Hologram Generation Research Articles

Learning-based compensation of spatially varying aberrations for holographic display [Invited

We propose a hologram generation technique to compensate for spatially varying aberrations of holographic displays through machine learning. The image quality of the holographic display is severely degraded when there exist optical aberrations due to misalignment of optical elements or off-axis projection. One of the main advantages of holographic display is that aberrations can be compensated for without additional optical elements. Conventionally, computer-generated holograms for compensation are synthesized through a point-wise integration method, which requires large computational loads. Here, we propose to replace the integration with a combination of fast-Fourier-transform-based convolutions and forward computation of a deep neural network. The point-wise integration method took approximately 95.14 s to generate a hologram of 1024×1024pixels, while the proposed method took about 0.13 s, which corresponds to ×732 computation speed improvement. Furthermore, the aberration compensation by the proposed method is verified through experiments.

Holographic display with optical computational Fresnel convolution to broaden distance.

As a method of near-field diffraction in the condition of the paraxial approximation, the Fresnel convolution (FR-CV) method is widely used in hologram generation and other applications. However, it is applicable to near-field diffraction, and the quality of holographic reconstruction degrades seriously with the increase of diffraction distance. Moreover, its hologram generation speed is limited due to the use of three fast Fourier transforms in the convolution operation. Nevertheless, there are also many application scenarios that need longer distance diffraction. To achieve a holographic display in broadened distance with high generation speed and reconstruction quality, an optical computational Fresnel convolution method is proposed in this paper. Since an optical Fourier lens is used to perform optical calculations for Fourier transforms in our proposed method, the hologram generation speed of the proposed method is approximately 8 times faster than that of the FR-CV method. Moreover, the reconstructed image with our proposed method can be successfully and clearly displayed at both short and longer diffraction distance by changing focal lengths of the Fourier lens. The effectiveness and superiority of the proposed method have been validated by both numerical simulations and optical experiments.

Theoretical and practical aspects of the design and production of synthetic holograms for transmission electron microscopy

Beam shaping—the ability to engineer the phase and the amplitude of massive and massless particles—has long interested scientists working on communication, imaging, and the foundations of quantum mechanics. In light optics, the shaping of electromagnetic waves (photons) can be achieved using techniques that include, but are not limited to, direct manipulation of the beam source (as in x-ray free electron lasers and synchrotrons), deformable mirrors, spatial light modulators, mode converters, and holograms. The recent introduction of holographic masks for electrons provides new possibilities for electron beam shaping. Their fabrication has been made possible by advances in micrometric and nanometric device production using lithography and focused on ion beam patterning. This article provides a tutorial on the generation, production, and analysis of synthetic holograms for transmission electron microscopy. It begins with an introduction to synthetic holograms, outlining why they are useful for beam shaping to study material properties. It then focuses on the fabrication of the required devices from theoretical and experimental perspectives, with examples taken from both simulations and experimental results. Applications of synthetic electron holograms as aberration correctors, electron vortex generators, and spatial mode sorters are then presented.

Recent Advances in Development of Fast Algorithms for Computed Hologram Generation Using Wavefront Recording Plane Technique

Recent Advances in Development of Fast Algorithms for Computed Hologram Generation Using Wavefront Recording Plane Technique

