Computer-generated Holograms Research Articles

Complex-valued generative adversarial network for real-time and high-quality computer-generated holography

Complex-valued generative adversarial network for real-time and high-quality computer-generated holography

Physics-aware cross-domain fusion aids learning-driven computer-generated holography

The rapid advancement of computer-generated holography has bridged deep learning with traditional optical principles in recent years. However, a critical challenge in this evolution is the efficient and accurate conversion from the amplitude to phase domain for high-quality phase-only hologram (POH) generation. Existing computational models often struggle to address the inherent complexities of optical phenomena, compromising the conversion process. In this study, we present the cross-domain fusion network (CDFN), an architecture designed to tackle the complexities involved in POH generation. The CDFN employs a multi-stage (MS) mechanism to progressively learn the translation from amplitude to phase domain, complemented by the deep supervision (DS) strategy of middle features to enhance task-relevant feature learning from the initial stages. Additionally, we propose an infinite phase mapper (IPM), a phase-mapping function that circumvents the limitations of conventional activation functions and encapsulates the physical essence of holography. Through simulations, our proposed method successfully reconstructs high-quality 2K color images from the DIV2K dataset, achieving an average PSNR of 31.68 dB and SSIM of 0.944. Furthermore, we realize high-quality color image reconstruction in optical experiments. The experimental results highlight the computational intelligence and optical fidelity achieved by our proposed physics-aware cross-domain fusion.

Unlocking mode programming with multi-plane light conversion using computer-generated hologram optimisation

Abstract Programmable optical devices provide performance enhancement and flexibility to spatial multiplexing systems enabling transmission of tributaries in high-order eigenmodes of spatially-diverse transmission media, like multimode fibre (MMF). Wavefront shaping with spatial light modulators (SLMs) facilitates scalability of the transmission media by allowing for channel diagonalization and quasi-single-input single-output operation. Programmable mode multiplexing configurations like multi-plane light conversion (MPLC) utilise the SLM and offer the potential to simultaneously launch an arbitrary subset of spatial tributaries in any N -mode MMF. Such programmable optical processor would enable the throughput of space-division multiplexing (SDM) systems to be progressively increased by addressing a growing number of tributaries over one MMF and in this way meet a growing traffic demand – similarly to the wavelength-division multiplexing evolution path. Conventionally, MPLC phasemasks are calculated using the wavefront matching algorithm (WMA). However, this method does not exploit the full potential of programmable mode multiplexers. We show, that computer-generated hologram algorithms like direct search enable significant improvement compared to the traditional WMA-approach. Such gains are enabled by tailored cost functions with dynamic constraints concerning insertion loss as wellas mode extinction ratio. We show that average mode extinction ratio can be greatly improved by as much as ≈ 15 dB at the expense of a small insertion loss35
deterioration of < 3 dB. One particular feature of programmable mode multiplexers is the adaptability to optimised transmission functions. Besides conventional LP modes transmission, we employ our approach on Schmidt modes, which are spatial eigenchannels with minimum crosstalk derived from a measured transmission matrix

Generating high-quality phase-only holograms of binary images using global loss and stochastic homogenization training strategy

Deep learning presents a highly effective for computer-generated holography (CGH). However, existing learning-based CGH algorithms may encounter significant obstacles in generating high-quality holograms for binary images. This study proposes a novel diffraction model-driven neural network, termed load sharing yielding holography (LSY-Holo), which leverages a dual-branch architecture and a global structural similarity index measure (Global_SSIM) loss function to generate phase-only holograms (POHs). LSY-Holo framework facilitates capturing global information, enhancing the network’s performance to address the ill-posed inverse problem. To further optimize the model for binary images, the research introduces a custom Binary dataset alongside a stochastic homogenization preprocessing method (SHPM), which mitigates the prevalent issue of excessive noise in reconstructed images. Additionally, this deep learning approach is integrated with an iterative algorithm, which employs holograms rapidly generated by LSY-Holo as the initial phase of the AdamW Holography (AH) algorithm. This strategy significantly accelerates the convergence of the iterative process. LSY-Holo is further extended to 3D scenes, enabling dynamic defocusing and focusing effects at varying depths. Results from numerical simulations and full-color optical reconstruction experiments demonstrate that the proposed method can enhance image quality and effectively reduce the artifacts in reconstructed images.

