Recurrence formulas for fast creation of synthetic three-dimensional holograms

Reducing the computational complexity of high-resolution hologram calculations using polynomial approximation

In this paper, we have proposed a hologram calculation method using polynomial approximations for reducing the computational complexity of point-cloud-based hologram calculations. The computational complexity of existing point-cloud-based hologram calculations is proportional to the product of the number of point light sources and hologram resolution, whereas that of the proposed method can be reduced to approximately proportional to the sum of the number of point light sources and hologram resolution by approximating the object wave with polynomials. The computation time and reconstructed image quality were compared with those of the existing methods. The proposed method was approximately 10 times faster than the conventional acceleration method, and did not produce significant errors when the object was far from the hologram.

Two-step acceleration calculation method to generate curved holograms using the intermediate plane in a three-dimensional holographic display

Nowadays, curved computer-generated holograms are widely applied to increase the field of view. However, heavy computational load restricts the development of curved computer-generated holograms. In this paper, we propose a two-step acceleration calculation method to generate curved holograms by using the intermediate plane, which is placed between the object and a curved computer-generated hologram. The first step is the calculation of the intermediate plane by an improved accurate highly compressed lookup-table method. In the second step, we execute diffraction calculation from the intermediate plane to obtain a curved computer-generated hologram. Numerical simulations and optical experiments are performed to demonstrate that the proposed method is an efficient method for reducing calculation time. Additionally, the increase of field of view using a curved hologram is also numerically demonstrated. It is expected that our method can be combined with a curved display screen to realize three-dimensional holographic displays in the future.

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.

Information retrieval using overlapping holograms with partial complementarity

An information retrieval technique from superimposed holograms representing 2D and 3D objects using complementary fringes is presented. By adding two different computer generated holograms with quasi-complementarity information is possible to retrieve information at a specific depth.

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.

Fast generation of full analytical polygon-based computer-generated holograms

A fast calculation method to obtain the full-analytical frequency spectrum of a spatial triangle based on the three-dimensional (3D) affine transformation is presented. Computer-generated holograms (CGHs) of an object can then be generated rapidly using the angular spectrum for propagation. The derivation process in the theory, which has more preciseness, indicates a difference from previous methods based on affine transformations ([Appl. Opt.47, 1567 (2008)Appl. Opt.52, A290 (2013)]). The proposed method to achieve 3D transformation from an arbitrary triangle to a primitive triangle includes two steps: 3D rotation and 2D affine transformation. The overall transform matrix is given by the product of a rotation matrix and a 2D affine matrix. A modified back-face culling is also introduced based on exterior normal for correct occlusion relation. Several complex 3D objects are implemented successfully using the proposed method in numerical simulations and optical experiments. The resulting computation time demonstrates that the efficiency of the proposed method is enhanced as compared to that of previous works.

Decomposition method for fast computation of gigapixel-sized Fresnel holograms on a graphics processing unit cluster

A parallel computation method for large-size Fresnel computer-generated hologram (CGH) is reported. The method was introduced by us in an earlier report as a technique for calculating Fourier CGH from 2D object data. In this paper we extend the method to compute Fresnel CGH from 3D object data. The scale of the computation problem is also expanded to 2 gigapixels, making it closer to real application requirements. The significant feature of the reported method is its ability to avoid communication overhead and thereby fully utilize the computing power of parallel devices. The method exhibits three layers of parallelism that favor small to large scale parallel computing machines. Simulation and optical experiments were conducted to demonstrate the workability and to evaluate the efficiency of the proposed technique. A two-times improvement in computation speed has been achieved compared to the conventional method, on a 16-node cluster (one GPU per node) utilizing only one layer of parallelism. A 20-times improvement in computation speed has been estimated utilizing two layers of parallelism on a very large-scale parallel machine with 16 nodes, where each node has 16 GPUs.

Ultrafast layer based computer-generated hologram calculation with sparse template holographic fringe pattern for 3-D object

In this paper, we propose a new ultrafast layer based CGH calculation that exploits the sparsity of hologram fringe pattern in 3-D object layer. Specifically, we devise a sparse template holographic fringe pattern. The holographic fringe pattern on a depth layer can be rapidly calculated by adding the sparse template holographic fringe patterns at each object point position. Since the size of sparse template holographic fringe pattern is much smaller than that of the CGH plane, the computational load can be significantly reduced. Experimental results show that the proposed method achieves 10-20 msec for 1024x1024 pixels providing visually plausible results.

