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The Maxwellian display presents always-focused images to the viewer, alleviating the vergence-accommodation conflict (VAC) in near-eye displays (NEDs). However, the limited eyebox of the conventional Maxwellian display prevents it from wider applications. In this paper, an exebox-extended holographic Maxwellian near-eye display is proposed by using a real grating and a virtual grating. A diffraction grating is used to duplicate multiple beams and produce duplicate viewpoints. A virtual grating phase is added in the hologram to steer the beams and deflect the viewpoints. The proposed method combines a slight steering with a large duplicated eyebox, realizing that the viewpoint position can be flexibly controlled. The optical experiment realizes a 49.2° FOV and 12.1 mm eyebox which contains 5 moveable viewpoints. This proposed system shows good display capabilities and has potential applications. • The proposed method combines a slight steering with a large duplicated eyebox, realizing that the viewpoint position can be flexibly controlled. • The optical experiment realizes a 49.2° FOV and 12.1 mm eyebox which contains 5 moveable viewpoints. [ABSTRACT FROM AUTHOR]

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. • Greatly improving the optimization speed of spherical computer holography. • Pre-compensation balances the numerical range of diffraction results enhancing the efficiency of the optimizer. • Easier to overcome local minima during the optimization process. • Applying simulated annealing gradient descent to the optimization of holograms. [ABSTRACT FROM AUTHOR]

In order to suppress the interference of speckle noise on the quality of hologram an attention-wavelet residual denoising network based on multi-level wavelet convolutional neural network is proposed. Firstly, the phase-only hologram is input into the network, and the wavelet transform of the shrinkage subnet is used instead of pooling to reduce the size of the hologram and expand the receptive field. Secondly, the attention-residual module which embeds the convolutional block attention module(CBAM) into the residual block is added to each layer of the network. The CBAM is used to capture the speckle noise of the hologram more accurately, and to improve the fusion capability of network feature information through the residual block. Finally, the hologram after denoising is obtained by up-sampling in the extended subnet by inverse wavelet transform. Simulation experiments show that the improved network effectively removes speckle noise while obtaining high quality holograms. • Denoising of phase-only holograms by attentional wavelet residual networks. • Discrete wavelet transform embedded in convolutional neural networks. • Speckle interference fringing maps simulate phase-only holograms. • Convolutional Block Attention Module and Residual Block to improve noise extraction. [ABSTRACT FROM AUTHOR]

Future holographic displays will require high-resolution holograms ranging from several hundred gigabytes to several terabytes. Hologram computations using the Fresnel approximation have been proposed; however, they are effective only in paraxial regions and result in significant errors for high-resolution holograms. This study proposes a high-resolution hologram calculation method using the Pade approximations, which can significantly improve the accuracy of the phase calculation despite a slight increase in computational complexity compared with the Fresnel approximation. In this study, image holograms with resolutions ranging from 10K to 30K pixels were generated using the Fresnel and Pade approximations, and the computation time and image quality of the reproduced images were evaluated. The Pade Approximation served as an effective solution for obtaining large holograms of high quality and reasonable computational complexity. • High-fidelity hologram computation: the Pade approximation emerges as a robust method for achieving accurate hologram computations, ensuring precision in holographic imaging. • Effectiveness of Pade approximation: the Pade approximation stands out as a viable and efficient solution, particularly noteworthy for generating large holograms with enhanced quality, all while maintaining a reasonable level of computational complexity. • Optimal balance: a compelling aspect of the Pade approximation lies in its ability to strike an optimal balance between computational efficiency and holographic quality, making it a promising avenue for advanced hologram applications. [ABSTRACT FROM AUTHOR]