Distortion correction for wide angle holographic projector

This letter presents distortion correction method enabling distortion minimized, large size image in wide angle holographic projector. The technique applies numerical predistortion of an input image used for hologram generation. It is based on estimation of distortion coefficients by comparing optically reconstructed point test chart with the original one. Obtained experimental results prove that the technique allows reconstruction of high-quality image. Full Text: PDF ReferencesM. Makowski, Experimental Aspects of Holographic Projection with a Liquid-Crystal-on-Silicon Spatial Light Modulator, in Holographic Materials and Optical Systems, M. Kumar, ed. (IntechOpen, 2019). CrossRef H. Pang, A. Cao, W. Liu, L. Shi, and Q. Deng, "Effective method for further magnifying the image in holographic projection under divergent light illumination", Appl. Opt. 58, 8713 (2019). CrossRef Y. Qi, C. Chang, and J. Xia, "Speckleless holographic display by complex modulation based on double-phase method", Opt. Express 24, 30368 (2016). CrossRef E. Buckley, "Holographic Laser Projection", J. Display Technol. 99, 1 (2010). DirectLink M. Chlipała, T. Kozacki, H. Yeom, J. Martinez-Carranza, R. Kukołowicz, J. Kim, J. Yang, J. Choi, J. Pi, and C. Hwang, "Wide angle holographic video projection display", Opt. Lett. 46, 4956 (2021). CrossRef Z. He, X. Sui, L. Cao and G. Jin, "Image-Distortion Correction Algorithm for Computer-Generated Holographic Display," 2018 IEEE 27th International Symposium on Industrial Electronics (ISIE), 1331 (2018). CrossRef A. Kaczorowski, G.S. Gordon, A. Palani, S. Czerniawski and T.D. Wilkinson, "Optimization-Based Adaptive Optical Correction for Holographic Projectors", J. Display Technol. 11(7), 596 (2015). CrossRef Z. He, X. Sui, G. Jin, L. Cao, "Distortion-Correction Method Based on Angular Spectrum Algorithm for Holographic Display", IEEE Trans. Industr. Inform. 15, 6162 (2019). CrossRef O. Mendoza-Yero, G. Mínguez-Vega, and J. Lancis, "Encoding complex fields by using a phase-only optical element", Opt. Lett. 39, 1740 (2014). CrossRef T. Kozacki, K. Falaggis, "Angular spectrum method with compact space–bandwidth: generalization and full-field accuracy", Appl. Opt. 55, 5014 (2016). CrossRef

Improved phase multiplexing using iterative and non-iterative hologram generation

In this work, we demonstrate how an adequate selection of hologram generation methods can lead to improved phase-only multiplexing. In particular, we show that the multiplexing of phase-only holograms is not a phase-only function, which means that amplitude truncation is required after multiplexing for applications involving phase-only modulation. This truncation produces a loss of quality. We demonstrate that this loss depends on the method used to generate the individual holograms to be multiplexed. Additionally, we evaluate the phase multiplexing performance of three iterative and non-iterative hologram generation methods, namely the one-step phase retrieval (OSPR), the iterative Fresnel algorithm (IFrTA), and the optimized Fresnel random phase (OFRAP). We make use of entropy metrics to analyze the amplitude obtained after multiplexing the phase holograms generated with these methods. To show the possible applications of our analysis for the generation of 3D scenes, the multiplexing is performed for two cases: in the first, all holograms have the same reconstruction plane, and in the second, the multiplexed holograms have different reconstruction planes. Our results show that the reconstruction obtained by multiplexing holograms generated with the IFrTA is more affected by the loss of amplitude information than the OFRAP result. In this way, we demonstrate that the use of OFRAP leads to better phase-only multiplexing performance compared to IFRTA or OSPR. To support our conclusions, we perform numerical reconstructions and corroborate these results with experimental reconstructions achieved with a phase-only SLM.

Non-iterative phase hologram generation for color holographic display.

The major challenges in traditional color phase hologram generation are the time-consuming iterative procedure and aberration caused by different wavelengths in color holographic display. Based on the original non-iterative phase hologram generation method-optimized random phase (ORAP), combined with the physical limitations of color holographic display, this paper proposes a full-support optimized random phase (FS-ORAP) method for non-iterative color phase hologram generation. FS-ORAP breaks through the limitation of the original ORAP method in the fixed support constraint of the target amplitude in the spatial domain, the full support constraint can be used to generate phase holograms of target amplitudes with arbitrary support size, which fits well with the generation mode of the three-color channel of the color phase hologram. In addition, the color aberration of the reconstructed image is eliminated by scaling the size of the three-color component. At the same time, FS-ORAP is used for the non-iterative fast generation of three-color channel holograms, which can greatly improve the generation speed of color phase holograms and can be adapted to various color holographic display techniques. Experimental results verify the feasibility of our proposed method.

Curved hologram generation method for speckle noise suppression based on the stochastic gradient descent algorithm

In this paper, a curved hologram generation method with suppressed speckle noise is proposed. In the process of generating the curved hologram, the angle spectrum method is used to calculate the 3D object in layers. By analyzing the loss function relationship between the diffraction image of the curved hologram and the target light field, the loss function is calculated. The phase of the hologram is updated based on the stochastic gradient descent algorithm, thereby obtaining the optimal phase distribution of the curved hologram. When the curved hologram is reproduced at different bending center angles, the reconstructed image of the corresponding angle can be seen. The proposed method has obvious advantages compared with the error diffusion method and Fresnel diffraction algorithm. The feasibility of the proposed method is verified by the experiments.