Fast generation of computer-generated holograms using wavelet shrinkage

Computer-generated holograms (CGHs) are generated by superimposing complex amplitudes emitted from a number of object points. However, this superposition process remains very time-consuming even when using the latest computers. We propose a fast calculation algorithm for CGHs that uses a wavelet shrinkage method, eliminating small wavelet coefficient values to express approximated complex amplitudes using only a few representative wavelet coefficients.

Acceleration of the calculation speed of computer-generated holograms using the sparsity of the holographic fringe pattern for a 3D object

In computer-generated hologram (CGH) calculations, a diffraction pattern needs to be calculated from all points of a 3-D object, which requires a heavy computational cost. In this paper, we propose a novel fast computer-generated hologram calculation method using sparse fast Fourier transform. The proposed method consists of two steps. First, the sparse dominant signals of CGHs are measured by calculating a wavefront on a virtual plane between the object and the CGH plane. Second, the wavefront on CGH plane is calculated by using the measured sparsity with sparse Fresnel diffraction. Experimental results proved that the proposed method is much faster than existing works while it preserving the visual quality.

Hybrid approach for fast occlusion processing in computer-generated hologram calculation

A hybrid approach for fast occlusion processing in computer-generated hologram calculation is studied in this paper. The proposed method is based on the combination of two commonly used approaches that complement one another: the point-source and wave-field approaches. By using these two approaches together, the proposed method thus takes advantage of both of them. In this method, the 3D scene is first sliced into several depth layers parallel to the hologram plane. Light scattered by the scene is then propagated and shielded from one layer to another using either a point-source or a wave-field approach according to a threshold criterion on the number of points within the layer. Finally, the hologram is obtained by computing the propagation of light from the nearest layer to the hologram plane. Experimental results reveal that the proposed method does not produce any visible artifact and outperforms both the point-source and wave-field approaches.

Three-directional motion-compensation mask-based novel look-up table on graphics processing units for video-rate generation of digital holographic videos of three-dimensional scenes

A three-directional motion-compensation mask-based novel look-up table method is proposed and implemented on graphics processing units (GPUs) for video-rate generation of digital holographic videos of three-dimensional (3D) scenes. Since the proposed method is designed to be well matched with the software and memory structures of GPUs, the number of compute-unified-device-architecture kernel function calls can be significantly reduced. This results in a great increase of the computational speed of the proposed method, allowing video-rate generation of the computer-generated hologram (CGH) patterns of 3D scenes. Experimental results reveal that the proposed method can generate 39.8 frames of Fresnel CGH patterns with 1920×1080 pixels per second for the test 3D video scenario with 12,088 object points on dual GPU boards of NVIDIA GTX TITANs, and they confirm the feasibility of the proposed method in the practical application fields of electroholographic 3D displays.

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.

Accelerated one-step generation of full-color holographic videos using a color-tunable novel-look-up-table method for holographic three-dimensional television broadcasting

A color-tunable novel-look-up-table (CT-NLUT) for fast one-step calculation of full-color computer-generated holograms is proposed. The proposed method is composed of four principal fringe patterns (PFPs) such as a baseline, a depth-compensating and two color-compensating PFPs. CGH patterns for one color are calculated by combined use of baseline-PFP and depth-compensating-PFP and from them, those for two other colors are generated by being multiplied by the corresponding color-compensating-PFPs. color-compensating-PFPs compensate for differences in the wavelength between two colors based on their unique achromatic thin-lens properties, enabling transformation of one-color CGH pattern into those for other colors. This color-conversion property of the proposed method enables simultaneous generation of full color-CGH patterns, resulting in a significant reduction of the full color-CGH calculation time. Experimental results with test scenario show that the full color-CGH calculation time of the proposed CT-NLUT has been reduced by 45.10%, compared to the conventional NLUT. It has been further reduced by 96.01% when a data compression algorithm, called temporal redundancy-based NLUT, was used together, which means 25-fold reduction of its full color-CGH calculation time. Successful computational and optical reconstructions of full color-CGH patterns confirm the feasibility of the proposed method.

Object tracking mask-based NLUT on GPUs for real-time generation of holographic videos of three-dimensional scenes

A new object tracking mask-based novel-look-up-table (OTM-NLUT) method is proposed and implemented on graphics-processing-units (GPUs) for real-time generation of holographic videos of three-dimensional (3-D) scenes. Since the proposed method is designed to be matched with software and memory structures of the GPU, the number of compute-unified-device-architecture (CUDA) kernel function calls and the computer-generated hologram (CGH) buffer size of the proposed method have been significantly reduced. It therefore results in a great increase of the computational speed of the proposed method and enables real-time generation of CGH patterns of 3-D scenes. Experimental results show that the proposed method can generate 31.1 frames of Fresnel CGH patterns with 1,920 × 1,080 pixels per second, on average, for three test 3-D video scenarios with 12,666 object points on three GPU boards of NVIDIA GTX TITAN, and confirm the feasibility of the proposed method in the practical application of electro-holographic 3-D displays.

