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Incoherent digital holography (IDH) is a technique that enables single-shot three-dimensional (3D) imaging by recording holograms with incoherent light, such as sunlight and LEDs. IDH is expected to be a next-generation 3D measurement technique, but there are two challenges: speeding up both denoising required for IDH due to insufficient light and the diffraction calculations required to obtain reconstructed images. We propose a real-time IDH system in which single-exposure phase-shifting digital holography, which can record multiple phase-shifted holograms in a single exposure, is combined with an embedded graphic processing unit (GPU). The proposed system enables real-time color imaging of the real world from incoherent holograms with $2448 \times 2048$ pixels while reducing noise at 21.2 frames per second. The effect of the denoising was evaluated by speckle contrast, showing that noises were well reduced. Compared to five existing studies using field programable gate arrays and GPUs, the proposed system is capable of computing large hologram reproduction at high speed. The proposed system is a prototype for future incoherent holographic cameras.

Incoherent digital holography is a three-dimensional (3D) imaging technique that uses a natural light source. Through computer-based diffraction calculations, 3D information can be reconstructed from self-interferometer-captured holograms. As practical applications require a computer capable of high-speed diffraction calculations, an investigation was conducted into a special-purpose computer that uses a field-programmable gate array (FPGA). This approach had not been used for incoherent digital holography. In this study, the computational performance of a proposed monochromatic diffraction circuit was improved. By using direct memory access transfer, the data transfer time bottleneck, which is a problem in conventional circuits, was eliminated. The calculation was also parallelized, and the processing speed was 150 times faster than that of conventional circuits. In addition, a special-purpose computer for 3D color imaging was developed by implementing the proposed circuits for the three wavelengths on a single FPGA board. As a result of the verification, a speedup of approximately nine times over a 10-core CPU was achieved. The results of this research strongly promote the realization of a holographic portable camera with real-time 3D color imaging capability.

Accelerating the calculation of computer-generated holograms (CGHs) is an urgent requirement for realizing practical electro-holography for three-dimensional (3D) displays. Although many algorithms have been developed for fast CGH calculations, sufficient acceleration of the CGH calculations is yet to be achieved. Simplifying CGH calculations using the redundancy of a hologram while recording a 3D image is a promising way for CGH acceleration. That is, the feature that a hologram can reproduce the 3D image almost correctly even if it was recorded with deviations originating from the approximation, etc., can be used to perform the CGH calculations rapidly. Therefore, this study proposes an approximation method for trigonometric functions, which have a heavy computational load and are heavily used in the composition process of the wavefronts emitted from a virtual 3D object such as point-light sources. The proposed method substitutes sin or cos functions with tiny logic operations that are expected to have lower computational loads than the normal functions for fixed or floating precision numbers. Numerical and optical experiments showed that the proposed method can calculate CGH 2.20 times faster on a central processing unit (CPU) and 8.43 times faster on a graphics processing unit (GPU) than the normal implementation, while maintaining sufficient image quality. The proposed method is not only effective in CPU and GPU implementations but also is expected to make a significant contribution to future circuit implementations for CGH-specific computers.

Holographic memory offers high-capacity optical storage with rapid data readout and long-term durability. Recently, read data pages have been classified using digital deep neural networks (DNNs). This approach is highly accurate, but the prediction time hinders the data readout throughput. This study presents a diffractive DNN (D2NN)-based classifier for holographic memory. D2NNs have so far attracted a great deal of attention for object identification and image transformation at the speed of light. A D2NN, consisting of trainable diffractive layers and devoid of electronic devices, facilitates high-speed data readout. Furthermore, we numerically investigated the classification performance of a D2NN-based classifier. The classification accuracy of the D2NN was 99.7% on 4-bit symbols, exceeding that of the hard decision method.

Phase unwrapping is a technique used to recover the original phase from the wrapped phase in the range (−π,π]. Various methods have been proposed for phase unwrapping. In particular, methods using convolutional neural networks (CNNs) have been extensively researched because of their high robustness against noise and fast inference speed. However, conventional CNN-based methods discard the local position information and relationships between pixels in the convolution process, resulting in poor phase-unwrapping performance. To obtain better phase unwrapping results, we propose a module that combines a global convolution network, which applies convolutional layers with a kernel size equivalent to that of the feature maps, and CoordConv, which acquires the positional relationships between pixels. We validated the performance of the proposed method by comparing it with a quality-guided path algorithm and deep learning-based phase unwrapping methods and found that the proposed method is highly robust against noise.

