances in the CtF process and manufacturing using new techniques in hologram production. These techniques include computer-to-plate, offset printing, and surface engraving utilizing the same CGH calculations and prepress. With an advantage in cost and the possibility to be mass manufactured, the aforementioned techniques combined with the presented method have a solid foundation to be implemented as security elements.

Automatic generation of a holographically shaped beam in an actual optical system for use in material laser processing.

In-system optimization involves designing a computer-generated hologram (CGH) in an actual optical system. An important advantage of this approach is automatic generation of a target shaped beam with compensation for imperfections in the actual optical system that would degrade the reconstruction performance. We developed a novel in-system optimization method for beam shaping based on our previous research where it had been applied only to generate parallel focused beams. The key point in the application to beam shaping is to accurately express the conditions and coordinates of the actual optical system in the CGH calculation.

A novel feed-forward neural network-based method for fast hologram generation

The enormous computing time is a challenge for computer-generated hologram (CGH) calculation in a holographic display. A learning-based method, hologram generation network (HGN), is proposed to accelerate CGH calculation. The method is a unique combination of point-source model and recent deep learning technique, showing how to obtain high-quality CGH quickly. HGN is a feed-forward neural network synthesized from different function blocks. The input of the network is a displacement tensor consisting of point clouds and hologram plane coordinates. The output is a holographic matrix whose column vector represents the coordinates of a single point hologram. The RBF network is then trained and tested by the numerical samples in the bounded field, thus the reconstruction quality of the CGH can be guaranteed strictly. Numerical simulation results show that HGN runs faster than the traditional method with high reconstruction accuracy. The optical experiments are performed to demonstrate its feasibility.

Accelerating a spatially varying aberration correction of holographic displays with low-rank approximation.

Correction of spatially varying aberrations in holographic displays often requires intractable computational loads. In this Letter, we introduce a low-rank approximation method that decomposes sub-holograms into a small number of modes, thereby reformulating the computer-generated hologram calculation into a summation of a few convolutions. The low-rank approximation is carried out with two different algorithms: the Karhunen-Loeve transform as the optimum solution with respect to the mean-squared error criterion and a novel, to the best of our knowledge, optimization method to provide uniform image quality over the entire field of view. The proposed method is two orders of magnitude faster than the conventional point-wise integration method in our experimental setup, with comparable image quality.

Diffraction Efficiency of MEMS Phase Light Modulator, TI-PLM, for Quasi-Continuous and Multi-Point Beam Steering.

The recent development of the Micro Electromechanical System (MEMS) Phase Light Modulator (PLM) enables fast laser beam steering for lidar applications by displaying a Computer-Generated Hologram (CGH) without employing an iterative CGH calculation algorithm. We discuss the application of MEMS PLM (Texas Instruments PLM) for quasi-continuous laser beam steering by deterministically calculated CGHs. The effect on the diffraction efficiency of PLM non-equally spaced phase levels was quantified. We also address the CGH calculation algorithm and an experimental demonstration that steered and scanned the beam into multiple regions of interest points, enabling beam steering for lidar without sequential raster scanning.

Autotuning GPU code for acceleration of CGH calculation

Computer-generated hologram (CGH) has a problem in that the calculation time is huge, we use a graphics processing unit (GPU) to enable fast calculation for CGH. Optimization of GPU calculation is studied to bring out the best performance of the GPU. We propose an autotuning method for GPU code that can be applied when the scene or calculation environment changes in CGH for practical use. We created a system that finds the optimal parameters by presenting three parameters for tuning in CGH. We applied autotuning to multiple objects and different GPUs and found optimal parameters for each. In addition, it was confirmed that the calculation time was 1.1 to 1.7 times faster by the autotuning.