We propose an approach for simultaneously shaping multiple three dimensional (3D) vector curve beams. The intensity distribution and polarization state variation of each 3D vector curve beam can be tuned along arbitrary prescribed trajectories. The scheme is based on the coaxial superposition of the orthogonally polarized 3D base vector curve beams through non-iterative holographic 3D beam shaping technique. In particular, the hybrid 3D vector curve beams array is also generated with identical depth range. The transversal position of each vector beam can be governed independently. Moreover, the multiplexing of 3D vector beams is realized with different depth ranges in the focal region along the beam propagation. The numerical results are identical to the experiments. This method will be benefit to the trapping and transportation of particles. • A method of non-iterative holographic beam shaping for generating 3D vector curve beams along arbitrary trajectories. • Each individual 3D vector curve beam possesses tunable intensity and polarization state distribution. • Generation of multiple 3D vector curve beams in different depth range regions is experimentally investigated. [ABSTRACT FROM AUTHOR]

Abstract The addition of a random phase is widely utilised to diffuse object information in computer-generated hologram calculations. However, different object regions have nonuniform initial information diffusion abilities. The conventional random phase addition method always causes the excessive diffusion of information, especially for high frequency regions, which influences the reconstructed quality. In this paper, a gradient-limited random phase addition method is developed to avoid excessively diffusing object information. Herein, an image is segmented into two regions according to its frequency characteristics. Correspondingly, wide and narrow optimum ranges of a limited random phase are provided for low and high frequency regions, respectively. The numerical simulation results show that the peak signal-to-noise ratio and structural similarity index of reconstructed images increase by approximately 10% and 13%, respectively. The resolution of the reconstructed test image is improved by approximately 2 line pairs. Additionally, using in time-average method reduces the superposition number. Optical experiments are also performed to verify its feasibility. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a speckle noise suppression method employing time multiplexing in holographic display is proposed. The recorded object is separated into object point groups by pixel separation. For each object point group, some phase-only subcomputer-generated holograms (sub-CGHs) with independent initial random phases are generated. In the reconstruction process, a spatial light modulator (SLM) is used to load the sub-CGHs. The reconstructed image is generated through time multiplexing technology. Meanwhile, the speckle noise of the reconstructed image is reduced effectively by averaging the speckle noise and separating the adjacent image points in space. Compared with the pixel separation method, both simulation and optical experiments are carried out to confirm that the proposed method suppresses the speckle noise effectively with less computation burden. [ABSTRACT FROM AUTHOR]

Abstract Large three-dimensional (3D) scene reconstruction is a challenge for current colour holographic displays. In this study, we develop a compact display system to reconstruct a large 3D scene using a 21-inch liquid crystal display (LCD) panel that serves as a spatial light modulator (SLM). We utilise a Fresnel lens instead of a conventional lens to reduce the complexity of the system. A spatial multiplexing colour filter attached to the SLM is used to simplify the structure of the colour display. Additionally, an independent block holographic algorithm is developed to record accurate depth information. Numerical simulations and optical experiments are performed to verify the proposed system. The optically reconstructed 3D colour scene is 480 mm × 300 mm × 500 mm in size. Therefore, the proposed display system represents development toward a commercial product for its low device requirements. [ABSTRACT FROM AUTHOR]

Abstract A method of color holographic display from computer-generated cylindrical hologram (CGCH) based on radial-division is proposed. A single phase-only CGCH is calculated by using a multi-cylindrical surface (MCS) based iterative algorithm. This algorithm allows calculating a phase CGCH from red, green and blue components of a color object simultaneously. The radial distances for red, green and blue component objects are calculated according to the ratio of RGB wavelengths. When the hologram is illuminated by three laser beams of RGB colors, it can then reconstruct the wanted RGB components on the same radial position to obtain a color compound. Numerical simulation results demonstrate that simple 3D object can be reconstructed from single phase-only CGCH at the expected position. [ABSTRACT FROM AUTHOR]

