Computer-generated Holograms Research Articles

A perspective on twisted light from on-chip devices

Twisted light, with spatially varying phase or polarization, has given rise to various applications, such as micro-particle manipulation, optical communication, and quantum information processing. In recent decades, to bring these applications into reality, various configurations such as conventional spiral phase plates, computer-generated holograms, metasurface-based setups, and on-chip devices have been explored for twisted light generation. In this Perspective, we focus on recent progress in generation twisted light from typical on-chip devices such as waveguides, plasmonic nanoslits, whispering gallery mode configurations, and meta-gratings. We aim at highlighting the key research advances and technical challenges in on-chip twisted light generation. Finally, we outlook the likely future trend of this emerging research field.

Benchmarking analysis of computer generated holograms for complex wavefront shaping using pixelated phase modulators.

Wavefront shaping with spatial light modulators (SLMs) enables aberration correction, especially for light control through complex media, like biological tissues and multimode fibres. High-fidelity light field shaping is associated with the calculation of computer generated holograms (CGHs), of which there are a variety of algorithms. The achievable performance of CGH algorithms depends on various parameters. In this paper, four different algorithms for CGHs are presented and compared for complex light field generation. Two iterative, double constraint Gerchberg-Saxton and direct search, and the two analytical, superpixel and phase encoding, algorithms are investigated. For each algorithm, a parameter study is performed varying the modulator's pixel number and phase resolution. The analysis refers to mode field generation in multimode fibre endoscopes and communication. This enables generality by generating specific mode combinations according to certain spatial frequency power spectra. Thus, the algorithms are compared varying spatial frequencies applied to different implementation scenarios. Our results demonstrate that the choice of algorithms has a significant impact on the achievable performance. This comprehensive study provides the required guide for CGH algorithm selection, improving holographic systems towards multimode fibre endoscopy and communications.

Proximal Algorithms for Discrete-Level Phase-Shifting Mask Design with Application to Optogenetics

This work studies the problem of designing computer-generated holograms using phase-shifting masks limited to represent only a small number of discrete phase levels. This problem has various applications, notably in the emerging field of optogenetics and lithography. A novel regularized cost function is proposed for the problem at hand that penalizes the unfeasible phase levels. Since the proposed cost function is non-smooth, we derive proper proximal gradient algorithms for its minimization. Simulation results, considering an optogenetics application, demonstrate that the proposed proximal gradient algorithm yields better performance as compared to other algorithms proposed in the literature.

Holographic 3D Display Using Depth Maps Generated by 2D-to-3D Rendering Approach

Holographic display has the potential to be utilized in many 3D application scenarios because it provides all the depth cues that human eyes can perceive. However, the shortage of 3D content has limited the application of holographic 3D displays. To enrich 3D content for holographic display, a 2D to 3D rendering approach is presented. In this method, 2D images are firstly classified into three categories, including distant view images, perspective view images and close-up images. For each category, the computer-generated depth map (CGDM) is calculated using a corresponding gradient model. The resulting CGDMs are applied in a layer-based holographic algorithm to obtain computer-generated holograms (CGHs). The correctly reconstructed region of the image changes with the reconstruction distance, providing a natural 3D display effect. The realistic 3D effect makes the proposed approach can be applied in many applications, such as education, navigation, and health sciences in the future.

Acceleration of polygon-based computer-generated holograms using look-up tables and reduction of the table size via principal component analysis.

In this study, we first analyze the fully analytical frequency spectrum solving method based on three-dimensional affine transform. Thus, we establish a new method for combining look-up tables (LUTs) with polygon holography. The proposed method was implemented and proved to be accelerated about twice compared to the existing methods. In addition, principal component analysis was used to compress the LUTs, effectively reducing the required memory without artifacts. Finally, we calculated very complex objects on a graphics processing unit using the proposed method, and the calculation speed was higher than that of existing polygon-based methods.

Diffractive Sensor Elements for Registration of Long-Term Instability at Writing of Computer-Generated Holograms.

The research and development of methods using of the specialized diffractive microstructure sensors embedded in the pattern of computer-generated holograms (CGH) manufactured on circular and X-Y laser writing systems is discussed. These microstructures consist of two parts: one of which is written before the CGH in the field of future hologram and the second one is written during the long-term writing of the CGH. The shift between the first and second part of the microstructure is the trace of the writing errors and allows one to determine and calculate the error of CGH fabrication along both orthogonal coordinates. The developed method is based on the principle of diffraction-based overlay with 1D and 2D built-in diffractive microstructure-sensors. Mathematical modeling and results of experimental test writings of such diffractive microstructure sensors are described. The efficiency of using these types of build-in sensors for the writing errors estimation for CGHs is demonstrated.