Computer-generated holography enables high-uniformity, high-efficiency depth-of-focus extension in endoscopic OCT

Computer-generated holography enables high-uniformity, high-efficiency depth-of-focus extension in endoscopic OCT

Research on Nanometer Precision Measurement Method of High Order Even Aspheres

Optical aspheres are demanded with extremely high precision to meet functional requirements in space telescopes, extreme ultraviolet lithography, and other modern large optical systems. The nano-precision fabrication of optical aspheres requires high-precision measurements to guide deterministic optical processing. Null test is the preferred method for high-precision measurements. Null optics are required to compensate for the incident wavefront in the null test of optical aspheres. However, wavefront aberrations caused by the transmission flat or transmission sphere of interferometer and null optics can limit measurement accuracy and need to be separated. A nano-precision measurement method is proposed for the even optical aspheres of high order in this paper. A computer-generated hologram is used as a null optic to realize a null test on optical aspheres. Mapping distortion correction is performed on the measurement results to ensure that the transverse coordinates of the measurement results correspond correctly to those of the test surface. Absolute testing is applied to separate the wavefront aberrations caused by the computer-generated hologram and interferometer optics. Finally, the results obtained by this method were used to guide deterministic optical processing, enabling the nano-precision fabrication of optical aspheres.

A Versatile Image Encryption Scheme Based on Optical Hologram Technology and Chess Rules

A novel versatile image encryption scheme about hologram technology and chess rules is proposed in this paper. This scheme can encrypt images by transferring them from the spatial domain to the frequency domain. First, the theory of computer-generated holograms is applied to record phase and amplitude features by imitating the optical hologram. The original image is transformed to a hologram and the phase values of the points in the image are recorded. Second, the parameters associated with the plaintext image are obtained by a Hash function and used as the initial values of the chaotic system, and then the pawns on the board are regarded as pixel points of the image, where the movement direction of the pawns is the movement direction of the pixel points of the image. The hologram is confused by combining the pawns’ movement rules with the chaotic sequences. Finally, the encrypted image is gained through a combination of the chaotic sequence and the selective diffusion method. The test results show that the scheme is able to resist various attacks and has good security performance in encryption.

Quantized neural network for complex hologram generation

Computer-generated holography (CGH) is a promising technology for augmented reality displays, such as head-mounted or head-up displays. However, its high computational demand makes it impractical for implementation. Recent efforts to integrate neural networks into CGH have successfully accelerated computing speed, demonstrating the potential to overcome the trade-off between computational cost and image quality. Nevertheless, deploying neural-network-based CGH algorithms on computationally limited embedded systems requires more efficient models with lower computational cost, memory footprint, and power consumption. In this study, we developed a lightweight model for complex hologram generation by introducing neural network quantization. Specifically, we built a model based on tensor holography and quantized it from 32-bit floating-point precision (FP32) to 8-bit integer precision (INT8). Our performance evaluation shows that the proposed INT8 model achieves hologram quality comparable to that of the FP32 model while reducing the model size by approximately 70% and increasing the speed fourfold. Additionally, we implemented the INT8 model on a system-on-module to demonstrate its deployability on embedded platforms and high power efficiency.

Three-dimensional computer holography with phase space tailoring

Computer holography is a prominent technique for reconstructing customized three-dimensional (3D) diffraction fields. However, the quality of optical reconstruction remains a fundamental challenge in 3D computer holography, especially for the 3D diffraction fields with physically continuous and extensive depth range. Here, we propose a 3D computer-generated hologram (CGH) optimization framework with phase space tailoring. Based on phase space analysis of the space and frequency properties in both lateral and axial directions, the intensity of the 3D diffraction field is adequately sampled across a large depth range. This sampling ensures the reconstructed intensity distribution to be comprehensively constrained with physical consistency. A physics-informed loss function is constructed based on the phase space tailoring to optimize the CGH with suppression of vortex stagnation. Numerical and optical experiments demonstrate the proposed method significantly enhances the 3D optical reconstructions with suppressed speckle noise across a continuous and extensive depth range.