In this paper, a projection-type dual-view holographic three-dimensional (3D) display consisting of a single spatial light modulator (SLM) and a grating light-guide plate is proposed and implemented. A synthetic phase-only hologram of two different 3D objects is calculated by the layer-based Fresnel diffraction method and uploaded onto the SLM for 3D reconstruction. A grating with special design and fabrication is used as the light-guide plate to re-direct the two reconstructed 3D images into the two separated viewing zones simultaneously. Optical experiments demonstrate that the proposed system can realize the function of dual-view holographic 3D display, and it can present 3D images to the human eye with sufficient depth cues, which enables the observers free of the accommodation-vergence conflict and visual fatigue problem. Furthermore, the proposed dual-view holographic 3D display system is applied to the see-through display for augmented reality (AR) applications, and the performance of this system is also tested in the experiments and the results show that the system can provide the dual-view AR 3D sensation successfully. [ABSTRACT FROM AUTHOR]

A new type of optical in-line holographic three-dimensional (3-D) video display system with omnidirectional viewing zones by using a center-symmetric multi-sideband filtering method is proposed. The frequency spectrum of the complex hologram is center-symmetrically divided into even numbers of multi-sidebands and partitioned into two groups by being alternately selected along the angular direction. One group corresponding to the conjugate image is filtered out in both of the digital-recording and optical-reconstruction processes with their specific filter masks. Then, from the other group, the real image, which can be viewed from almost all directions with a set of angularly-subdivided viewing zones, is reconstructed on the optical 4- f lens system without a conjugate image. Fourier-optical analysis and experiments with 3-D objects in motion confirm the feasibility of the proposed system. [ABSTRACT FROM AUTHOR]

We propose a method of efficiently calculating computer-generated hologram for holographic stereoscopic display. The stereoscopic hologram is generated by sequentially tiling all the hogels that are calculated from respective parallax intensity and depth maps based on nonuniform sampled wavefront recording plane (NS-WRP) algorithm. The whole computational procedure is simplified by diffraction calculation of hogels from 2D planar images of each viewpoint, instead of massive 3D point-source. Numerical and optical experiments are carried out to confirm the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

We propose a large-scale hologram calculation using WAvelet ShrinkAge-Based superpositIon (WASABI), a wavelet transform-based algorithm. An image-type hologram calculated using the WASABI method is printed on a glass substrate with the resolution of 65 , 536 × 65 , 536 pixels and a pixel pitch of 1 μ m. The hologram calculation time amounts to approximately 354 s on a commercial CPU, which is approximately 30 times faster than conventional methods. [ABSTRACT FROM AUTHOR]

We propose a fast calculation method for a computer-generated hologram (CGH) of real objects that uses a point cloud gridding method. The depth information of the scene is acquired using a depth camera and the point cloud model is reconstructed virtually. Because each point of the point cloud is distributed precisely to the exact coordinates of each layer, each point of the point cloud can be classified into grids according to its depth. A diffraction calculation is performed on the grids using a fast Fourier transform (FFT) to obtain a CGH. The computational complexity is reduced dramatically in comparison with conventional methods. The feasibility of the proposed method was confirmed by numerical and optical experiments. [ABSTRACT FROM AUTHOR]

Cylindrical computer-generated hologram is a promising approach to realize a display with 360°field of view. However, conventional cylindrical hologram employs an inside-out propagation model and suffers from two main drawbacks: limited object size and lack of effective reconstructed method. Previously, we proposed to fix these problems using an outside-in propagation model with reversed propagation direction of the inside-out model. We also derived corresponding diffraction calculation formula for the outside-in propagation model. In this work, we investigate a non-constant obliquity factor in the outside-in propagation model, and show that it is the projection of the unit complex amplitude in the propagation direction onto the outer normal of the observation point. We then propose to apply fast Fourier transform to accelerate the convolution operation needed for diffraction calculation. We conducted experiments on inverse diffraction and reconstruction of the cylindrical objects. Very encouraging results demonstrate the validity of this proposed approach. [ABSTRACT FROM AUTHOR]

We propose a method to calculate computer-generated hologram (CGH) from 3D object of arbitrary size and viewing angle. The spectrum relation between a 3D voxel object and the CGH wavefront is established. The CGH is generated via diffraction calculation from 3D voxel object based on the development of a scaled Fresnel diffraction algorithm. This CGH calculation method overcomes the limitations on sampling imposed by conventional Fourier transform based algorithm. The calculation and reconstruction of 3D object with arbitrary size and viewing angle is achieved. Both of simulation and optical experiments proves the validation of the proposed method. [ABSTRACT FROM AUTHOR]