Abstract Unlike conventional imaging, the single-pixel imaging technique uses a single-element detector, which enables high sensitivity, broad wavelength, and noise robustness imaging. However, it has several challenges, particularly requiring extensive computations for image reconstruction with high image quality. Therefore, high-performance computers are required for real-time reconstruction with higher image quality. In this study, we developed a compact dedicated computer for single-pixel imaging using a system on a chip field-programmable gate array (FPGA), which enables real-time reconstruction at 40 frames per second with an image size of 128 × 128 pixels. An FPGA circuit was implemented with the proposed reconstruction algorithm to obtain higher image quality by introducing encoding mask pattern optimization. The dedicated computer can accelerate the reconstruction 10 times faster than a recent CPU. Because it is very compact compared with typical computers, it can expand the application of single-pixel imaging to the Internet of Things and outdoor applications.

Holographic displays have the promise to be the ultimate 3D display technology, able to account for all visual cues. Recent advances in photonics and electronics gave rise to high-resolution holographic display prototypes, indicating that they may become widely available in the near future. One major challenge in driving those display systems is computational: computer generated holography (CGH) consists of numerically simulating diffraction, which is very computationally intensive. Our goal in this paper is to give a broad overview of the state-of-the-art in CGH. We make a classification of modern CGH algorithms, we describe different algorithmic CGH acceleration techniques, discuss the latest dedicated hardware solutions and indicate how to evaluate the perceptual quality of CGH. We summarize our findings, discuss remaining challenges and make projections on the future of CGH.

We designed and implemented a special-purpose computer for incoherent digital holography for application in three-dimensional (3D) microscopy. We focused on multiwavelength-multiplexed phase-shifting incoherent color digital holography as a method for acquiring 3D color-reconstructed images. This method records holograms faster than conventional temporal division methods. However, the reconstruction calculation of this method requires a significant amount of time, similar to the conventional method. Therefore, we designed a circuit for high-speed image reconstruction. We designed a Fresnel diffraction circuit that requires repetitive calculations to obtain a 3D color image but incurs a high calculation cost. We implemented the circuit on a field-programmable gate array (FPGA) and successfully calculated reconstructed images that were of the same quality as those calculated by the central processing unit (CPU) of a personal computer (PC). The calculation time was approximately 2.6 times faster than that of the CPU.

Incoherent digital holography (IDH) is a technique used to obtain a three-dimensional (3D) image of spatially incoherent light diffracted from an object as an incoherent hologram. Color holographic 3D motion picture imaging of daily-use light at the frame rate of a color polarization imaging camera can be achieved by the combination of IDH and single-shot phase-shifting interferometry. We show experimental results for color 3D motion picture imaging in this proceedings article.

We demonstrate an interactive holographic display system for real-time drawing and erasing of 3D point-cloud images. This system detects the position of the observer's fingertip with a motion sensor, which it uses to calculate the complex amplitude distribution for the hologram. Because the calculated distribution is added to or subtracted from the complex amplitude distribution of the previous frame, the calculation time per frame is independent of the number of points comprising the 3D point cloud. Then, the system can quickly update the hologram even when the number of points comprising the 3D point cloud is increased. Because the 3D point-cloud image reconstructed from the calculated hologram is projected at the same position as the observer's fingertip with almost no latency, the system can draw and erase a 3D point-cloud image through interactions with the observer's fingertip. We experimentally confirmed that the system successfully draws and erases a 3D point-cloud image.

