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A controllable energy method, which considers the undersampling issue of the transfer function and valid spectral energy of a source signal, is proposed to implement angular spectrum diffraction calculation in near and far fields. The proposed method provides an optimized frequency boundary $f_{CE}$ within which it always keeps controllable energy to be diffracted. The controllable energy angular spectrum method significantly reduces the number of samples while having the same accuracy as previous angular spectrum methods, implying a higher calculation efficiency. The new perspective of analyzing spectral energy is shown to improve the performance of relevant diffraction calculations.

Holographic information hiding is a technique for embedding holograms or images into another hologram, used for copyright protection and steganography of holograms. Using deep neural networks, we offer a way to improve the visual quality of embedded holograms. The brightness of an embedded hologram is set to a fraction of that of the host hologram, resulting in a barely damaged reconstructed image of the host hologram. However, it is difficult to perceive because the embedded hologram's reconstructed image is darker than the reconstructed host image. In this study, we use deep neural networks to restore the darkened image.

High-order Gaussian beams with multiple propagation modes have been studied for free-space optical communications. Fast classification of beams using a diffractive deep neural network, D2NN, has been proposed. D2NN optimization is important because it has numerous hyperparameters, such as interlayer distances and mode combinations. In this study, we classify Hermite-Gaussian beams, which are high-order Gaussian beams, using a D2NN, and automatically tune one of its hyperparameters known as the interlayer distance. We used the tree-structured Parzen estimator, a hyperparameter auto-tuning algorithm, to search for the best model. Results indicated that classification accuracy obtained by auto-tuning hyperparameters was higher than that obtained by manually setting interlayer distances at equal intervals. In addition, we confirmed that accuracy by auto-tuning improves as the number of classification modes increases.

Computer-generated holograms (CGHs) are used in holographic three-dimensional (3D) displays and holographic projections. The quality of the reconstructed images using phase-only CGHs is degraded because the amplitude of the reconstructed image is difficult to control. Iterative optimization methods such as the Gerchberg-Saxton (GS) algorithm are one option for improving image quality. They optimize CGHs in an iterative fashion to obtain a higher image quality. However, such iterative computation is time consuming, and the improvement in image quality is often stagnant. Recently, deep learning-based hologram computation has been proposed. Deep neural networks directly infer CGHs from input image data. However, it is limited to reconstructing images that are the same size as the hologram. In this study, we use deep learning to optimize phase-only CGHs generated using scaled diffraction computations and the random phase-free method. By combining the random phase-free method with the scaled diffraction computation, it is possible to handle a zoomable reconstructed image larger than the hologram. In comparison to the GS algorithm, the proposed method optimizes both high quality and speed.

For this work, we introduced the use of binary amplitude for our proposed complex amplitude encoding of a phase-only hologram. By principle, a complex amplitude in a hologram plane can be represented by the amplitude and its phase. However, a phase-only hologram contains only phase information of the complex amplitude, which results in degradation of reconstruction quality from the hologram. In our method, by approximating the amplitude in the hologram plane using a binary amplitude, we can finally record the complex amplitude of an original light in the phase-only hologram. We validated the effectiveness of our method with two examples, hologram reconstruction and generation of Hermite-Gaussian beams.

This paper proposes a particle volume reconstruction directly from an in-line hologram using a deep neural network. Digital holographic volume reconstruction conventionally uses multiple diffraction calculations to obtain sectional reconstructed images from an in-line hologram, followed by detection of the lateral and axial positions, and the sizes of particles by using focus metrics. However, the axial resolution is limited by the numerical aperture of the optical system, and the processes are time-consuming. The method proposed here can simultaneously detect the lateral and axial positions, and the particle sizes via a deep neural network (DNN). We numerically investigated the performance of the DNN in terms of the errors in the detected positions and sizes. The calculation time is faster than conventional diffracted-based approaches.

Computational ghost imaging is a promising technique for single-pixel imaging because it is robust to disturbance and can be operated over broad wavelength bands, unlike common cameras. However, one disadvantage of this method is that it has a long calculation time for image reconstruction. In this paper, we have designed a dedicated calculation circuit that accelerated the process of computational ghost imaging. We implemented this circuit by using a field-programmable gate array, which reduced the calculation time for the circuit compared to a CPU. The dedicated circuit reconstructs images at a frame rate of 300 Hz.