Faster generation of holographic video of 3-D scenes with a Fourier spectrum-based NLUT method.

In this article, a new type of Fourier spectrum-based novel look-up table (FS-NLUT) method is proposed for the faster generation of holographic video of three-dimensional (3-D) scenes. This proposed FS-NLUT method consists of principal frequency spectrums (PFSs) which are much smaller in size than the principal fringe patterns (PFPs) found in the conventional NLUT-based methods. This difference in size allows for the number of basic algebraic operations in the hologram generation process to be reduced significantly. In addition, the fully one-dimensional (1-D) calculation framework of the proposed method also allows for a significant reduction of overall hologram calculation time. In the experiments, the total number of basic algebraic operations needed for the proposed FS-NLUT method were found to be reduced by 81.23% when compared with that of the conventional 1-D NLUT method. In addition, the hologram calculation times of the proposed method, when implemented in the CPU and the GPU, were also found to be 60% and 66% faster than that of the conventional 1-D NLUT method, respectively. It was also confirmed that the proposed method implemented with two GPUs can generate a holographic video of a test 3-D scene in real-time (>24f/s).

Comparison of state-of-the-art Computer Generated Holography algorithms and a machine learning approach

This work studies the use of machine learning and, in particular, a Convolutional Neural Network (CNN) to generate digital holograms and how such a network compares to state-of-the-art iterative methods, both in terms of reconstruction quality and computation time. Since CNNs only require a single pass through the network by a target image to generate a result, and not tens or hundreds of expensive iterations as in the iterative methods, they may be able to accomplish real-time hologram generation; an ability that could open the technology to proper commercial use.In this work, a CNN built on the UNet architecture, capable of hologram generation, is presented. The network is trained on 4096 images of varying spatial frequencies, both user-generated and from the DIV2K dataset. It is compared to the most common iterative method for hologram generation, namely the Gerchberg–Saxton (GS) algorithm and its modern and improved implementations. In reconstruction quality, the neural network outperforms the original implementation of GS when evaluating Mean Square Error (MSE), geometric error (GE), Structural Similarity Index Measurement (SSIM), and Peak Signal-Noise Ratio (PSNR) of 64 unseen test images. However, on the same test images, the network lacks behind the modern, optimized GS implementations in all error and accuracy measurements. The network does, however, achieve these results at a rate 70–280 times faster than the iterative methods, depending on the particular implementation of the GS algorithm, which corresponds to a possible generation rate of the network of 32 FPS on average.

Alternative constraints for improved multiplane hologram generation.

In this work, we introduce a modified hologram plane constraint to improve the accuracy of the global Gerchberg-Saxton (GGS) algorithm used for multiplane phase-only hologram generation. This constraint consists of a modified phase factor that depends on the amplitude of the field in the hologram plane. We demonstrate that this constraint produces an increase in the mean correlation coefficient between the reconstructed planes from a multiplane hologram and the corresponding amplitude targets for each plane. Furthermore, this constraint can be applied together with a mixed constraint in the reconstruction planes, leading to a more uniform and controllable reproduction of a target intensity distribution. To confirm the validity of our proposal, we show numerical and experimental results for multiplane holograms with six discrete planes, using both high and low contrast targets. For the experimental results, we implement a holographic projection scheme based on a phase-only spatial light modulator.

Wide angle holographic video projection display.

Holographic projection displays provide high diffraction efficiency. However, they have a limited projection angle. This work proposes a holographic projection display with a wide angle, which gives an image of size 306mm×161mm at 700 mm and reduced speckle noise. The solution uses single Fourier lens imaging with a frequency filter and hologram generation utilizing complex coding and nonparaxial diffraction. The experiment was performed with a 4K phase-only spatial light modulator (SLM) to prove the high efficiency of the developed numerical tools. Optical reconstruction shows high resolution and high image quality achieved from a single frame. Hence, displaying video at a full frame rate of the SLM is possible.