Computer-generated hologram (CGH) is a promising 3D display technology while it is challenged by heavy computation load and vast memory requirement. To solve these problems, a depth compensating CGH calculation method based on symmetry and similarity of zone plates is proposed and implemented on graphics processing unit (GPU). An improved LUT method is put forward to compute the distances between object points and hologram pixels in the XY direction. The concept of depth compensating factor is defined and used for calculating the holograms of points with different depth positions instead of layer-based methods. The proposed method is suitable for arbitrary sampling objects with lower memory usage and higher computational efficiency compared to other CGH methods. The effectiveness of the proposed method is validated by numerical and optical experiments. [ABSTRACT FROM AUTHOR]

An improved polygon-based method is proposed for subwavelength pixel pitch computer generated holograms (CGHs). By employing the basic principle of image-plane holograms, and by optimizing the parameters, objects are reconstructed with high quality from the CGHs whose pixel pitch is smaller than wavelength. It is believed that the proposed method is potentially promising for future large viewing angle holographic 3D displays. [ABSTRACT FROM AUTHOR]

A method of calculating computer-generated hologram (CGH) for color holographic 3D projection is proposed. A color 3D object is decomposed into red, green and blue components. For each color component, a virtual wavefront recording plane (WRP) is established which is nonuniformly sampled according to the depth map of the 3D object. The hologram of each color component is calculated from the nonuniform sampled WRP using the shifted Fresnel diffraction algorithm. Finally three holograms of RGB components are encoded into one single CGH based on the multiplexing encoding method. The computational cost of CGH generation is reduced by converting diffraction calculation from huge 3D voxels to three 2D planar images. Numerical experimental results show that the CGH generated by our method is capable to project zoomable color 3D object with clear quality. [ABSTRACT FROM AUTHOR]

Limited-random-phase time average method is proposed to suppress the speckle noise of three dimensional (3D) holographic display. The initial phase and the range of the random phase are studied, as well as their influence on the optical quality of the reconstructed images, and the appropriate initial phase ranges on object surfaces are obtained. Numerical simulations and optical experiments with 2D and 3D reconstructed images are performed, where the objects with limited phase range can suppress the speckle noise in reconstructed images effectively. It is expected to achieve high-quality reconstructed images in 2D or 3D display in the future because of its effectiveness and simplicity. [ABSTRACT FROM AUTHOR]

Spherical holography can expand the viewing angle, while the unavailability of spherical spatial light modulators (SLM) and the huge sampling number are challenges for spherical holography. In this paper, we propose a spherical crown holographic display method based on planar SLM. First by analyzing the diffraction formula of concentric spheres, the relationship between it and the plane diffraction is found. Then it is proposed that a spherical hologram loaded on a commercial planar SLM can reproduce the target object correctly with a reasonable number of sampling points. The method can be combined with spatiotemporal multiplexing and curved multiplexing to further expand the viewing angle and information capacity, respectively. It provides a new perspective for spherical holography, and has broad prospects in the field of 3D holographic display. • A spherical crown holographic display method based on planar SLM. • The relationship between the model and the plane diffraction model is found. • Spatiotemporal and curved multiplexing for viewing angle and information capacity improvements. [ABSTRACT FROM AUTHOR]

We present a technique for generating three-dimensional (3-D) computer-generated holograms (CGHs) with realistic lighting effects based on a phase-only spatial light modulator (SLM). Phong reflection model is employed in the calculation of reflectance distribution for CGH synthesizing. Directional point-based algorithm produces realistic lighting effects of the 3-D scenes in processing the ambient, diffuse and specular reflections. A phase-only SLM is used to perform the optical experiments, and the results show that the proposed technique can perform quality reconstructions of the 3-D scenes with high optical efficiency and efficient utilization of the system space-bandwidth product. [ABSTRACT FROM AUTHOR]