Hybrid Refractive and Diffractive Testing Method for Free-Form Convex Mirror in High-Resolution Remote-Sensing Cameras

The development of high-resolution and large field of view remote-sensing cameras is inextricably linked to the application of free-form mirrors. The free-form mirror offers higher design of freedom and is more effective at correcting aberrations in optical systems. The surface shape error of a free-form mirror directly affects the imaging quality of remote-sensing cameras. Consequently, a high-precision free-form mirror detection method is of paramount importance. For the convex free-form surface mirror with a large aperture, a hybrid refractive and diffractive testing method combining computer-generated holography (CGH) and spherical mirrors for high-precision null test is proposed in this paper. When comparing the effect of error and the detection sensitivity of different designs, the results showed that the influence of the system error is reduced by about 42% and the sensitivity is increased by more than 2.6 times. The proposed method can achieve higher testing accuracy and represents an effective and feasible approach for the surface shape detection method.

Multiple-image authentication method based on phase-only holograms and a logistic map

An interesting security method for a multiple-image authentication scheme is proposed based on computer-generated holograms and a logistic map. First, each original image is encoded as the complex-valued hologram under the point light source model. The resulting hologram is then converted to a phase-only hologram using the Floyd-Steinberg dithering algorithm. Second, each phase-only hologram is randomly sampled with the aid of a binary mask. Through the catenation of all selected pixels, a phase-only pixel sequence is formed. Finally, a non-periodic and non-converging sequence generated with the logistic map is used to scramble this sequence. After only preserving the phase data of the scrambled sequence, the real-valued ciphertext carrying the information of all original images is obtained. In the process of authentication, although no valid information can be discerned from noisy reconstructed images at a small sampling rate, the verification of original images can be efficiently accomplished using the nonlinear correlation maps. Besides binary masks, the parameters of the logistic map are served as secret keys. Due to their high sensitivity, the security of the proposed method is greatly enhanced. The proposed authentication mechanism has been demonstrated to be effective and robust through experiments. To our knowledge, it is the first time to implement multiple-image authentication using phase-only holograms, which can provide a new perspective for optical information security.

Speckle-free holography with a diffraction-aware global perceptual model

Computer-generated holography (CGH) based on neural networks has been actively investigated in recent years, and convolutional neural networks (CNNs) are frequently adopted. A convolutional kernel captures local dependencies between neighboring pixels. However, in CGH, each pixel on the hologram influences all the image pixels on the observation plane, thus requiring a network capable of learning long-distance dependencies. To tackle this problem, we propose a CGH model called Holomer. Its single-layer perceptual field is 43 times larger than that of a widely used 3×3 convolutional kernel, thanks to the embedding-based feature dimensionality reduction and multi-head sliding-window self-attention mechanisms. In addition, we propose a metric to measure the networks’ learning ability of the inverse diffraction process. In the simulation, our method demonstrated noteworthy performance on the DIV2K dataset at a resolution of 1920×1024, achieving a PSNR and an SSIM of 35.59 dB and 0.93, respectively. The optical experiments reveal that our results have excellent image details and no observable background speckle noise. This work paves the path of high-quality hologram generation.

Positioning of the test surface in a CGH null test by cat's eye interference

Interferometric null test of optical aspheres and freeforms is one of the most established methods, in spite of recognized limitations related to positioning of the test surface. Slight misalignment of the surface in the null test system can introduce remarkable wave aberrations. Current approaches for positioning the test surface are based on a series of fiducial marks or retroreflectors set at given spots around the test surface, which consequently suffer the problem of datum transformation. We propose a method for positioning the test surface in a null test by cat's eye interference without any fiducial marks or retroreflectors. A computer-generated hologram (CGH) is used as null optics fabricated with null test pattern, alignment pattern and positioning pattern. A part of test beam with relatively small f/number is diffracted through the positioning pattern and then focuses on certain spots of the test surface. The cat's eye reflection from the test surface returns to the interferometer and interferes with the reference beam. It is then possible to precisely position the test surface by measuring the wavefront error of the cat's eye interference. The design method for such a CGH positioning pattern is presented, following the physical constraint that the surface normal at the cay's eye reflection is right the angular bisector of the positioning beam. Analysis on the positioning performance is then presented to show the sensitivity to misalignment including defocus, lateral shift and tip-tilt, which at last is experimentally verified by measuring an even asphere with a CGH.