Occlusion Culling for Wide-Angle Computer-Generated Holograms Using Phase Added Stereogram Technique

A computer-generated hologram (CGH) allows synthetizing view of 3D scene of real or virtual objects. Additionally, CGH with wide-angle view offers the possibility of having a 3D experience for large objects. An important feature to consider in the calculation of CGHs is occlusion between surfaces because it provides correct perception of encoded 3D scenes. Although there is a vast family of occlusion culling algorithms, none of these, at the best of our knowledge, consider occlusion when calculating CGHs with wide-angle view. For that reason, in this work we propose an occlusion culling algorithm for wide-angle CGHs that uses the Fourier-type phase added stereogram (PAS). It is shown that segmentation properties of the PAS can be used for setting efficient conditions for occlusion culling of hidden areas. The method is efficient because it enables processing of dense cloud of points. The investigated case has 24 million of point sources. Moreover, quality of the occluded wide-angle CGHs is tested by two propagation methods. The first propagation technique quantifies quality of point reproduction of calculated CGH, while the second method enables the quality assessment of the occlusion culling operation over an object of complex shape. Finally, the applicability of proposed occlusion PAS algorithm is tested by synthetizing wide-angle CGHs that are numerically and optically reconstructed.

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.

Diffractive distortion of a pixelated computer-generated hologram with oblique illumination.

Computer-generated holograms (CGHs) have their phase and/or amplitude modulation pattern calculated rather than recorded as for traditional holograms. In practice, the CGH devices are normally pixelated, no matter if they are passive or active ones. In many cases, the reconstruction light illuminates on the CGH devices obliquely, and the pattern generated on the target plane will be distorted from the originally desired one, even if the modulation on the CGH devices has been calibrated for the corresponding illumination angle in CGH calculation and optimization. The distortion is purely related to the diffraction behavior resulting from the geometry of the pixel on the CGH, and therefore diffractive distortion has been coined for this specific phenomenon. In this paper, quantitative analysis of diffractive distortion and a corresponding scheme for correction have been given based on scalar diffraction theory. The proposed concept is that the distortion of the reconstructed image is proportional to the distortion of the signal window. An experiment has been conducted with a phase-type liquid crystal on silicon spatial light modulator (SLM). Both the distortion analysis and the correction scheme have been verified quantitatively for various illumination angles and the direction of the reconstruction light.

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.

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.

Rapid tilted-plane Gerchberg-Saxton algorithm for holographic optical tweezers.

Benefitting from the development of commercial spatial light modulator (SLM), holographic optical tweezers (HOT) have emerged as a powerful tool for life science, material science and particle physics. The calculation of computer-generated holograms (CGH) for generating multi-focus arrays plays a key role in HOT for trapping of a bunch of particles in parallel. To realize dynamic 3D manipulation, we propose a new tilted-plane GS algorithm for fast generation of multiple foci. The multi-focal spots with a uniformity of 99% can be generated in a tilted plane. The computation time for a CGH with 512×512 pixels is less than 0.1 second. We demonstrated the power of the algorithm by simultaneously trapping and rotating silica beads with a 7×7 spots array in three dimensions. The presented algorithm is expected as a powerful kernel of HOT.

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.

Real-time spatiotemporal division multiplexing electroholography for 1,200,000 object points using multiple-graphics processing unit cluster

Computationally, the calculation of computer-generated holograms is extremely expensive, and the image quality deteriorates when reconstructing three-dimensional (3D) holographic video from a point-cloud model comprising a huge number of object points. To solve these problems, we implement herein a spatiotemporal division multiplexing method on a cluster system with 13 GPUs connected by a gigabit Ethernet network. A performance evaluation indicates that the proposed method can realize a real-time holographic video of a 3D object comprising ∼1,200,000 object points. These results demonstrate a clear 3D holographic video at 32.7 frames per second reconstructed from a 3D object comprising 1,064,462 object points.

Real-time color holographic video reconstruction using multiple-graphics processing unit cluster acceleration and three spatial light modulators

We demonstrate real-time three-dimensional (3D) color video using a color electroholographic system with a cluster of multiple-graphics processing units (multi-GPU) and three spatial light modulators (SLMs) corresponding respectively to red, green, and blue (RGB)-colored reconstructing lights. The multi-GPU cluster has a computer-generated hologram (CGH) display node containing a GPU, for displaying calculated CGHs on SLMs, and four CGH calculation nodes using 12 GPUs. The GPUs in the CGH calculation node generate CGHs corresponding to RGB reconstructing lights in a 3D color video using pipeline processing. Real-time color electroholography was realized for a 3D color object comprising approximately 21,000 points per color.

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.