There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Recently developed integral imaging techniques are reviewed. Integral imaging captures and reproduces the light rays from the object space, enabling the acquisition and the display of the three-dimensional information of the object in an efficient way. Continuous effort on integral imaging has been improving the performance of the capture and display process in various aspects, including distortion, resolution, viewing angle, and depth range. Digital data processing of the captured light rays can now visualize the three-dimensional structure of the object with a high degree of freedom and enhanced quality. This recent progress is of high interest for both industrial applications and academic research.

Recent progress in three-dimensional information processing based on integral imaging.

Several approaches for increasing the speed in computation of the digital holograms of three-dimensional objects have been presented with applications to real-time display of holographic images. Among them, a look-up table (LUT) approach, in which the precalculated principal fringe patterns for all possible image points of the object are provided, has gained a large speed increase in generation of computer-generated holograms. But the greatest drawback of this method is the enormous memory size of the LUT. A novel approach to dramatically reduce the size of the conventional LUT, still keeping its advantage of fast computational speed, is proposed, which is called here a novel LUT (N-LUT) method. A three-dimensional object can be treated as a set of image planes discretely sliced in the z direction, in which each image plane having a fixed depth is approximated as some collection of self-luminous object points of light. In the proposed method, only the fringe patterns of the center points on each image plane are precalculated, called principal fringe patterns (PFPs) and stored in the LUT. Then, the fringe patterns for other object points on each image plane can be obtained by simply shifting this precalculated PFP according to the displaced values from the center to those points and adding them together. Some experimental results reveal that the computational speed and the required memory size of the proposed approach are found to be 69.5 times faster than that of the ray-tracing method and 744 times smaller than that of the conventional LUT method, respectively.

Effective generation of digital holograms of three-dimensional objects using a novel look-up table method

True-3D imaging and display systems are based on physical duplication of light distribution. Holography is a true-3D technique. There are significant developments in electro-holographic displays in recent years. Liquid crystal, liquid crystal on silicon, optically addressed, mirror-based, holographic polymer-dispersed, and acousto-optic devices are used as holographic displays. There are complete electro-holographic display systems and some of them are already commercialized.

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State of the Art in Holographic Displays: A Survey

The invention provides an image display device that has an especially satisfactory display quality for animated images, and sufficiently suppresses the irregularities of display quality among pixels. The image display device includes a light emitting drive means that drives a light emitting means, based on an analog display signal inputted to the pixels, and a light emitting control switch for controlling a light-on or light-off of the light emitting means on one end of the light emitting drive means in each pixel.

Image Display Device

In this paper we propose a new approach for fast generation of computer-generated holograms (CGHs) of a 3D object by using the run-length encoding (RLE) and the novel look-up table (N-LUT) methods. With the RLE method, spatially redundant data of a 3D object are extracted and regrouped into the N-point redundancy map according to the number of the adjacent object points having the same 3D value. Based on this redundancy map, N-point principle fringe patterns (PFPs) are newly calculated by using the 1-point PFP of the N-LUT, and the CGH pattern for the 3D object is generated with these N-point PFPs. In this approach, object points to be involved in calculation of the CGH pattern can be dramatically reduced and, as a result, an increase of computational speed can be obtained. Some experiments with a test 3D object are carried out and the results are compared to those of the conventional methods.

Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods

We propose a novel approach to massively reduce the memory of the novel look-up table (N-LUT) for computer-generated holograms by employing one-dimensional (1-D) sub-principle fringe patterns (sub-PFPs). Two-dimensional (2-D) PFPs used in the conventional N-LUT method are decomposed into a pair of 1-D sub-PFPs through a trigonometric relation. Then, these 1-D sub-PFPs are pre-calculated and stored in the proposed method, which results in a remarkable reduction of the memory of the N-LUT. Experimental results reveal that the memory capacity of the LUT, N-LUT and proposed methods have been calculated to be 149.01 TB, 2.29 GB and 1.51 MB, respectively for the 3-D object having image points of 500 × 500 × 256, which means the memory of the proposed method could be reduced by 103 × 10(6) fold and 1.55 × 10(3) fold compared to those of the conventional LUT and N-LUT methods, respectively.

Effective memory reduction of the novel look-up table with one-dimensional sub-principle fringe patterns in computer-generated holograms

Even though there are many types of methods to generate CGH (computer-generated hologram) patterns of three-dimensional (3D) objects, most of them have been applied to still images but not to video images due to their computational complexity in applications of 3D video holograms. A new method for fast computation of CGH patterns for 3D video images is proposed by combined use of data compression and lookup table techniques. Temporally redundant data of the 3D video images are removed with the differential pulse code modulation (DPCM) algorithm, and then the CGH patterns for these compressed videos are generated with the novel lookup table (N-LUT) technique. To confirm the feasibility of the proposed method, some experiments with test 3D videos are carried out, and the results are comparatively discussed with the conventional methods in terms of the number of object points and computation time.

Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques

We have implemented experimental code to compute a compensated phase-added stereogram (CPAS), which was proposed in a previous paper, on a graphic processing unit (GPU). In this paper, we show an acceleration method for CPAS computation by means of the GPU and compare the computation time between CPU-based and GPU-based calculations, which are programmed in our laboratories. In addition, we demonstrate their reconstructed images. As a result, we could achieve a performance gain of a factor of over 33 compared with a CPU-based computing environment and digital holograms can be displayed at 30 frames per second with 15,000 points.

Seung-Cheol Kim

Papers

Effective generation of digital holograms of three-dimensional objects using a novel look-up table method

Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods

Effective memory reduction of the novel look-up table with one-dimensional sub-principle fringe patterns in computer-generated holograms

Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques

Acceleration method of computing a compensated phase-added stereogram on a graphic processing unit