Slim-panel holographic video display

Non-convex optimization for inverse problem solving in computer-generated holography

Computer-generated holography is a promising technique that modulates user-defined wavefronts with digital holograms. Computing appropriate holograms with faithful reconstructions is not only a problem closely related to the fundamental basis of holography but also a long-standing challenge for researchers in general fields of optics. Finding the exact solution of a desired hologram to reconstruct an accurate target object constitutes an ill-posed inverse problem. The general practice of single-diffraction computation for synthesizing holograms can only provide an approximate answer, which is subject to limitations in numerical implementation. Various non-convex optimization algorithms are thus designed to seek an optimal solution by introducing different constraints, frameworks, and initializations. Herein, we overview the optimization algorithms applied to computer-generated holography, incorporating principles of hologram synthesis based on alternative projections and gradient descent methods. This is aimed to provide an underlying basis for optimized hologram generation, as well as insights into the cutting-edge developments of this rapidly evolving field for potential applications in virtual reality, augmented reality, head-up display, data encryption, laser fabrication, and metasurface design.

Full-angle chip scale package of mini LEDs with a V-shape packaging structure

The light distribution of light-emitting diodes (LEDs) generally resembles that of a Lambertian light source. When used as large-area light sources, the light distribution angle of LEDs must be modified through secondary optics design to achieve uniformity and minimize the number of light sources. However, secondary optical components pose several challenges such as demanding alignment accuracy, material aging, detachment, and lower reliability. Therefore, this paper proposes a primary optical design approach to achieve full-angle emission in LEDs without the need for lenses. The design employs a flip-chip as the light source and incorporates a V-shaped packaged structure, including a white wall layer, optical structure layers, and a V-shaped diffuse structure. With this design, the LEDs achieve full-angle emission without relying on lenses. Our experimental results demonstrated a peak intensity angle of 77.7°, a 20.3% decrease in the intensity of the central point ratio, and a full width at half maximum (FWHM) of the light distribution of 175.5°. This design is particularly suitable for thin, large-area, and flexible backlight light sources. Moreover, the absence of secondary optical components allows for a thinner light source module.

Color liquid crystal grating based color holographic 3D display system with large viewing angle

Holographic 3D display is highly desirable for numerous applications ranging from medical treatments to military affairs. However, it is challenging to simultaneously achieve large viewing angle and high-fidelity color reconstruction due to the intractable constraints of existing technology. Here, we conceptually propose and experimentally demonstrate a simple and feasible pathway of using a well-designed color liquid crystal grating to overcome the inevitable chromatic aberration and enlarge the holographic viewing angle, thus enabling large-viewing-angle and color holographic 3D display. The use of color liquid crystal grating allows performing secondary diffraction modulation on red, green and blue reproduced images simultaneously and extending the viewing angle in the holographic 3D display system. In principle, a chromatic aberration-free hologram generation mechanism in combination with the color liquid crystal grating is proposed to pave the way for on such a superior holographic 3D display. The proposed system shows a color viewing angle of ~50.12°, which is about 7 times that of the traditional system with a single spatial light modulator. This work presents a paradigm for achieving desirable holographic 3D display, and is expected to provide a new way for the wide application of holographic display.

Waveguide holography for 3D augmented reality glasses

Near-eye displays are fundamental technology in the next generation computing platforms for augmented reality and virtual reality. However, there are remaining challenges to deliver immersive and comfortable visual experiences to users, such as compact form factor, solving vergence-accommodation conflict, and achieving a high resolution with a large eyebox. Here we show a compact holographic near-eye display concept that combines the advantages of waveguide displays and holographic displays to overcome the challenges towards true 3D holographic augmented reality glasses. By modeling the coherent light interactions and propagation via the waveguide combiner, we demonstrate controlling the output wavefront using a spatial light modulator located at the input coupler side. The proposed method enables 3D holographic displays via exit-pupil expanding waveguide combiners, providing a large software-steerable eyebox. It also offers additional advantages such as resolution enhancement capability by suppressing phase discontinuities caused by pupil replication process. We build prototypes to verify the concept with experimental results and conclude the paper with discussion.