HoloGen: An open-source toolbox for high-speed hologram generation

The rise of virtual and augmented reality systems has prompted an increase in interest in the fields of 2D and 3D computer-generated holography (CGH). The numerical processing required to generate a hologram is high and requires significant domain expertise. This has historically slowed the adoption of CGH in emerging fields.In this paper we introduce HoloGen, an open-source Cuda C and ▪ framework for computer-generated holography. HoloGen unites, for the first time, a wide array of existing hologram generation algorithms with state of the art performance while attempting to remain intuitive and easy to use. This is enabled by a ▪ and Windows Presentation Framework (WPF) graphical user interface (GUI). A novel reflection based parameter hierarchy is used to ensure ease of modification. Extensive use of ▪ templates based on the Standard Template Library (STL), compile time flexibility is preserved while maintaining runtime performance.The current release of HoloGen unites implementations of well known generation algorithms including Gerchberg-Saxton (GS), Liu-Taghizadeh (LT), direct search (DS), simulated annealing (SA) and one-step phase-retrieval (OSPR) with less known specialist variants including weighted GS and Adaptive OSPR.Benchmarking results are presented for several key algorithms. The software is freely available under an MIT license. Program summaryProgram title: HoloGen v2.2.1.17177CPC Library link to program files:https://doi.org/10.17632/nzk4swwsrg.1Developer's repository link:https://gitlab.com/CMMPEOpenAccess/HoloGenLicensing provisions: MITProgramming language: Cuda, ▪, ▪External packages: Cuda, ManagedCuda, MathNet, Newtonsoft.Json, NUnit, AForge, Accord, ClosedXML, CefSharp, PdfiumViewer, Xceed, NHotkey, SharpDX, MaterialSkin, Xamarin.forms, HelixToolkit, Dragablz, LiveCharts, MahAppsNature of problem: Hologram generation for two-dimensional Fourier and Fresnel holograms displayed on amplitude or phase modulating spatial light modulators with binary or multi-level controlSolution method: Algorithmic variants including Gerchberg-Saxton, Liu-Taghizadeh, Direct Search, Simulated Annealing and One-Step Phase-Retrieval. Includes real-time reporting, batch processing and complex field manipulationAdditional comments include restrictions and unusual features: Graphical user interface only exposes access to two-dimensional hologram generation. Includes a novel reflection based parameter hierarchy for ease of modification.

Deep-learning-based hologram generation using a generative model.

We propose a new learning and inferring model that generates digital holograms using deep neural networks (DNNs). This DNN uses a generative adversarial network, trained to infer a complex two-dimensional fringe pattern from a single object point. The intensity and fringe patterns inferred for each object point were multiplied, and all the fringe patterns were accumulated to generate a perfect hologram. This method can achieve generality by recording holograms for two spaces (16 Space and 32 Space). The reconstruction results of both spaces proved to be almost the same as numerical computer-generated holograms by showing the performance at 44.56 and 35.11 dB, respectively. Through displaying the generated hologram in the optical equipment, we proved that the holograms generated by the proposed DNN can be optically reconstructed.

Large field-of-view holographic display by gapless splicing of multisegment cylindrical holograms.

A holographic three-dimensional (3D) display is a recognized and ideal 3D display technology. In the field of holographic research, cylindrical holography with the merit of 360° field of view (FOV) has recently become a hot issue, as it naturally solves the problem of limited FOV in planar holography. The recently proposed approximate phase compensation (APC) method successfully obtains larger FOV and fast generation of segment cylindrical hologram (SCH) in the visible light band. However, the FOV of SCH remains limited due to its intrinsic limitations, and, to our best knowledge, the issue has not been effectively addressed. In this paper, the restricted conditions are first analyzed for the generation of SCH by the APC method. Then, an FOV expansion method is proposed for realizing a large FOV holographic display by gapless splicing of multi-SCH. The proposed method can successfully obtain larger FOV cylindrical holograms and effectively eliminate the splicing gaps; its effectiveness is verified by the results of numerical simulation and optical experiments. Therefore, the proposed method can effectively solve the FOV limitation problem of the APC method for the generation of SCH in the visible band, realize a large FOV 3D display, and provide a useful reference for holographic 3D display.

Deep learning for hologram generation

This work exploits deep learning to develop real-time hologram generation. We propose an original concept of introducing hologram modulators to allow the use of generative models to interpret complex-valued frequency data directly. This new mechanism enables the pre-trained learning model to generate frequency samples with variations in the underlying generative features. To achieve an object-based hologram generation, we also develop a new generative model, named the channeled variational autoencoder (CVAE). The pre-trained CVAE can then interpret and learn the hidden structure of input holograms. It is thus able to generate holograms through the learning of the disentangled latent representations, which can allow us to specify each disentangled feature for a specific object. Additionally, we propose a new technique called hologram super-resolution (HSR) to super-resolve a low-resolution hologram input to a super-resolution hologram output. Combining the proposed CVAE and HSR, we successfully develop a new approach to generate super-resolved, complex-amplitude holograms for 3D scenes.