This study proposes a gradient descent method for enhancing the quality of reconstructed images encoded by double-phase holograms (DPHs). Holographic displays are often noisy because of optical hardware problems. However, owing to the conversion from complex-amplitude holograms to phase-only holograms, the reconstructed images still have noise and cannot be ignored. In this paper, the proposed method uses a spectrum loss function instead of image loss function in the gradient descent optimization process. The spectrum loss function ensures that DPHs can be optimized by gradient descent method, and this method requires only several iterations. The simulations and experimental results have validated the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: By the multiple angular orthogonal projection images, a novel method for a straightforward computer-generated Fresnel hologram is demonstrated. With the angular orthogonal projection images at various viewpoints obtained from a computer designed three-dimensional object, an incoherent Fresnel hologram can be synthesized. After the shifted angular orthogonal projection images are multiplied by the constant phase factors and integrated, a two-dimensional complex matrix including three-dimensional information is achieved. The proposed Fresnel hologram is verified to be equivalent to an optical coherent Fresnel hologram. Since the diffraction and Fourier transform calculations are not necessary, the calculation complexity of the Fresnel hologram synthetic process can be greatly simplified. [Copyright &y& Elsevier]

Abstract: A novel method of three-dimensional computer-generated holographic algorithm based on conformal geometry theory was introduced. Firstly, three-dimensional object is transformed to a corresponding two-dimensional image via conformal transformation by making use of conformal geometry theory in mathematics, and then the Fresnel computer-generated hologram of the two-dimensional image is produced. During the reconstruction process, the three-dimensional reconstruction image of the original object is obtained by means of conformal coordinate transformation. The research results show that the algorithm introduced in this paper is characterized by fast running speed and good effects, providing a good reference for the research on three-dimensional computer-generated holographic algorithm. [Copyright &y& Elsevier]

A method of holographic reconstruction under partially spatial coherent illumination with different degree of coherence is proposed to suppress speckle noise based on theoretical analysis. The core factor of speckle reduction based on partially spatial coherent light is convolution operation in CGH reconstruction process. Numerical simulations and optical experiments are both performed to verify the proposed theory. The results reconstructed by proposed and traditional method are compared, and the speckle contrasts can be reduced to 0.05 and 0.08 at most in Fresnel and Fraunhofer zone respectively. The image quality is obviously improved. This method can provide further applications for three-dimensional holographic display, beam shaping and coherence degree modulation techniques. [ABSTRACT FROM AUTHOR]

We present two simple yet effective methods to realize holographic three-dimensional (3D) display by partitioned Fresnel diffraction (PFreD) and partitioned Fraunhofer diffraction (PFraD). After a 3D object is divided into a set of layers in axial direction, these layers are calculated into corresponding sub-holograms. These two methods are used to develop a tiling approach to hologram construction and reconstruction. Both simulations and experiments are carried out to verify the feasibility of the proposed methods. The similarities and differences between PFreD and PFraD are analyzed in details for better understanding. These two methods may provide promising solutions in future holographic 3D realization with their own characteristics and scope of application. • Two methods, PFreD and PFraD, have been proposed. • The methods are simple in 3D modeling and fast in calculation. • Comparison among four methods have been conducted. [ABSTRACT FROM AUTHOR]

We present a simple yet effective method to realize holographic three-dimensional (3D) display by optimizing arrangement of holograms. After a 3D object is divided into a set of layers in axial direction, these layers are calculated into corresponding sub-holograms by Fraunhofer diffraction. The hologram uploaded on SLM consists of sub-holograms side-by-side. Both simulations and experiments are carried out to verify the feasibility of the proposed method. The difference between Fresnel diffraction and Fraunhofer diffraction in the proposed method is analyzed. Aiming at the problems exposed in the experiments, reconstructed results are discussed and further improved by optimizing arrangement of sub-holograms. The process of 3D modeling is simple and the computational complexity is accordingly reduced. This method may provide a promising solution in future holographic 3D realization. [ABSTRACT FROM AUTHOR]