Ghost imaging reconstructs images using a single-element photodetector; it performs imaging by illuminating an object with binary modulation patterns. This technique has various advantages, including a wide wavelength, noise robustness, and high measurement sensitivity. However, one challenge is the low image quality in the undersampling. The examination of modulation patterns is intended to solve this issue. In ghost imaging, randomly generated or basis patterns have been studied as modulation patterns; however, in undersampling, random patterns exhibit noise robustness but low image quality, whereas basis patterns exhibit high image quality but are sensitive to noise and low resolution. Thus, ghost imaging requires patterns that simultaneously achieve high image quality, resolution, and noise robustness. This study proposes a method of pattern optimization using gradient descent and a binarization method to further improve image quality. Numerical simulation and experimental results show that the proposed approach offers high image quality, high resolution, and robustness to noise.

Abstract Holography is a promising technology for photo-realistic three-dimensional (3D) displays because of its ability to replay the light reflected from an object using a spatial light modulator (SLM). However, the enormous computational requirements for calculating computer-generated holograms (CGHs)—which are displayed on an SLM as a diffraction pattern—are a significant problem for practical uses (e.g., for interactive 3D displays for remote navigation systems). Here, we demonstrate an interactive 3D display system using electro-holography that can operate with a consumer’s CPU. The proposed system integrates an efficient and fast CGH computation algorithm for line-drawn 3D objects with inter-frame differencing, so that the trajectory of a line-drawn object that is handwritten on a drawing tablet can be played back interactively using only the CPU. In this system, we used an SLM with 1,920 $$\times $$ × 1,080 pixels and a pixel pitch of 8 μm × 8 μm, a drawing tablet as an interface, and an Intel Core i9–9900K 3.60 GHz CPU. Numerical and optical experiments using a dataset of handwritten inputs show that the proposed system is capable of reproducing handwritten 3D images in real time with sufficient interactivity and image quality.

The Ramanujan sum, introduced by S. Ramanujan, has been utilized-among other applications-for signal processing. It has recently been suggested that transforms using the Ramanujan sums may also provide the benefit of data compression. This study presents a lossless hologram-compression method that employs transforms using the Ramanujan sums. In general, lossless compression of holograms is difficult, because the statistical properties of holograms are different from natural images. We compared the compression ratios of different hologram datasets, both with and without using Ramanujan- sums-based transforms. We found that the Ramanujan periodic transform improves the compression ratio of hologram data when using data having prime number dimensions.

Holographic projection is a simple projection as it enlarges or reduces reconstructed images without using a zoom lens. However, one major problem associated with this projection is the deterioration of image quality as the reconstructed image enlarges. In this paper, we propose a time-division holographic projection, in which the original image is divided into blocks and the holograms of each block are calculated. Using a digital micromirror device (DMD), the holograms were projected at high speed to obtain the entire reconstructed image. However, the holograms on the DMD need to be binarized, thereby causing uneven brightness between the divided blocks. We correct this by controlling the displaying time of each hologram. Additionally, combining both the proposed and noise reduction methods, the image quality of the reconstructed image was improved. Results from the simulation and optical reconstructions show we obtained a full-color reconstruction image with reduced noise and uneven brightness.

Generating new motion parallax holograms is required for holographic head-mounted displays when the head moves. Additionally, it is required for hologram generation from light field data that consist of a number of motion parallax images. However, re-rendering three-dimensional (3D) scenes and re-calculating holograms are computationally complex. Therefore, we propose a generation strategy of holograms with different motion parallax from an existing hologram without re-rendering 3D scenes and re-calculating holograms. The proposed method employs Fourier band-pass filtering and the simple relation of trigonometric functions, which makes it capable of skipping the computationally complex processes.

A complex amplitude hologram can reconstruct perfect light waves. However, as there are no spatial light modulators that are able to display complex amplitudes, we need to use amplitude, binary, or phase-only holograms. The images reconstructed from such holograms will deteriorate; to address this problem, iterative hologram optimization algorithms have been proposed. One of the iterative algorithms utilizes a blank area to help converge the optimization; however, the calculation time and memory usage involved increases. In this study, we propose to reduce the computational complexity and memory usage of the iterative optimization using scaled diffraction, which can calculate light propagation with different sampling pitches on a hologram plane and object plane. Scaled diffraction can introduce a virtual blank area without using physical memory. We further propose a combination of scaled diffraction-based optimization and conventional methods. The combination algorithm improves the quality of a reconstructed complex amplitude while accelerating optimization.