Digital holography enables us to reconstruct objects in three-dimensional space from holograms captured by an imaging device. For the reconstruction, we need to know the depth position of the recoded object in advance. In this study, we propose depth prediction using convolutional neural network (CNN)-based regression. In the previous researches, the depth of an object was estimated through reconstructed images at different depth positions from a hologram using a certain metric that indicates the most focused depth position; however, such a depth search is time-consuming. The CNN of the proposed method can directly predict the depth position with millimeter precision from holograms.

Computational ghost imaging (CGI) is a single-pixel imaging technique that exploits the correlation between known random patterns and the measured intensity of light transmitted (or reflected) by an object. Although CGI can obtain two- or three- dimensional images with a single or a few bucket detectors, the quality of the reconstructed images is reduced by noise due to the reconstruction of images from random patterns. In this study, we improve the quality of CGI images using deep learning. A deep neural network is used to automatically learn the features of noise-contaminated CGI images. After training, the network is able to predict low-noise images from new noise-contaminated CGI images.

We propose a large-scale hologram calculation using WAvelet ShrinkAge-Based superpositIon (WASABI), a wavelet transform-based algorithm. An image-type hologram calculated using the WASABI method is printed on a glass substrate with the resolution of $65,536 \times 65,536$ pixels and a pixel pitch of $1 \mu$m. The hologram calculation time amounts to approximately 354 s on a commercial CPU, which is approximately 30 times faster than conventional methods.

We propose a deep-learning-based classification of data pages used in holographic memory. We numerically investigated the classification performance of a conventional multi-layer perceptron (MLP) and a deep neural network, under the condition that reconstructed page data are contaminated by some noise and are randomly laterally shifted. The MLP was found to have a classification accuracy of 91.58%, whereas the deep neural network was able to classify data pages at an accuracy of 99.98%. The accuracy of the deep neural network is two orders of magnitude better than the MLP.

In this study, a method to construct a full-colour volumetric display is presented using a commercially available inkjet printer. Photoreactive luminescence materials are minutely and automatically printed as the volume elements, and volumetric displays are constructed with high resolution using easy-to-fabricate means that exploit inkjet printing technologies. The results experimentally demonstrate the first prototype of an inkjet printing-based volumetric display composed of multiple layers of transparent films that yield a full-colour three-dimensional (3D) image. Moreover, we propose a design algorithm with 3D structures that provide multiple different 2D full-colour patterns when viewed from different directions and experimentally demonstrates prototypes. It is considered that these types of 3D volumetric structures and their fabrication methods based on widely deployed existing printing technologies can be utilised as novel information display devices and systems, including digital signage, media art, entertainment and security.

We propose a holographic image restoration method using an autoencoder, which is an artificial neural network. Because holographic reconstructed images are often contaminated by direct light, conjugate light, and speckle noise, the discrimination of reconstructed images may be difficult. In this paper, we demonstrate the restoration of reconstructed images from holograms that record page data in holographic memory and QR codes by using the proposed method.

Our proposed method of random phase-free holography using virtual convergence light can obtain large reconstructed images exceeding the size of the hologram, without the assistance of random phase. The reconstructed images have low-speckle noise in the amplitude and phase-only holograms (kinoforms); however, in low-resolution holograms, we obtain a degraded image quality compared to the original image. We propose an iterative random phase-free method with virtual convergence light to address this problem.

We propose a random phase-free kinoform for large objects. When not using the random phase in kinoform calculation, the reconstructed images from the kinoform are heavy degraded, like edge-only preserved images. In addition, the kinoform cannot record an entire object that exceeds the kinoform size because the object light does not widely spread. In order to avoid this degradation and to widely spread the object light, the random phase is applied to the kinoform calculation; however, the reconstructed image is contaminated by speckle noise. In this paper, we overcome this problem by using our random phase-free method and error diffusion method.