Kaczmarz holography: holographic projection in the Fraunhofer region

The Kaczmarz algorithm is an iterative method for solving linear equations in the form of Ax = b. It is widely used in computed tomography and digital signal processing (DSP) but has yet to be adopted in computer-generated holography. Phase retrieval algorithms, such as Gerchberg–Saxton or Fienup, are significantly more popular in this field. However, we propose a unique and alternative approach to projecting a replay field through discrete Fourier transform matrices and have shown that there are legitimate benefits to implementing this approach. The gradient descent iteration mechanism adopted by Kaczmarz, for instance provides finer granularity control over the individual pixels in the replay field. We consequently demonstrate the quality of the image is significantly improved when compared with Gerchberg–Saxton.

Single-shot higher-order transport-of-intensity quantitative phase imaging using deep learning.

Single-shot higher-order transport-of-intensity quantitative phase imaging (SHOT-QPI) is proposed to realize simple, in-line, scanless, and single-shot QPI. However, the light-use efficiency of SHOT-QPI is low because of the use of an amplitude-type computer-generated hologram (CGH). Although a phase-type CGH overcomes the problem, the accuracy of the measured phase is degraded owing to distortion of the defocused intensity distributions, which is caused by a quantization error of the CGH. Alternative SHOT-QPI with the help of deep learning, termed Deep-SHOT, is proposed to solve a nonlinear problem between the distorted intensities and the phase. In Deep-SHOT, a neural network learns the relationship between a series of distorted intensity distributions and the ground truth phase distribution. Because the distortion of intensity distributions is intrinsic to an optical system, the neural network is optimized for the system, and the proposed method improves the accuracy of the measured phase. The results of a proof-of-principle experiment indicate that the use of multiple defocused intensities also improves accuracy, even the nonlinear problem.

Optimization of computer-generated holograms featuring phase randomness control.

In this Letter, we introduce a computer-generated hologram (CGH) optimization technique that can control the randomness of the reconstructed phase. The phase randomness significantly affects the eyebox size and depth of field in holographic near-eye displays. Our proposal is to synthesize the CGH through the sum of two terms computed from the target scene with a random phase. We set a weighting pattern for summation as the optimization variable, which enables the CGH to reflect the random phase during optimization. We evaluate the proposed algorithm on single-depth and multi-depth contents, and the performance is validated via simulations and experiments.

Speckleless color dynamic three-dimensional holographic display based on complex amplitude modulation.

In this paper, we propose a method to implement a speckleless color dynamic three-dimensional holographic display by modulating amplitude and phase distribution simultaneously. Computer-generated holograms are calculated with an initial uniform phase, and the speckle noise of reconstructed images is suppressed effectively. We perform both numerical simulations and optical experiments to demonstrate the effectiveness of the proposed method. The numerical simulations show that the proposed method can achieve speckleless reconstruction and the optical experiments provide a good color dynamic display effect. It is expected that the proposed method could be widely applied to realize high-quality color dynamic holographic displays in the future.

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.

Holographic Near-Eye 3D Display Method Based on Large-Size Hologram

In this paper, we propose a holographic near-eye 3D display method based on large-size computer-generated hologram (CGH). The reconstructed image with a large viewing angle is obtained by using a time multiplexing and spatial tiling system. The large-size CGHs are generated and they record the information of the 3D object from different angles. The CGHs are reproduced at different moments. For a certain reconstructed moment, three spatial light modulators (SLMs) spatially spliced into a linear structure are used to load a single CGH. The diffraction boundary angle of the reconstructed light forming each image point is equal to the maximum diffraction angle of the SLM, so the viewing angle of the image generated by the CGH is enlarged. For different CGHs, the incident angle of reconstructed light is changed. Through time multiplexing, the reconstructed images of the CGHs are combined into a reconstructed image whose viewing angle is further enlarged. Due to the large viewing angle of the reconstructed image, the proposed method has unique advantages in near-eye display. The feasibility of the proposed method is proved by experimental results.

Two-step acceleration calculation method to generate curved holograms using the intermediate plane in a three-dimensional holographic display.

