Computer-generated Holograms Research Articles

Quality improvement of unfiltered holography by optimizing high diffraction orders with fill factor.

Computer-generated holography (CGH) suffers from high diffraction orders (HDOs) due to the pixelated nature of spatial light modulators (SLMs), typically requiring bulky optical filtering systems. To address this issue, a novel unfiltered holography approach known as the high-order gradient descent (HOGD) algorithm was previously introduced to optimize HDOs without optical filtering, enabling compact holographic displays. However, this algorithm overlooks a crucial physical parameter of SLMs-the fill factor-leading to limited optical quality. Here, we introduce a fill factor-based HOGD (FF-HOGD) algorithm, specifically designed to improve the quality of unfiltered holography by incorporating the fill factor into the optimization process. The quality advantage of FF-HOGD is demonstrated through numerical simulations and optical experiments.

Compact binocular holographic near-eye 3D display system based on a liquid crystal polarization grating

Holographic technology is considered as one of the most ideal 3D display technologies and has significant potential in near-eye display. However, binocular holographic near-eye 3D display still faces challenges such as serious visual fatigue and complex system. Here, we propose a compact binocular holographic near-eye 3D display system based on a liquid crystal polarization grating (LCPG). Based on the LCPG, the reconstructed light can be deflected respectively to left and right viewing areas. The proposed system achieves binocular display with only one phase-only spatial light modulator used to load computer-generated hologram, which makes the binocular display system more compact. Simultaneously, the proposed system reduces mismatches in the images perceived by two eyes, thus achieving a better binocular display effect. Experimental results demonstrate the feasibility of the proposed binocular holographic near-eye 3D display system with dual viewing areas. Additionally, based on the time-division multiplexing method, dynamic binocular holographic near-eye display can be achieved. The proposed system has potential applications in holographic virtual reality and augmented reality display.

Pre-compensated annealing gradient descent for spherical holography

Spherical holography technology, a 3D display technology with the advantage of an infinite viewing zone and 360°observation, has received widespread attention. However, the quality of existing computer-generated spherical holograms is limited. To address this issue, we propose a Pre-compensated annealing gradient descent method (PAGD) to quickly obtain spherical holography. Compared to traditional SGD algorithms, the PAGD algorithm significantly improves convergence speed. The annealed gradient descent helps avoid local optima during the optimization process, while pre-compensation enhances the optimizer’s rate. Numerical simulations have confirmed the effectiveness of this method. The optimization rate of PAGD is 16.81 times faster than that of traditional SGD. It is noteworthy that this method has broad application prospects in spherical holographic display and three-dimensional display.

Phase space framework enables a variable-scale diffraction model for coherent imaging and display

The fast algorithms in Fourier optics have invigorated multifunctional device design and advanced imaging technologies. However, the necessity for fast computations limits the widely used conventional Fourier methods, where the image plane has a fixed size at certain diffraction distances. These limitations pose challenges in intricate scaling transformations, 3D reconstructions, and full-color displays. Currently, the lack of effective solutions makes people often resort to pre-processing that compromises fidelity. In this paper, leveraging a higher-dimensional phase space method, a universal framework is proposed for customized diffraction calculation methods. Within this framework, a variable-scale diffraction computation model is established for adjusting the size of the image plane and can be operated by fast algorithms. The model’s robust variable-scale capabilities and its aberration automatic correction capability are validated for full-color holography, and high fidelity is achieved. The tomography experiments demonstrate that this model provides a superior solution for holographic 3D reconstruction. In addition, this model is applied to achieve full-color metasurface holography with near-zero crosstalk, showcasing its versatile applicability at nanoscale. Our model presents significant prospects for applications in the optics community, such as beam shaping, computer-generated holograms (CGHs), augmented reality (AR), metasurface optical elements (MOEs), and advanced holographic head-up display (HUD) systems.