We propose an optical encryption framework that can encrypt and decrypt large-sized images beyond the size of the encrypted image using our two methods: random phase-free method and scaled diffraction. In order to record the entire image information on the encrypted image, the large-sized images require the random phase to widely diffuse the object light over the encrypted image; however, the random phase gives rise to the speckle noise on the decrypted images, and it may be difficult to recognize the decrypted images. In order to reduce the speckle noise, we apply our random phase-free method to the framework. In addition, we employ scaled diffraction that calculates light propagation between planes with different sizes by changing the sampling rates.

This paper numerically investigates the feasibility of lensless zoomable holographic multiple projections to tilted planes. We have already developed lensless zoomable holographic single projection using scaled diffraction, which calculates diffraction between parallel planes with different sampling pitches. The structure of this zoomable holographic projection is very simple because it does not need a lens; however, it only projects a single image to a plane parallel to the hologram. The lensless zoomable holographic projection in this paper is capable of projecting multiple images onto tilted planes simultaneously.

Ptychography is a promising phase retrieval technique for visible light, X-ray and electron beams. Conventional ptychography reconstructs the amplitude and phase of an object light from a set of the diffraction intensity patterns obtained by the X-Y moving of the probe light. The X-Y moving of the probe light requires two control parameters and accuracy of the locations. We propose ptychography by changing the area of the probe light using only one control parameter, instead of the X-Y moving of the probe light. The proposed method has faster convergence speed. In addition, we propose scaled ptychography using scaled diffraction calculation in order to magnify retrieved object lights clearly.

We report fast computation of computer-generated holograms (CGHs) using Xeon Phi coprocessors, which have massively x86-based processors on one chip, recently released by Intel. CGHs can generate arbitrary light wavefronts, and therefore, are promising technology for many applications: for example, three-dimensional displays, diffractive optical elements, and the generation of arbitrary beams. CGHs incur enormous computational cost. In this paper, we describe the implementations of several CGH generating algorithms on the Xeon Phi, and the comparisons in terms of the performance and the ease of programming between the Xeon Phi, a CPU and graphics processing unit (GPU).

Scalar diffraction calculations such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, X-rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using fast Fourier transform (FFT); unfortunately, acceleration of the calculation of non-uniform sampled planes is limited due to the property of the FFT that imposes uniform sampling. In addition, it gives rise to wasteful sampling data if we calculate a plane having locally low and high spatial frequencies. In this paper, we developed non-uniform sampled ASM and Fresnel diffraction to improve the problem using the non-uniform FFT.

We report a calculation reduction method for color computer-generated holograms (CGHs) using color space conversion. Color CGHs are generally calculated on RGB space. In this paper, we calculate color CGHs in other color spaces: for example, YCbCr color space. In YCbCr color space, a RGB image is converted to the luminance component (Y), blue-difference chroma (Cb) and red-difference chroma (Cr) components. In terms of the human eye, although the negligible difference of the luminance component is well-recognized, the difference of the other components is not. In this method, the luminance component is normal sampled and the chroma components are down-sampled. The down-sampling allows us to accelerate the calculation of the color CGHs. We compute diffraction calculations from the components, and then we convert the diffracted results in YCbCr color space to RGB color space.

We demonstrate a gigapixel inline digital holographic microscopy using a consumer scanner. The consumer scanner can maximally scan an A4 size image (297mm x 210mm) with 4800 dpi (= 5.29 um), theoretically achieving a resolution of 56,144 x 39,698 = 2.22 gigapixels. The system using a consumer scanner has a simple structure, compared with synthetic aperture digital holography using a camera mounted on a two-dimensional moving stage. In this demonstration, we captured an inline hologram with 23,602 x 18,023 pixels (= 0.43 gigapixels). In addition, to accelerate the reconstruction time of the gigapixel hologram and decrease the amount of memory for the reconstruction, we applied the band-limited double-step Fresnel diffraction to the reconstruction.

Numerical simulation of Fresnel diffraction with fast Fourier transform (FFT) is widely used in optics, especially computer holography. Fresnel diffraction with FFT cannot set different sampling rates between source and destination planes, while shifted-Fresnel diffraction can set different rates. However, an aliasing error may be incurred in shifted-Fresnel diffraction in a short propagation distance, and the aliasing conditions have not been investigated. In this paper, we investigate the aliasing conditions of shifted-Fresnel diffraction and improve its properties based on the conditions.