Lens array-based holographic 3D display with an expanded field of view and eyebox

Conventional spatial light modulator (SLM)-based holographic 3D display faces limited field of view (FOV) and eyebox, due to its limited pixel number. In this paper, a lens array is used to expand the FOV and eyebox of an SLM-based holographic display. The hologram is calculated to reconstruct a 3D sub-image array, each sub-image corresponding to a specific perspective of the 3D object. Then, the 3D sub-image array is imaged and magnified by the lens array to integrate to the original 3D image. The FOV is expanded due to the large numerical aperture of the lens, and the eyebox is expanded because the lens array generates multiple viewpoints with a large pitch. The optical experiment realizes a 17.6° FOV and 50 mm eyebox, which contains 4 × 4 viewpoints. Apparent motion parallax is observed through the viewpoint array, which is usually hard to observe in a conventional SLM-based holographic display. The proposed method provides a novel, to the best of our knowledge, way to expand the FOV and eyebox of holographic 3D display without increasing the total pixel number of the SLM.

Holographic display using layered computer-generated volume hologram

The spatial frequency of the reconstructed image of planar computer-generated hologram(CGH) is limited by the sampling interval and the lack of thickness. To break through this limitation of planar CGH, we propose a new computer-generated volume hologram(CGVH) for full-color dynamic holographic three-dimensional(3D) display, and an iteration-free layered CGVH generation method. The proposed CGVH is equivalent to a volume hologram sampled discretely in three directions. The generation method employs the layered angular spectral diffraction to calculate the light field in the layered CGVH, and then encodes it into a CGVH. Numerical simulation results show that the CGVH can accurately reconstruct full-color 3D objects, where better imaging quality, more concentrated diffraction energy, denser reconstructed spatial frequency information, and larger viewing angle are achieved. The proposed CGVH is expected to be applied to realize dynamic modulation, wavelength multiplexing, and angle multiplexing in various optical fields in the future.

Deep learning-based incoherent holographic camera enabling acquisition of real-world holograms for holographic streaming system

While recent research has shown that holographic displays can represent photorealistic 3D holograms in real time, the difficulty in acquiring high-quality real-world holograms has limited the realization of holographic streaming systems. Incoherent holographic cameras, which record holograms under daylight conditions, are suitable candidates for real-world acquisition, as they prevent the safety issues associated with the use of lasers; however, these cameras are hindered by severe noise due to the optical imperfections of such systems. In this work, we develop a deep learning-based incoherent holographic camera system that can deliver visually enhanced holograms in real time. A neural network filters the noise in the captured holograms, maintaining a complex-valued hologram format throughout the whole process. Enabled by the computational efficiency of the proposed filtering strategy, we demonstrate a holographic streaming system integrating a holographic camera and holographic display, with the aim of developing the ultimate holographic ecosystem of the future.

Extended depth of field in augmented reality

The 3D display device shows an image with depth information. Conventional 3D display devices based on binocular parallax can focus accurately only on the depth of a specific screen. Because the human eye has a narrow depth of field (DOF) under normal circumstances, 3D displays that provide a relatively wide range of virtual depth areas have limitations on the DOF where clear 3D images are seen. To resolve this problem, it is necessary to find the optical conditions to extend the DOF and analyze the phenomena related to it. For this, by using the Rayleigh criterion and the Strehl ratio, a criterion for this extension of the DOF is suggested. A practical optical structure that can effectively extend the DOF is devised using a flat panel display. This optical structure could be applied to AR, VR, and MR in the field of near-eye displays. From the results of this research, the fundamental optical conditions and standards are proposed for 3D displays that will provide 3D images with extended DOF in the future. Furthermore, it is also expected that these conditions and criteria can be applied to optical designs for the required performance in the development of 3D displays in various fields.

Nano-electromechanical spatial light modulator enabled by asymmetric resonant dielectric metasurfaces

Spatial light modulators (SLMs) play essential roles in various free-space optical technologies, offering spatio-temporal control of amplitude, phase, or polarization of light. Beyond conventional SLMs based on liquid crystals or microelectromechanical systems, active metasurfaces are considered as promising SLM platforms because they could simultaneously provide high-speed and small pixel size. However, the active metasurfaces reported so far have achieved either limited phase modulation or low efficiency. Here, we propose nano-electromechanically tunable asymmetric dielectric metasurfaces as a platform for reflective SLMs. Exploiting the strong asymmetric radiation of perturbed high-order Mie resonances, the metasurfaces experimentally achieve a phase-shift close to 290^∘, over 50% reflectivity, and a wavelength-scale pixel size. Electrical control of diffraction patterns is also achieved by displacing the Mie resonators using nano-electro-mechanical forces. This work paves the ways for future exploration of the asymmetric metasurfaces and for their application to the next-generation SLMs.