ConIQA: A deep learning method for perceptual image quality assessment with limited data

Effectively assessing the realism and naturalness of images in virtual (VR) and augmented (AR) reality applications requires Full Reference Image Quality Assessment (FR-IQA) metrics that closely align with human perception. Deep learning-based IQAs that are trained on human-labeled data have recently shown promise in generic computer vision tasks. However, their performance decreases in applications where perfect matches between the reference and the distorted images should not be expected, or whenever distortion patterns are restricted to specific domains. Tackling this issue necessitates training a task-specific neural network, yet generating human-labeled FR-IQAs is costly, and deep learning typically demands substantial labeled data. To address these challenges, we developed ConIQA, a deep learning-based IQA that leverages consistency training and a novel data augmentation method to learn from both labeled and unlabeled data. This makes ConIQA well-suited for contexts with scarce labeled data. To validate ConIQA, we considered the example application of Computer-Generated Holography (CGH) where specific artifacts such as ringing, speckle, and quantization errors routinely occur, yet are not explicitly accounted for by existing IQAs. We developed a new dataset, HQA1k, that comprises 1000 natural images each paired with an image rendered using various popular CGH algorithms, and quality-rated by thirteen human participants. Our results show that ConIQA achieves superior Pearson (0.98), Spearman (0.965), and Kendall’s tau (0.86) correlations over fifteen FR-IQA metrics by up to 5%, showcasing significant improvements in aligning with human perception on the HQA1k dataset.

Single-pulse three-dimensional parallel recording in glass using a feedback system.

High-quality three-dimensional computer-generated holograms (3D-CGHs) are crucial for programmable 3D femtosecond laser parallel recording (3D-FLPR). In this study, we introduced an innovative feedback approach for the rapid optimization of 3D-CGHs by incorporating the superposition of the calculated lens phases (CLPs) onto the 3D-CGHs within a feedback system. This feedback system, governed by coordinated control of a spatial light modulator (SLM) and a camera, served to avoid the poor quality of the ordinary CGH system. As a result, we successfully demonstrated coaxial 3D-FLPR in Ag-doped phosphate glass solely using a single fs laser pulse. Additionally, we regulated the energy distribution of the generated 3D multi-focus (3D-MF) to compensate the laser energy losses inside the glass. The presented single-pulse 3D parallel recording indicated the significant advancement facilitated by our method, particularly in enhancing the writing efficiency of optical storage.

Holo-U2Net for High-Fidelity 3D Hologram Generation.

Traditional methods of hologram generation, such as point-, polygon-, and layer-based physical simulation approaches, suffer from substantial computational overhead and generate low-fidelity holograms. Deep learning-based computer-generated holography demonstrates effective performance in terms of speed and hologram fidelity. There is potential to enhance the network's capacity for fitting and modeling in the context of computer-generated holography utilizing deep learning methods. Specifically, the ability of the proposed network to simulate Fresnel diffraction based on the provided hologram dataset requires further improvement to meet expectations for high-fidelity holograms. We propose a neural architecture called Holo-U2Net to address the challenge of generating a high-fidelity hologram within an acceptable time frame. Holo-U2Net shows notable performance in hologram evaluation metrics, including an average structural similarity of 0.9988, an average peak signal-to-noise ratio of 46.75 dB, an enhanced correlation coefficient of 0.9996, and a learned perceptual image patch similarity of 0.0008 on the MIT-CGH-4K large-scale hologram dataset.

Frequency domain method for wide angle computer generated hologram

In this work, we propose a novel computational approach to point-cloud wide-angle computer-generated hologram (WA-CGH), which is based on the spatial frequency representation of a spherical wave and, unlike other approaches, the process of updating the object’s geometry information is done in the frequency domain. Using this frequency domain method (FDM), a WA-CGH can be synthesized with both retained high accuracy and increased computational efficiency. FDM is analyzed using phase space, which proves the sparsity of the algorithm. Moreover, this analysis shows that the sparsity and corresponding performance of the algorithm increases with the viewing angle. The presented evidence shows that the FDM can accurately and efficiently calculate holograms with FoV in the range of 60°–100° and for 4 K, 8 K and 16 K resolutions of large and highly detailed 3D objects.