High-quality and high-speed computer-generated holography via deep-learning-assisted bidirectional error diffusion method

Computer-generated holography (CGH) is an effective light field manipulation technique based on diffractive optics. Deep learning provides a promising way to break the trade-off between quality and speed in the phase-only hologram (POH) generation process. In this paper, a neural network called BERDNet is proposed for high-quality and high-speed POH generation. A high-quality POH dataset without speckle noise and shifting noise is generated by the band-limited bidirectional error diffusion (BERD) algorithm. Based on the dataset, BERDNet is trained to learn the potential hologram coding method for real-time POH prediction. Furthermore, the training process is constrained by both data loss and physical loss, so it is necessary to explore higher-fidelity reconstructions that are more consistent with the bandwidth limitation. Finally, the POHs of numerical reconstructions with an average of 23.13 dB PSNR can be obtained in 0.037 s, achieving 1-2 orders of magnitude acceleration. Experimental reconstructions validated the generalization of the BERDNet.

Finite-element Adaptive Meshing Statistics of Liquid Crystal Coaxial Phase Shifters for mmW Electronics and THz Photonics Beyond Display: A Comparative Study

Sub-mmW and THz frequencies offer ultra-high-speed communications for next-generation 5G/6G networks, wherein research advancing the understanding will benefit the electronics and photonics community. Specifically, meshing resolutions across varying frequency ranges and material properties are central to the solution accuracy, reliability, and cost (memory and time) of computational mmW and THz simulations, particularly for the emerging reconfigurable coaxial phase shifters employing nematic liquid crystals (LCs) as tunable media. In the present study, a comparative meshing statistics analysis is conducted for two devices designed for 60 GHz and 0.3 THz, respectively. Each design features two distinct tuning states (LC permittivity of 2.754 and 3.3, respectively), all pertinent to the coaxial TEM (Transverse Electromagnetic) mode. By quantifying the broadband meshing and solution statistics of diverse frequencies and dielectric tuning states for the first time, we establish memory-conserving computational metrology involving reconfigurable coaxial devices operationalized with LC-filled tunable dielectrics tailored for mmW electronics and THz photonics. Full Text: PDF References M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, A. Kowalczyk, "Performance of the 4k phase-only spatial light modulator in image projection by computer-generated holography", Phot. Lett. Poland 8, 1 (2016). CrossRef J.F. Li, H.R. Li, "Liquid Crystal-Filled 60 GHz Coaxially Structured Phase Shifter Design and Simulation with Enhanced Figure of Merit by Novel Permittivity-Dependent Impedance Matching", Electronics 13, 3 (2024). CrossRef J.F. Li, H.R. Li, "Modeling 0.3 THz Coaxial Single-Mode Phase Shifter Designs in Liquid Crystals with Constitutive Loss Quantifications", Crystals 14, 4 (2024). CrossRef J.F. Li, D.P. Chu, "Liquid Crystal-Based Enclosed Coplanar Waveguide Phase Shifter for 54–66 GHz Applications", Crystals 9, 12 (2019). CrossRef Z. Cendes, "The development of HFSS", USNC-URSI Radio Science Meeting (Fajardo, IEEE 2016). CrossRef T. Vaupel, "Accuracy And Modeling Improvements For An Integral Equation Framework Applied To Thin Layer Microstrip And Substrate Integrated Waveguide (Siw) Structures", EuCAP (Copenhagen, IEEE 2020). CrossRef L.J. Jiang, W.C. Chew, "Low-frequency fast inhomogeneous plane-wave algorithm (LF-FIPWA)", Microwave Opt. Tech. Lett. 40, 2 (2004). CrossRef J. Zhu, D. Jiao, "Eliminating the Low-Frequency Breakdown Problem in 3-D Full-Wave Finite-Element-Based Analysis of Integrated Circuits", IEEE Trans. Microw. Theory Tech. 58, 10 (2010). CrossRef