This work experimentally demonstrates nano-electromechanically tunable asymmetric dielectric metasurfaces. The metasurfaces enable large phase tuning, high reflection, a wavelength-scale pixel size, and electrical control of diffraction patterns.

End-to-end learning of 3D phase-only holograms for holographic display

Computer-generated holography (CGH) provides volumetric control of coherent wavefront and is fundamental to applications such as volumetric 3D displays, lithography, neural photostimulation, and optical/acoustic trapping. Recently, deep learning-based methods emerged as promising computational paradigms for CGH synthesis that overcome the quality-runtime tradeoff in conventional simulation/optimization-based methods. Yet, the quality of the predicted hologram is intrinsically bounded by the dataset's quality. Here we introduce a new hologram dataset, MIT-CGH-4K-V2, that uses a layered depth image as a data-efficient volumetric 3D input and a two-stage supervised+unsupervised training protocol for direct synthesis of high-quality 3D phase-only holograms. The proposed system also corrects vision aberration, allowing customization for end-users. We experimentally show photorealistic 3D holographic projections and discuss relevant spatial light modulator calibration procedures. Our method runs in real-time on a consumer GPU and 5 FPS on an iPhone 13 Pro, promising drastically enhanced performance for the applications above.

Review of computer-generated hologram algorithms for color dynamic holographic three-dimensional display

Holographic three-dimensional display is an important display technique because it can provide all depth information of a real or virtual scene without any special eyewear. In recent years, with the development of computer and optoelectronic technology, computer-generated holograms have attracted extensive attention and developed as the most promising method to realize holographic display. However, some bottlenecks still restrict the development of computer-generated holograms, such as heavy computation burden, low image quality, and the complicated system of color holographic display. To overcome these problems, numerous algorithms have been investigated with the aim of color dynamic holographic three-dimensional display. In this review, we will explain the essence of various computer-generated hologram algorithms and provide some insights for future research.

Variable-intensity line 3D images drawn using kinoform-type electroholography superimposed with phase error

Three-dimensional (3D) display using electroholography is a promising technology for next-generation television systems; however, its applicability is limited by the heavy computational load for obtaining computer-generated holograms (CGHs). The CG-line method is an algorithm that calculates CGHs to display 3D line-drawn objects at a very high computational speed but with limited expressiveness; for instance, the intensity along the line must be constant. Herein, we propose an extension for drawing gradated 3D lines using the CG-line method by superimposing phase noise. Consequently, we succeeded in drawing gradated 3D lines while maintaining the high computational speed of the original CG-line method.

Tunable liquid crystal grating based holographic 3D display system with wide viewing angle and large size

As one of the most ideal display approaches, holographic 3-dimensional (3D) display has always been a research hotspot since the holographic images reproduced in such system are very similar to what humans see the actual environment. However, current holographic 3D displays suffer from critical bottlenecks of narrow viewing angle and small size. Here, we propose a tunable liquid crystal grating-based holographic 3D display system with wide viewing angle and large size. Our tunable liquid crystal grating, providing an adjustable period and the secondary diffraction of the reconstructed image, enables to simultaneously implement two different hologram generation methods in achieving wide viewing angle and enlarged size, respectively. By using the secondary diffraction mechanism of the tunable liquid crystal grating, the proposed system breaks through the limitations of narrow viewing angle and small size of holographic 3D display. The proposed system shows a viewing angle of 57.4°, which is nearly 7 times of the conventional case with a single spatial light modulator, and the size of the reconstructed image is enlarged by about 4.2. The proposed system will have wide applications in medical diagnosis, advertising, education and entertainment and other fields.