Nowadays, curved computer-generated holograms are widely applied to increase the field of view. However, heavy computational load restricts the development of curved computer-generated holograms. In this paper, we propose a two-step acceleration calculation method to generate curved holograms by using the intermediate plane, which is placed between the object and a curved computer-generated hologram. The first step is the calculation of the intermediate plane by an improved accurate highly compressed lookup-table method. In the second step, we execute diffraction calculation from the intermediate plane to obtain a curved computer-generated hologram. Numerical simulations and optical experiments are performed to demonstrate that the proposed method is an efficient method for reducing calculation time. Additionally, the increase of field of view using a curved hologram is also numerically demonstrated. It is expected that our method can be combined with a curved display screen to realize three-dimensional holographic displays in the future.

Performance Estimation of Intensity Accumulation Display by Computer-Generated Holograms

The image generated by binary computer-generated holograms (CGHs) always suffers from serious speckle noise. Thanks to the fast frame rate of the binary spatial light modulator, the speckle can be significantly suppressed by intensity accumulation, i.e., the sequential display of multiple CGHs of the same scene. If enough randomness is added to the CGHs, the speckle noise can be mostly averaged out. Intuitively, the quality of the reconstructed image should be proportional to the number of intensity accumulation. However, there is no simple method to predict the dependence of the average noise and accumulation number, and we can only know the results after finishing the full computation. In this paper, we propose an empirical formula of the average noise based on the speckle phenomenon in a laser projector. Using this model, we have confirmed that the randomness induced by random phase is equivalent to that induced by random down-sampling for the generation of binary CGHs. In addition, if the computational efficiency is a concern, the CGH calculated with iterations is not recommended for intensity accumulation display. Finally, there is an upper-quality limit of the reconstructed image by intensity accumulation. Thus, a strategy for efficient intensity accumulation is suggested.

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.

Tailoring Ince-Gaussian arrays based on a computer-generated hologram.

The continually expanding interest in Ince-Gaussian modes has arisen due to their highly complex and widely varying spatial structures, which allow these fascinating diverse light modes to be significant to various topics. In this paper, we propose a technique for generating beam arrays that contain four Ince-Gaussian modes. By utilizing a single digital hologram, the intensity distributions of each mode in the array can be manipulated independently and flexibly. This work provides a feasible method to realize the controllable multiplexing of Ince-Gaussian modes, which has potential application in numerous important areas.

Fast calculation of computer generated hologram based on single Fourier transform for holographic three-dimensional display

We present an efficient method for the fast calculation of computer generated hologram (CGH). The 3D object is split into sub-layers according to its depth information. A 2D all-in-focus image is generated by sequential tiling all the layers in one plane. A Fourier hologram that contains all the information of 3D object is calculated from the fast Fourier transform (FFT) of the reassembled 2D image. By multiplying a pre-calculated multifocal off-axis digital phase mask (DPM) to the Fourier hologram, the content of each layer is axially relocated to different depth in the Fourier transform optical system to reconstruct the 3D object. The computation speed of the proposed method is greatly improved with only single FFT calculation process. Both of simulation and experimental results proves the validation of the proposed method.

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.

Computer-Generated Hologram Based on Reference Light Multiplexing for Holographic Display

In this article, we propose a reference light wave multiplexing scheme to increase the information capacity of computer-generated holograms. The holograms were generated by different reference light waves and superimposed together as a multiplexed hologram. A modified Gerchberg–Saxton algorithm was used to improve image quality, and different images could be reconstructed when the multiplexed hologram was illuminated by corresponding reference light waves. We performed both numerical simulations and optical experiments to demonstrate the feasibility of the proposed scheme. Numerical simulations showed that the proposed method could reconstruct multiple images successfully by a single multiplexed hologram and optical experiments are consistently good with numerical simulations. It is expected that the proposed method has great potential to be widely applied in holographic displays in the future.

Distortion mapping correction in the AIMS primary mirror testing by a computer-generated hologram

The National Solar Observatory is currently developing the Accurate Infrared Magnetic Field Measurements of the Sun (AIMS). The primary mirror of the AIMS solar telescope is an off-axis parabolic with a diameter of 1 m and with a large off-axis amount of 1 m. Due to the surface figure of the primary mirror under the used state is directly related to image quality of the whole system, a computer-generated hologram (CGH) is carried out to test the primary mirror, and the test results are used to polish the mirror to a higher surface accuracy. However, the fact that the distortion exists in the testing results leads to the failure of a further guide to deterministic optical processing. In this paper, a distortion correction method is proposed, which uses an orthogonal set of vector polynomials to mapping the coordinates of the mirror and the pixels of fringes, and then an interpolation method is adopted to obtain the corrected results. The testing accuracy by using CGH is also verified by an auto-collimate test experiment. According to the distorted corrected results, the root-mean-square of the surface figure is about 1/50λ (λ = 632.8 nm) after polishing.