Fast one-step calculation of holographic videos of three-dimensional scenes by combined use of baseline and depth-compensating principal fringe patterns

As a new approach for rapid generation of holographic videos, a so-called compressed novel-look-up-table(C-NLUT), which is composed of only two principal fringe patterns (PFPs) of baseline and depth-compensating PFPs (B-PFP, DC-PFP), is proposed. Here, the hologram pattern for a 3-D video frame are generated by calculating the fringe patterns for all depth layers only by using the B-PFP, and then transforming them into those for their depth layers by being multiplied with corresponding DC-PFPs. With this one-step calculation process, the computational speed (CS) of the proposed method can be greatly enhanced. Experimental results show that the CS of the proposed method has been improved by 30.2% on the average compared to that of the conventional method. Furthermore, the average calculation time of a new hybrid MC/C-NLUT method, in which both of motion-compensation (MC) and one-step calculation schemes are employed, has been reduced by 99.7%, 65.4%, 60.2% and 30.2%, respectively compared to each of the conventional ray-tracing, LUT, NLUT, and MC-NLUT methods. In addition, the memory size of the proposed method has been also reduced by 82 × 10(6)-fold and 128-fold compared to those of the conventional LUT and NLUT methods, respectively.

Three-directional motion compensation-based novel-look-up-table for video hologram generation of three-dimensional objects freely maneuvering in space

A new three-directional motion compensation-based novel-look-up-table (3DMC-NLUT) based on its shift-invariance and thin-lens properties, is proposed for video hologram generation of three-dimensional (3-D) objects moving with large depth variations in space. The input 3-D video frames are grouped into a set of eight in sequence, where the first and remaining seven frames in each set become the reference frame (RF) and general frames (GFs), respectively. Hence, each 3-D video frame is segmented into a set of depth-sliced object images (DOIs). Then x, y, and z-directional motion vectors are estimated from blocks and DOIs between the RF and each of the GFs, respectively. With these motion vectors, object motions in space are compensated. Then, only the difference images between the 3-directionally motion-compensated RF and each of the GFs are applied to the NLUT for hologram calculation. Experimental results reveal that the average number of calculated object points and the average calculation time of the proposed method have been reduced compared to those of the conventional NLUT, TR-NLUT and MPEG-NLUT by 38.14%, 69.48%, and 67.41% and 35.30%, 66.39%, and 64.46%, respectively.

Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams

We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a two-dimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.

Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display

A fast algorithm with low memory usage is proposed to generate the hologram for full-color 3D display based on a compressed look-up table (C-LUT). The C-LUT is described and built to reduce the memory usage and speed up the calculation of the computer-generated hologram (CGH). Numerical simulations and optical experiments are performed to confirm this method, and several other algorithms are compared. The results show that the memory usage of the C-LUT is kept low when number of depth layers of the 3D object is increased, and the time for building the C-LUT is independent of the number of depth layers of the 3D object. The algorithm based on C-LUT is an efficient method for saving memory usage and calculation time, and it is expected that it could be used for realizing real-time and full-color 3D holographic display in the future.

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.

Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition

We introduce a local signal decomposition method for the analysis of three-dimensional (3D) diffraction fields involving curved surfaces. We decompose a given field on a two-dimensional curved surface into a sum of properly shifted and modulated Gaussian-shaped elementary signals. Then we write the 3D diffraction field as a sum of Gaussian beams, each of which corresponds to a modulated Gaussian window function on the curved surface. The Gaussian beams are propagated according to a derived approximate expression that is based on the Rayleigh-Sommerfeld diffraction model. We assume that the given curved surface is smooth enough that the Gaussian window functions on it can be treated as written on planar patches. For the surfaces that satisfy this assumption, the simulation results show that the proposed method produces quite accurate 3D field solutions.

Rendering of specular surfaces in polygon-based computer-generated holograms

A technique is presented for realistic rendering in polygon-based computer-generated holograms (CGHs). In this technique, the spatial spectrum of the reflected light is modified to imitate specular reflection. The spectral envelopes of the reflected light are fitted to a spectral shape based on the Phong reflection model used in computer graphics. The technique features fast computation of the field of objects, composed of many specular polygons, and is applicable to creating high-definition CGHs with several billions of pixels. An actual high-definition CGH is created using the proposed technique and is demonstrated for verification of the optical reconstruction of specular surfaces.