Design of Interactive Teaching System of Physical Training Based on Artificial Intelligence

Nowadays, with the continuous change and innovation of teaching methods in Colleges and universities, the curriculum system of students is also constantly enriched and developed. Therefore, people’s requirements for teaching management and teaching system are also improving. Physical education curriculum is usually based on outdoor teaching, and some schools have not established a complete teaching system. Therefore, the interactive teaching system of physical training based on artificial intelligence is designed. First of all, through the construction of the interactive teaching system of the total control circuit, determine the corresponding circuit address decoding, improve the audio control circuit, associated video connection interactive drive three parts, the intelligent sports training interactive system hardware design. Then, through the creation of intelligent training function module, the design of training database and the realisation of effective training and teaching of intelligent sports, the software design of intelligent sports training interactive system is carried out. Finally, through the test of the system, to verify the corresponding effect, further improve the relevant system, make it more safe and accurate, improve the efficiency of sports training interactive system, enhance the integrity of the teaching process.

Optimization of Optical Phase Profile in Beam Deflector with Advanced Simulation Method for High Diffraction Efficiency

Controlling the phase of light with a high efficiency and precision is essential for applications in imaging, tunable devices, and optical systems. Spatial light modulators (SLMs) based on liquid crystals (LCs) have been regarded as one of the best choices for the generation of phase profiles for the steering of light. The upper glass substrate has an unpatterned electrode for a common electrode, while the lower glass substrate has one-dimensional micro-patterned electrodes for controlling the single pixel level by the applied voltages. By applying different voltages to each electrode to create a sawtooth-shaped phase profile, the collimated input beam is deflected to the desired angle. To maximize the diffraction efficiency (DE) values, an advanced simulation method has been developed to find the optimized phase profile through the analysis of LC director distributions. The resulting diffraction patterns are investigated both computationally and experimentally, with a good agreement between the results obtained. Finally, the beam deflector (BD) system with an advanced driving algorithm has a high 1st order DE, about 60%, 37%, and 7.5% at 1°, 2.5°, and a maximum steering angle of 7.5°, respectively. The LC director distributions in relation to various diffraction angles are simulated and an experimental success in realizing enhanced DE for the beam steering device is presented.

Wide-viewing holographic stereogram based on self-interference incoherent digital holography

We propose a holographic stereogram synthesis method which uses holograms that are optically captured by self-interference incoherent digital holography (SIDH) based on a geometric phase lens. SIDH is a promising solution for hologram acquisition under low-coherence lighting condition. A mechanical scanning system is constructed to acquire multiple perspective holograms. Numerical simulations and experimental analyses conducted using high-resolution diffractive optical element demonstrate that the proposed method can produce a wide-viewing hologram which can realize realistic 3D scenarios with depth cues such as accommodation and motion parallax. The future objectives include the implementation of a multiple-camera system for holographic videos.

Metasurface-empowered spectral and spatial light modulation for disruptive holographic displays

The holographic display, one of the most realistic ways to reconstruct optical images in three-dimensional (3D) space, has gained a lot of attention as a next-generation display platform for providing deeper immersive experiences to users. So far, diffractive optical elements (DOEs) and spatial light modulators (SLMs) have been used to generate holographic images by modulating electromagnetic waves at each pixel. However, such architectures suffer from limitations in terms of having a resolution of only a few microns and the bulkiness of the entire optical system. In this review, we describe novel metasurfaces-based nanophotonic platforms that have shown exceptional control of electromagnetic waves at the subwavelength scale as promising candidates to overcome existing restrictions, while realizing flat optical devices. After introducing the fundamentals of metasurfaces in terms of spatial and spectral wavefront modulation, we present a variety of multiplexing approaches for high-capacity and full-color metaholograms exploiting the multiple properties of light as an information carrier. We then review tunable metaholograms using active materials modulated by several external stimuli. Afterward, we discuss the integration of metasurfaces with other optical elements required for future 3D display platforms in augmented/virtual reality (AR/VR) displays such as lenses, beam splitters, diffusers, and eye-tracking sensors. Finally, we address the challenges of conventional nanofabrication methods and introduce scalable preparation techniques that can be applied to metasurface-based nanophotonic technologies towards commercially and ergonomically viable future holographic displays.