Three-Dimensional (3D) Printing Implemented by Computer-Generated Holograms for Generation of 3D Layered Images in Optical Near Field

Photocurable three-dimensional (3D) printing is a stepwise layer-by-layer fabrication process widely used in the manufacture of highly specialized objects. Current 3D printing techniques are easily implemented; however, the build rate is slow and the surface quality is less than ideal. Holographic 3D display (3DHD) technology makes it possible to reform planar wavefronts into a 3D intensity distribution, which appears as a 3D image in space. This paper examined the application of holographic imaging technology to 3D printing based on photocurable polymers. The proposed system uses a 3DHD diffractive optics system based on a liquid-crystal-on-silicon spatial light modulator (LCoS-SLM), wherein a 3D layered image is created in the optical near field, based on a computer-generated hologram (CGH) optimized using the iterative angular spectrum algorithm (IASA) and a circular IASA. From a single CGH, multiple 2D sliced images are created in space to form a 3D optical image used to initiate the photopolymerization of photocurable resin to form 3D objects. In experiments, the proposed 3D printing system was used to create five polymer objects with a maximum axial length of 25 mm and minimum feature width of 149 μm. The phase-only CGH reformed the incident light into a distribution of optical intensity with high diffraction efficiency suitable for photocuring. Despite limitations pertaining to fabrication area and axial complexity in this initial study, the proposed method demonstrated high light efficiency, high resolution in the lateral direction, rapid fabrication, and good object continuity.

Computing 3D Phase-Type Holograms Based on Deep Learning Method

Computer holography is a technology that use a mathematical model of optical holography to generate digital holograms. It has wide and promising applications in various areas, especially holographic display. However, traditional computational algorithms for generation of phase-type holograms based on iterative optimization have a built-in tradeoff between the calculating speed and accuracy, which severely limits the performance of computational holograms in advanced applications. Recently, several deep learning based computational methods for generating holograms have gained more and more attention. In this paper, a convolutional neural network for generation of multi-plane holograms and its training strategy is proposed using a multi-plane iterative angular spectrum algorithm (ASM). The well-trained network indicates an excellent ability to generate phase-only holograms for multi-plane input images and to reconstruct correct images in the corresponding depth plane. Numerical simulations and optical reconstructions show that the accuracy of this method is almost the same with traditional iterative methods but the computational time decreases dramatically. The result images show a high quality through analysis of the image performance indicators, e.g., peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and contrast ratio. Finally, the effectiveness of the proposed method is verified through experimental investigations.

Multifunctional wide-angle optics and lasing based on supercell metasurfaces

Metasurfaces are arrays of subwavelength spaced nanostructures that can manipulate the amplitude, phase, and polarization of light to achieve a variety of optical functions beyond the capabilities of 3D bulk optics. However, they suffer from limited performance and efficiency when multiple functions with large deflection angles are required because the non-local interactions due to optical coupling between nanostructures are not fully considered. Here we introduce a method based on supercell metasurfaces to demonstrate multiple independent optical functions at arbitrary large deflection angles with high efficiency. In one implementation the incident laser is simultaneously diffracted into Gaussian, helical and Bessel beams over a large angular range. We then demonstrate a compact wavelength-tunable external cavity laser with arbitrary beam control capabilities – including beam shaping operations and the generation of freeform holograms. Our approach paves the way to novel methods to engineer the emission of optical sources.

Fast generation of 360-degree cylindrical photorealistic hologram using ray-optics based methods.

Due to the large pixel pitch and limited size of spatial light modulator (SLM), the field of view (FOV) of current holographic display is greatly restricted. Cylindrical holography can effectively overcome the constraints of FOV. However, the existent algorithms of cylindrical hologram are all based on the wave-optics based approach. In this paper, to the best of our knowledge, we adopt the ray-optics based approach in the generation of cylindrical computer generated hologram (CCGH) for the first time. Information of parallax images captured from three-dimensional (3D) objects using a curved camera array is recorded into a cylindrical hologram. Two different recording specific algorithms are proposed, one is based on the Fast Fourier Transform (FFT) method, and another is based on the pinhole-type integral imaging (PII) method. The simulation results confirm that our proposed methods are able to realize a fast generation of the cylindrical photorealistic hologram.