Method to calculate the far field of three-dimensional objects for computer-generated holography

Here, a new method for calculating the computer-generated holograms of three-dimensional (3D) objects is presented along with a review of current techniques. The method, the planar layers method (PLM), is established on the idea of representing 3D objects in discrete planar layers perpendicular to the observation plane, then calculating the total far field pattern by summing up the far field patterns of each layer. Simulation results, computational complexity, and error comparisons reveal that this new method can be used to calculate far field patterns--hence, the holograms--of computer-synthesized objects very efficiently.

Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method

A large-scale full-parallax computer-generated hologram (CGH) with four billion (2(16) x 2(16)) pixels is created to reconstruct a fine true 3D image of a scene, with occlusions. The polygon-based method numerically generates the object field of a surface object, whose shape is provided by a set of vertex data of polygonal facets, while the silhouette method makes it possible to reconstruct the occluded scene. A novel technique using the segmented frame buffer is presented for handling and propagating large wave fields even in the case where the whole wave field cannot be stored in memory. We demonstrate that the full-parallax CGH, calculated by the proposed method and fabricated by a laser lithography system, reconstructs a fine 3D image accompanied by a strong sensation of depth.

One-unit system to reconstruct a 3-D movie at a video-rate via electroholography

We have developed a one-unit system, including creating and displaying a hologram for real-time reproduction of a three-dimensional image via electroholography. We have constructed this one-unit system by connecting a special-purpose computer for holography and a special display board with a reflective liquid crystal display as a spatial light modulator. Using this one-unit system, we succeeded in reproducing a three-dimensional image composed of 10,000 points at a speed of 30 frames per second, which is the video rate in NTSC format. In addition, we were able to control a three-dimensional image in real-time using our system.

Simplified electroholographic color reconstruction system using graphics processing unit and liquid crystal display projector

We have constructed a simple color electroholography system that has excellent cost performance. It uses a graphics processing unit (GPU) and a liquid crystal display (LCD) projector. The structure of the GPU is suitable for calculating computer-generated holograms (CGHs). The calculation speed of the GPU is approximately 1,500 times faster than that of a central processing unit. The LCD projector is an inexpensive, high-performance device for displaying CGHs. It has high-definition LCD panels for red, green and blue. Thus, it can be easily used for color electroholography. For a three-dimensional object consisting of 1,000 points, our system succeeded in real-time color holographic reconstruction at rate of 30 frames per second.

Hologram synthesis for photorealistic reconstruction

Computation of diffraction patterns, and thus holograms, of scenes with photorealistic properties is a highly complicated and demanding process. An algorithm, based primarily on computer graphics methods, for computing full-parallax diffraction patterns of complicated surfaces with realistic texture and reflectivity properties is proposed and tested. The algorithm is implemented on single-CPU, multiple-CPU and GPU platforms. An alternative algorithm, which implements reduced occlusion diffraction patterns for much faster but somewhat lower quality results, is also developed and tested. The algorithms allow GPU-aided calculations and easy parallelization. Both numerical and optical reconstructions are conducted. The results indicate that the presented algorithms compute diffraction patterns that provide successful photorealistic reconstructions; the computation times are acceptable especially on the GPU implementations.

A framework for holographic scene representation and image synthesis

We present a framework for the holographic representation and display of graphics objects. As opposed to traditional graphics representations, our approach reconstructs the light wave reflected or emitted by the original object directly from the underlying digital hologram. Our novel holographic graphics pipeline consists of several stages including the digital recording of a full-parallax hologram, the reconstruction and propagation of its wavefront, and rendering of the final image onto conventional, framebuffer-based displays. The required view-dependent depth image is computed from the phase information inherently represented in the complex-valued wavefront. Our model also comprises a correct physical modeling of the camera taking into account optical elements, such as lens and aperture. It thus allows for a variety of effects including depth of field, diffraction, interference, and features built-in anti-aliasing. A central feature of our framework is its seamless integration into conventional rendering and display technology which enables us to elegantly combine traditional 3D object or scene representations with holograms. The presented work includes the theoretical foundations and allows for high quality rendering of objects consisting of large numbers of elementary waves while keeping the hologram at a reasonable size.

Computer generated holography using a graphics processing unit

We have applied the graphics processing unit (GPU) to computer generated holograms (CGH) to overcome the high computational cost of CGH and have compared the speed of a GPU implementation to a standard CPU implementation. The calculation speed of a GPU (GeForce 6600, nVIDIA) was found to be about 47 times faster than that of a personal computer with a Pentium 4 processor. Our system can realize real-time reconstruction of a 64-point 3-D object at video rate using a liquid-crystal display of resolution 800x600.