Recent Advances in Planar Optics-Based Glasses-Free 3D Displays

Glasses-free three-dimensional (3D) displays are one of the technologies that will redefine human-computer interfaces. However, many geometric optics-based 3D displays suffer from a limited field of view (FOV), severe resolution degradation, and visual fatigue. Recently, planar optical elements (e.g., diffraction gratings, diffractive lenses and metasurfaces) have shown superior light manipulating capability in terms of light intensity, phase, and polarization. As a result, planar optics hold great promise to tackle the critical challenges for glasses-free 3D displays, especially for portable electronics and transparent display applications. In this review, the limitations of geometric optics-based glasses-free 3D displays are analyzed. The promising solutions offered by planar optics for glasses-free 3D displays are introduced in detail. As a specific application and an appealing feature, augmented reality (AR) 3D displays enabled by planar optics are comprehensively discussed. Fabrication technologies are important challenges that hinder the development of 3D displays. Therefore, multiple micro/nanofabrication methods used in 3D displays are highlighted. Finally, the current status, future direction and potential applications for glasses-free 3D displays and glasses-free AR 3D displays are summarized.

High-contrast, speckle-free, true 3D holography via binary CGH optimization

Holography is a promising approach to implement the three-dimensional (3D) projection beyond the present two-dimensional technology. True 3D holography requires abilities of arbitrary 3D volume projection with high-axial resolution and independent control of all 3D voxels. However, it has been challenging to implement the true 3D holography with high-reconstruction quality due to the speckle. Here, we propose the practical solution to realize speckle-free, high-contrast, true 3D holography by combining random-phase, temporal multiplexing, binary holography, and binary optimization. We adopt the random phase for the true 3D implementation to achieve the maximum axial resolution with fully independent control of the 3D voxels. We develop the high-performance binary hologram optimization framework to minimize the binary quantization noise, which provides accurate and high-contrast reconstructions for 2D as well as 3D cases. Utilizing the fast operation of binary modulation, the full-color high-framerate holographic video projection is realized while the speckle noise of random phase is overcome by temporal multiplexing. Our high-quality true 3D holography is experimentally verified by projecting multiple arbitrary dense images simultaneously. The proposed method can be adopted in various applications of holography, where we show additional demonstration that realistic true 3D hologram in VR and AR near-eye displays. The realization will open a new path towards the next generation of holography.

Past, current, and future of holographic video display [Invited]

Holography has been considered as the ultimate technology for three-dimensional visual experience. Compared to the well-established static holographic technology, holographic video display is still in the research and development stage, before commercial products. This paper reviews various kinds of researches and related systems from the beginning of holographic video display to recent improvements, compares each specification, and describes their features. We discuss the key requirements for holographic display to be commercialized and widely used in everyday life.

Colour volumetric display based on holographic-laser-excited graphics using drawing space separation

A volumetric display generates a graphics that can be viewed from 360\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}∘ by representing the 3D information of an object as voxels in physical space. However, the natural properties of physical objects, such as 3D information and colors, and the seamless relationships between graphics and humans make it difficult to implement such displays. Here, we introduce a novel system that combines the spatial generation of femtosecond-laser-excited emission points using computer-generated holograms and beam scanning with the drawing space separation method. We demonstrate the drawing of volumetric graphics that can be color-expressed in voxel units in the air. This system enables the drawing of volumetric graphics in the air, accurate color representations, and robust graphics that are not destroyed by contact with users or objects. It also lays the foundation for the implementation of future volumetric displays.

Pupil replication waveguide system for autostereoscopic imaging with a wide field of view

Augmented reality head-up displays (HUDs) require virtual-object distance matching to the real scene along an adequate field of view (FoV). At the same time, pupil-replication-based waveguide systems provide a wide FoV while affording compact HUDs. To provide 3D imaging and enable virtual-object distance matching in such waveguide systems, we propose a time-sequential autostereoscopic imaging architecture using a synchronized multi-view picture generation and eyebox formation units. Our simulation setup to validate the system feasibility yields an FoV of 15° × 7.5° with clear crosstalk-less images with a resolution of 60 pix/deg for each eye. Our proof-of-concept prototype with reduced specs yields results that are consistent with the simulation in terms of the viewing-zone formation. Thus, viewing zones for the left and right eyes in plane of the eyebox can be clearly observed. Finally, we discuss how the initial distance of the virtual image can be set for quantified fatigue-free 3D imaging, and an FoV can be further extended in such types of waveguide systems by varying parameters of the eyebox formation unit.