Interpolation-Filtering Method for Image Improvement in Digital Holography

Digital holography is actively used for the characterization of objects and 3D-scenes, tracking changes in medium parameters, 3D shape reconstruction, detection of micro-object positions, etc. To obtain high-quality images of objects, it is often necessary to register a set of holograms or to select a noise suppression method for specific experimental conditions. In this paper, we propose a method to improve filtering in digital holography. The method requires a single hologram only. It utilizes interpolation upscaling of the reconstructed image size, filtering (e.g., median, BM3D, or NLM), and interpolation to the original image size. The method is validated on computer-generated and experimentally registered digital holograms. Interpolation methods coefficients and filter parameters were analyzed. The quality is improved in comparison with digital image filtering up to 1.4 times in speckle contrast on the registered holograms and up to 17% and 29% in SSIM and NSTD values on the computer-generated holograms. The proposed method is convenient in practice since its realization requires small changes of standard filters, improving the quality of the reconstructed image.

CGH calculation algorithm for expressing reflection on a curved mirror surface

Rendering techniques are important in computer-generated holograms (CGHs) for expressing various types of holo-realistic 3D images. Rendering techniques such as hidden surface removal and reflection by a planar mirror have been proposed thus far, but reflection on a curved mirror surface has yet to be achieved. In this study, we propose a calculation algorithm that can express the reflection of the surrounding environment on a mirror surface defined as a Bézier surface. The results of optical experiments demonstrate that the proposed algorithm enables reflection on such a mirror surface and that the calculation can be accelerated by using a graphics processing unit (GPU).

Frequency aware high-quality computer-generated holography via multilevel wavelet learning and channel attention.

Deep learning-based computer-generated holography offers significant advantages for real-time holographic displays. Most existing methods typically utilize convolutional neural networks (CNNs) as the basic framework for encoding phase-only holograms (POHs). However, recent studies have shown that CNNs suffer from spectral bias, resulting in insufficient learning of high-frequency components. Here, we propose a novel, to our knowledge, frequency aware network for generating high-quality POHs. A multilevel wavelet-based channel attention network (MW-CANet) is designed to address spectral bias. By employing multi-scale wavelet transformations, MW-CANet effectively captures both low- and high-frequency features independently, thus facilitating an enhanced representation of high-frequency information crucial for accurate phase inference. Furthermore, MW-CANet utilizes an attention mechanism to discern and allocate additional focus to critical high-frequency components. Simulations and optical experiments confirm the validity and feasibility of our method.

High-speed arbitrary pure phase hologram generation method based on a specific multi-phase

This paper presents a novel design method, to the best of our knowledge, for the creation of computer-generated holograms (CGHs) with arbitrary phases based on a specific multi-phase. This approach combines the design, production, and fabrication of holographic phase structures and requires only their assembly according to specific phase values. The arrangement of eight different specific phase values enables the production of 2D and 3D holograms comparable in quality to random phase holograms obtained through optimized Gerchberg–Saxton (GS) algorithms and requires only one-sixth of the computational time. The results of simulations and experiments indicate that this method provides a convenient approach to designing, processing, manufacturing, and reproducing high-quality phase holograms. It has the potential for widespread use in holography.

Rapid hologram generation through backward ray tracing and adaptive-resolution wavefront recording plane

Abstract An advanced method for rapidly computing holograms of large three-dimensional (3D) objects combines backward ray tracing with adaptive resolution wavefront recording plane (WRP) and adaptive angular spectrum propagation. In the initial phase, a WRP with adjustable resolution and sampling interval based on the object’s size is defined to capture detailed information from large 3D objects. The second phase employs an adaptive angular spectrum method (ASM) to efficiently compute the propagation from the large-sized WRP to the small-sized computer-generated hologram (CGH). The computation process is accelerated using CUDA and OptiX. Optical experiments confirm that the algorithm can generate high-quality holograms with shadow and occlusion effects at a resolution of 1024 × 1024 in 29 ms.