Absolute testing of rotationally symmetric surfaces with computer-generated holograms

Extremely high accuracy is demanded for optics working at very short wavelength. Interferometric testing of optical aspheres or freeform surfaces requires null optics, typically computer-generated holograms (CGHs), to balance the wave aberrations. The measurement uncertainty is primarily limited by the accuracy of the test wavefront, which is predominantly influenced by the CGH and the interferometer optics. Absolute testing is fundamental to achieving accuracy much higher than that of the test wavefront through error separation. This paper presents a method for absolute testing of rotationally symmetric surfaces with CGH null optics. The basic assumption is that the off-axis hologram fabricated by raster scanning beam writing has negligible error of rotationally symmetric component due to pattern error of the CGH. Consequently, the wavefront error contributed by the CGH and the transmission flat can be completely separated from the absolute surface shape by combining the N-position method and the shift-rotation method. A theoretical model for absolute testing is proposed under the assumption. Experimental cross test is then presented to validate the method with sub-nanometer uncertainty. The assumption is further confirmed by characterizing the fabrication error of the hologram structures using a white light interferometer. Finally, the effect of noise, translation error, rotation error and eccentricity of rotation on the absolute testing is analyzed.

Tailoring an arbitrary large vectorial structured light beam array utilizing the tensor theory of multiplexed polarization holograms

Vectorial structured light beams, characterized by their topological charge and non-uniform polarization distribution, are highly promising beam modes for several applications in different domains of optics and photonics. To harness its potential specifically in optical communication, data encryption, and optical trapping, it is necessary to tailor a multitude of these beams with arbitrary and large topological charge and polarization distribution. However, achieving the above-mentioned requires bulky optical setups that necessitate the superposition of two beams or involve complex material fabrication techniques that can directly generate these beams. In this paper, we report the generation of a large structured light beam array by utilizing multiplexed polarization holograms, computer-generated holography, and azo-carbazole polymer film. We have developed a theoretical framework for double-exposure polarization holography that enables the possibility of tailoring such a vectorial light beam array. Utilizing the developed theory, we showcase the experimental generation of a structured vector beam array of size 8 × 8 with arbitrary topological charges and polarization distribution in 3 mm × 3 mm area of the polymer film. Exploiting the large space bandwidth of the polymer film, we also demonstrate the generation of vector vortex beam arrays with exceptionally large topological charges (l=100). All the above has been experimentally realized by simply illuminating the hologram with a plane Gaussian beam, and no additional optics are needed. This reported method offers huge potential and opens up new possibilities for the utilization of vectorial structured light beams.

Fast calculation of a cylindrical hologram by a preloaded stochastic gradient descent with skip connection

Cylindrical holography has received widespread attention due to its unique 360° viewing zone. To achieve commercial quality requirements, introducing stochastic gradient descent (SGD) is a potential approach for computer-generated cylindrical holography (CGCH). However, SGD applied to CGCH suffers from both slow convergence speed and unstable convergence, severely impacting its application. To address these issues, a preloaded SGD method with skip connection is proposed for fast calculation of cylindrical holograms in this paper. Preloaded-SGD (PSGD) exhibits a significant enhancement in convergence speed compared to the conventional SGD. Furthermore, the skip connection prevents oscillations from occurring by directly connecting the input and output, which is highly beneficial for obtaining high-quality holograms in the later stages of convergence. Numerical simulations demonstrate the effectiveness of our proposed method. PSGD with skip connection(SC-PSGD) achieves a 6.3-fold acceleration over conventional SGD. Notably, our proposed method has broad application prospects in cylindrical holographic displays and 3D displays.