Foveated glasses-free 3D display with ultrawide field of view via a large-scale 2D-metagrating complex

Glasses-free three-dimensional (3D) displays are one of the game-changing technologies that will redefine the display industry in portable electronic devices. However, because of the limited resolution in state-of-the-art display panels, current 3D displays suffer from a critical trade-off among the spatial resolution, angular resolution, and viewing angle. Inspired by the so-called spatially variant resolution imaging found in vertebrate eyes, we propose 3D display with spatially variant information density. Stereoscopic experiences with smooth motion parallax are maintained at the central view, while the viewing angle is enlarged at the periphery view. It is enabled by a large-scale 2D-metagrating complex to manipulate dot/linear/rectangular hybrid shaped views. Furthermore, a video rate full-color 3D display with an unprecedented 160° horizontal viewing angle is demonstrated. With thin and light form factors, the proposed 3D system can be integrated with off-the-shelf purchased flat panels, making it promising for applications in portable electronics.

Review of Organic Photorefractive Materials and Their Use for Updateable 3D Display

Photorefractive materials are capable of reversibly changing their index of refraction upon illumination. That property allows them to dynamically record holograms, which is a key function for developing an updateable holographic 3D display. The transition from inorganic photorefractive crystals to organic polymers meant that large display screens could be made. However, one essential figure of merit that needed to be worked out first was the sensitivity of the material that enables to record bright images in a short amount of time. In this review article, we describe how polymer engineering was able to overcome the problem of the material sensitivity. We highlight the importance of understanding the energy levels of the different species in order to optimize the efficiency and recording speed. We then discuss different photorefractive compounds and the reason for their particular figures of merit. Finally, we consider the technical choices taken to obtain an updateable 3D display using photorefractive polymer. By leveraging the unique properties of this holographic recording material, full color holograms were demonstrated, as well as refreshing rate of 100 hogels/second.

Augmented Reality Vector Light Field Display with Large Viewing Distance Based on Pixelated Multilevel Blazed Gratings

Glasses-free augmented reality (AR) 3D display has attracted great interest in its ability to merge virtual 3D objects with real scenes naturally, without the aid of any wearable devices. Here we propose an AR vector light field display based on a view combiner and an off-the-shelf purchased projector. The view combiner is sparsely covered with pixelated multilevel blazed gratings (MBG) for the projection of perspective virtual images. Multi-order diffraction of the MBG is designed to increase the viewing distance and vertical viewing angle. In a 20-inch prototype, multiple sets of 16 horizontal views form a smooth parallax. The viewing distance of the 3D scene is larger than 5 m. The vertical viewing angle is 15.6°. The light efficiencies of all views are larger than 53%. We demonstrate that the displayed virtual 3D scene retains natural motion parallax and high brightness while having a consistent occlusion effect with natural objects. This research can be extended to applications in areas such as human–computer interaction, entertainment, education, and medical care.

Wide-viewing full-color depthmap computer-generated holograms

An efficient synthesis algorithm for wide-viewing full-color depthmap computer-generated holograms is proposed. We develop a precise computational algorithm integrating wave-optic geometry-mapping, color-matching, and noise-filtering to multiplex multiview elementary computer-generated holograms (CGHs) into a single high-definition CGH without three-dimensional perspective distortion or color dispersion. Computational parallelism is exploited to achieve significant computational efficiency improvement in the production throughput of full-color wide-viewing angle CGHs. The proposed algorithm is verified through the full-color binary hologram reconstruction experiments utilizing an off-axis R·G·B simultaneous illumination method, which suggests the feasibility of the full-color sub-wavelength binary spatial light modulator technology.

Optical Fireworks Based on Multifocal Three-Dimensional Color Prints

Colorful three-dimensional (3D) prints are promising as practical anticounterfeiting labels with easily recognizable and striking visual effects. However, existing colorful 3D displays either require specific illumination conditions with multiple coherent lasers, hence suffer from speckles, or are unsuitable as passive labels. Here, we report a concept of a virtual 3D color object consisting of colorful focal spots in free space. The colors and corresponding "floating heights" of these spots are independently controlled via the design of 3D printed microlens profiles and heights of nanopillars that act as structural-color filters. Despite the unremarkable appearance of the printed substrate under both optical and electron microscopy, illumination with incoherent white light reveals information in the form of bright colorful spots appearing at designated heights above the plane of the substrate. The term "optical fireworks" refers to the way these spots appear and disappear under an optical microscope as one continuously shifts the focal plane. Our 3D printed optical fireworks security labels introduce applications for optical elements integrated with nanostructures in 3D colorful displays and anticounterfeiting labels.

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.