Rapid hologram updates for real-time volumetric information displays

We have demonstrated that holograms incorporating changes in three-dimensional (3D) scenes can be recalculated in real time to present dynamic updates on information displays. This approach displays 3D information in a compatible format for fast and reliable interpretation of changes in the 3D scenes. The rapid-update algorithm has been demonstrated by real-time computation and transcription of the holograms to our digital micromirror device hologram projection system for visual validation of the reconstruction. The reported algorithm enables full parallax 1024 x 768 pixel holograms of 3D scenes to be updated at a rate of 0.8 s with a 1.8 GHz personal computer. Volumetric information displays that can enhance reliable data assimilation and decrease reaction times for applications such as air-traffic control, cockpit heads-up displays, mission crew stations, and undersea navigation can benefit from this research.

Computer-generated holograms for three-dimensional surface objects with shade and texture

Digitally synthetic holograms of surface model objects are investigated for reconstructing three-dimensional objects with shade and texture. The objects in the proposed techniques are composed of planar surfaces, and a property function defined for each surface provides shape and texture. The field emitted from each surface is independently calculated by a method based on rotational transformation of the property function by use of a fast Fourier transform (FFT) and totaled on the hologram. This technique has led to a reduction in computational cost: FFT operation is required only once for calculating a surface. In addition, another technique based on a theoretical model of the brightness of the reconstructed surfaces enables us to shade the surface of a reconstructed object as designed. Optical reconstructions of holograms synthesized by the proposed techniques are demonstrated.

Electroholographic display unit for three-dimensional display by use of special-purpose computational chip for holography and reflective LCD panel

We developed an electroholography unit, which consists of a special-purpose computational chip for holography and a reflective liquid-crystal display (LCD) panel, for a three-dimensional (3D) display. The special-purpose chip can compute a computer-generated hologram of 800x600 grids in size from a 3D object consisting of approximately 400 points in approximately 0.15 seconds. The pixel pitch and resolution of the LCD panel are 12 mum and 800x600 grids, respectively. We implemented the special purpose chip and LCD panel on a printed circuit board of approximately 28cmx13cm in size. After the calculation, the computer-generated hologram produced by the special-purpose chip is displayed on the LCD panel. When we illuminate a reference light to the LCD panel, we can observe a 3D animation of approximately 3cmx3cmx3cm in size. In the present paper, we report the electroholographic display unit together with a simple 3D display system.

Special-purpose computer HORN-5 for a real-time electroholography

In electroholography, a real-time reconstruction is one of the grand challenges. To realize it, we developed a parallelized high performance computing board for computer-generated hologram, named HORN-5 board, where four large-scale field programmable gate array chips were mounted. The number of circuits for hologram calculation implemented to the board was 1,408. The board calculated a hologram at higher speed by 360 times than a personal computer with Pentium4 processor. A personal computer connected with four HORN-5 boards calculated a hologram of 1,408 x 1,050 made from a three-dimensional object consisting of 10,000 points at 0.0023 s. In other words, beyond at video rate (30 frames / s), it realized a real-time reconstruction.

One-unit system for electroholography by use of a special-purpose computational chip with a high-resolution liquid-crystal display toward a three-dimensional television

We developed a one-unit system for electroholography, which consists of a special-purpose computational chip and a high-resolution, reflective mode, liquid-crystal display panel as a spatial light modulator. We implemented them on one board whose size is approximately 20 cm x 20 cm. The chip makes a computer-generated hologram whose size is 800 x600 at nearly real time (~0.5 s) for an object consisting of 1000 points. The pixel pitch of the display panel is 12 microm, and the resolution is 800 x 600. It reconstructs a three-dimensional motion image whose size is approximately 3 cm x 3 cm x 3 cm. The system can be readily scaled up, since the units consisting of the chip and the display are easily set in parallel.

Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves

A novel method for simulating field propagation is presented. The method, based on the angular spectrum of plane waves and coordinate rotation in the Fourier domain, removes geometric limitations posed by conventional propagation calculation and enables us to calculate complex amplitudes of diffracted waves on a plane not parallel to the aperture. This method can be implemented by using the fast Fourier transformation twice and a spectrum interpolation. It features computation time that is comparable with that of standard calculation methods for diffraction or propagation between parallel planes. To demonstrate the method, numerical results as well as a general formulation are reported for a single-axis rotation.