High-security holographic display with content and copyright protection based on complex amplitude modulation

The computer-generated hologram provides an approach to modulate the coherent wavefront and has been widely applied in holographic displays. In the actual application, holograms need to be transmitted through the network, which results in the illegal acquisition and malicious manipulation of holographic images. Therefore, it is necessary to develop a practical method to protect the content and copyright of holographic images. In this paper, we develop a high-security holographic display method based on complex amplitude modulation. In our proposed method, the complex hologram of a holographic image is decomposed into two phase-only holograms, one of which is designed as the ciphertext, and the other is regarded as the key. As a result, the holographic image can be reconstructed only when the ciphertext and the key are paired, which boosts the security of the holographic image. Meanwhile, the copyright of the holographic image is protected via a watermark that is embedded in the ciphertext in the form of a hologram. Due to the simultaneous use of encryption and watermark technology, our proposed method could transmit holographic images at a high security level, and has great potential to be applied in holographic displays in the future.

Facile fabrication of THz metasurfaces by a spatially shaped femtosecond laser printing system

Terahertz (THz) metasurfaces provide unprecedented abilities to realize versatile THz wavefronts manipulations. Nevertheless, these high degree of freedom, non-periodic, densely arranged subwavelength unit cells pose numerous extreme parameter requirements for the fabrication of metasurfaces, presenting significant challenges to their practical application. Herein, a spatial shaping femtosecond laser printing system, based on spatial light modulation (SLM), is proposed for the creation of THz metasurfaces. Through programming the SLM with a sequence of computer-generated holograms (CGH) corresponding to C-shaped Bessel beams with varying opening angles and orientation angles, the C-shaped slit resonant rings with different geometric parameters—fundamental units of the metasurface—were precisely printed onto a gold film. To validate this technique, a THz metalens based on a phased gradient design and a THz holographic plate employing simultaneous phase and amplitude modulation were meticulously fabricated, displaying outstanding performance. Owing to the simple processing flow, high reproducibility, and wide applicability of materials, this technique stands out as a versatile and efficient approach for fabricating THz metasurfaces, with the potential to promote the commercialization of terahertz metasurfaces.

Holographic Parallax Improves 3D Perceptual Realism

Holographic near-eye displays are a promising technology to solve long-standing challenges in virtual and augmented reality display systems. Over the last few years, many different computer-generated holography (CGH) algorithms have been proposed that are supervised by different types of target content, such as 2.5D RGB-depth maps, 3D focal stacks, and 4D light fields. It is unclear, however, what the perceptual implications are of the choice of algorithm and target content type. In this work, we build a perceptual testbed of a full-color, high-quality holographic near-eye display. Under natural viewing conditions, we examine the effects of various CGH supervision formats and conduct user studies to assess their perceptual impacts on 3D realism. Our results indicate that CGH algorithms designed for specific viewpoints exhibit noticeable deficiencies in achieving 3D realism. In contrast, holograms incorporating parallax cues consistently outperform other formats across different viewing conditions, including the center of the eyebox. This finding is particularly interesting and suggests that the inclusion of parallax cues in CGH rendering plays a crucial role in enhancing the overall quality of the holographic experience. This work represents an initial stride towards delivering a perceptually realistic 3D experience with holographic near-eye displays.

Design framework of a computer-generated hologram that performs volumetric beam shaping for advanced laser processing

Axial beam shaping is very effective for material laser processing, typically laser cutting, drilling, and grooving. We demonstrate a framework for designing a computer-generated hologram (CGH) that performs volumetric beam shaping. The procedure performs axial beam shaping with a continuous intensity distribution, unlike our previous research in which only discrete focal points were arranged three-dimensionally. This research is the more general approach for volumetric beam shaping. An important point in this research is finding an optimal interval in the optical axis direction and in calculating the CGH design. The design interval is half of the focusing length (the full width at half-maximum of the laser beam profile in the axial direction) given by the diffraction limit of the optical system. The optimal value is obtained using an axially shaped beam that is the reconstruction of the CGH calculated from Zernike polynomials. We also demonstrate that the optimal interval for evaluating the axially shaped beam is also half of the beam length. Following the CGH design procedure, we demonstrate CGHs that generate long-focus beams with an arbitrary axially shaped beam. We found a tradeoff relation between the focusing length and the intensity of the long-focus beam, suggesting that the use of a focused beam with an appropriate length according to the purpose will lead to improved processing efficiency.

Substrate calibration method of a computer-generated hologram based on ray propagation in a three-dimensional model.

In interferometry with a computer-generated hologram (CGH), the substrate error of the CGH limits its high-precision aspheric measurement application. The propagation form of the substrate error is still ambiguous although 0th-order calibration can partly correct it. We established the ray propagation in a three-dimensional model in order to solve the ambiguity of substrate error propagation. This method shows the modulation process of the CGH substrate error on the transmitted wavefront for the first time, until now, to the best of our knowledge. The experiments show that the propagation of the substrate error can be accurately analyzed, and the CGH design efficiency also is significantly improved after applying this method.

Adaptive phase control of a phase-only spatial light modulator using the Shack-Hartmann wavefront sensor

We present a method to study both static and dynamic phase errors in a phase-only spatial light modulator (SLM) caused by surface irregularities and an imperfect response of each pixel to the applied field. This, in turn, degrades optical reconstruction, particularly in holographic projection applications. The approach uses the Shack-Hartmann wavefront sensor (SHWFS) to measure these errors. A plane wave illuminates the SLM, and the reflected wavefront is measured by the SHWFS and converted into a phase-only computer-generated hologram (CGH). This CGH is displayed on the SLM to compensate for phase errors, which are verified by subsequent wavefront measurements. Experimental results demonstrate the simplicity, robustness to vibration, and real-time capabilities of the SHWFS in contrast to interferometric methods.

Real-Time High-Quality Computer-Generated Hologram Using Complex-Valued Convolutional Neural Network.

Holographic displays are ideal display technologies for virtual and augmented reality because all visual cues are provided. However, real-time high-quality holographic displays are difficult to achieve because the generation of high-quality computer-generated hologram (CGH) is inefficient in existing algorithms. Here, complex-valued convolutional neural network (CCNN) is proposed for phase-only CGH generation. The CCNN-CGH architecture is effective with a simple network structure based on the character design of complex amplitude. A holographic display prototype is set up for optical reconstruction. Experiments verify that state-of-the-art performance is achieved in terms of quality and generation speed in existing end-to-end neural holography methods using the ideal wave propagation model. The generation speed is three times faster than HoloNet and one-sixth faster than Holo-encoder, and the Peak Signal to Noise Ratio (PSNR) is increased by 3 dB and 9 dB, respectively. Real-time high-quality CGHs are generated in 1920 × 1072 and 3840 × 2160 resolutions for dynamic holographic displays.

Adaptive non-iterative histogram-based hologram quantization

Quantization is widely used for compression, storage, transmission and display of computer-generated and digital holograms. It reduces number of hologram gradations to obtain better ratio of the quality of reconstructed 2D and 3D objects to the size of holographic images or videos. This paper proposes 2 methods of non-iterative quantization of holograms: adaptive non-uniform quantization based on histogram processing with peak shift (ANHS method) and additional application of logarithmic companding (ANHSL method). They were compared with 4 methods of iterative and non-iterative quantization on holograms with sizes up to 2048 × 2048 pixels. The proposed methods showed the best reconstruction quality that is higher up to 59 % in comparison with non-iterative uniform quantization. Especially the proposed methods give higher quality at little number of hologram gradations (from 2 to 16 gradations). In comparison with the most qualitative iterative methods (Lloyd-Max and k-means) the quality is increased up to 9 %, and processing time is reduced in 10–1000 times.

Image optimization of a computer-generated hologram by reusing zero-order beams and reflectors vibration.

In computer-generated holography, spatial light modulators are predominantly used for image reconstruction. However, the quality of the reconstructed images is often compromised by laser speckle and zero-order light diffraction. To address these problems, we propose the reuse of the zero-order beam, which not only eliminates the interference caused by zero-order diffraction in the reconstructed images but also considerably enhances image brightness. Moreover, we propose the use of vibrating reflectors in the proposed structure for reusing the zero-order beam to reduce speckle, thereby suppressing the speckle contrast in reconstructed images to less than 4%.