Computer-generated Holograms Research Articles

Smoothing of inter-layer edge artifacts in depth-map computer-generated holograms.

In the depth-map computer-generated hologram (CGH), inter-layer edge artifacts are observed in the discontinuous edges of section-wise depth-map objects. CGH synthesis, utilizing the hybrid smoothing method of silhouette masking and edge-apodization, alleviates unwanted inter-layer edge artifacts. The proposed method achieves improved de-artifact filtering that generates holographic images closer to the ground truth image of the depth-map object unattainable by the conventional CGH synthesis method.

Optimized computer-generated hologram for enhancing depth cue based on complex amplitude modulation.

In this Letter, we introduce a computer-generated hologram (CGH) optimization method to enhance the depth cue based on complex amplitude modulation (CAM). An iterative algorithm is designed to generate the optimized random phase (ORAP) according to the size of the target image and the bandwidth limitation condition. The ORAP with limited bandwidth is used as the initial phase of the target image and the hologram is encoded based on the analytical formula. Our proposal can maintain the advantages of CAM and achieve holographic three-dimensional (3D) display with an enhanced depth cue. It is expected that the proposed method could be widely used in holographic field in the future.

Flexible Method for Generating Arbitrary Vector Beams Based on Modified Off-Axis Interference-Type Hologram Encoding

A novel experimental setup for the generation of arbitrary vector beams is proposed. The system major includes two reflective liquid crystal spatial light modulators (RLC-SLM) and a polarizing beam splitting prism. Moreover, this method is not limited by the wavelength of light wave and the pixel size of SLM. Theoretical analysis shows that when Gaussian beam or a plane beam is illuminated on a computer-generated hologram (CGH) specially designed in this work, the complex amplitudes of the vector field’s two orthogonal polarization components may be changed by modifying the encoding parameters, resulting in a vector beam with arbitrary complex amplitude and polarization in the output field. The experimental results also show that the two independent coding channels of the device have good polarization-selective imaging ability, which greatly improves the flexibility of generating arbitrary vector beams.

Speckle-free compact holographic near-eye display using camera-in-the-loop optimization with phase constraint.

We present a compact holographic near-eye display system with high-quality speckle-free optical reconstructions using camera-in-the-loop (CITL) optimization with phase constraint strategy. The CITL optimization with phase constraint is used to iteratively synthesize the computer-generated holograms (CGHs) based on the in-system optical feedback. The phase constraint embedded into the whole CGH optimization process can effectively smooth the phase profile of reconstructed wave field, which helps to suppress the speckle noise caused by the phase singularities in CGH reconstruction. Numerical and optical experiments have been performed to demonstrate that the proposed method can provide speckle-free optical reconstructions with excellent image fidelity for holographic near-eye display in a compact setup.

Fast generation of arbitrary optical focus array

We report a novel method to generate arbitrary optical focus arrays (OFAs). Our approach rapidly produces computer-generated holograms (CGHs) to precisely control the positions and the intensities of the foci. This is achieved by replacing the fast Fourier transform (FFT) operation in the conventional iterative Fourier-transform algorithm (IFTA) with a linear algebra one, identifying/removing zero elements from the matrices, and employing a generalized weighting strategy. On the premise of accelerating the calculation speed by >70 times, we demonstrate OFA with 99% intensity precision in the experiment. Our method proves effective and is applicable to systems in which real-time OFA generation is essential.

Fabrication of 3D computer-generated hologram inside glass by femtosecond laser direct writing

The three-dimensional holography technique offers a powerful method for storing the depth information of objects, and it provides more realistic scene reconstruction compared with the two-dimensional case, so it is widely used in beam shaping, holographic display, and image encryption. However, the fabrication of holograms is currently limited to complex and time-consuming traditional nanofabrication techniques. Here, we demonstrate the fabrication of a hologram containing depth information inside glass using femtosecond laser direct writing. The whole process is simple and flexible because there is no complex operation like mask preparation. Then the reconstruction of the three-dimensional object is demonstrated and evaluated, and the experimental optimization as well as the limitations are also discussed.

Dynamic complex opto-magnetic holography

Despite recent significant progress in real-time, large-area computer-generated holography, its memory requirements and computational loads will be hard to tackle for several decades to come with the current paradigm based on a priori calculations and bit-plane writing to a spatial light modulator. Here we experimentally demonstrate a holistic approach to serial computation and repeatable writing of computer-generated dynamic holograms without Fourier transform, using minimal amounts of computer memory. We use the ultrafast opto-magnetic recording of holographic patterns in a ferrimagnetic film with femtosecond laser pulses, driven by the on-the-fly hardware computation of a single holographic point. The intensity-threshold nature of the magnetic medium allows sub-diffraction-limited, point-by-point toggling of arbitrarily localized magnetic spots on the sample, according to the proposed circular detour-phase encoding, providing complex modulation and symmetrical suppression of upper diffractive orders and conjugated terms in holographically reconstructed 3-D images.

A novel feed-forward neural network-based method for fast hologram generation

The enormous computing time is a challenge for computer-generated hologram (CGH) calculation in a holographic display. A learning-based method, hologram generation network (HGN), is proposed to accelerate CGH calculation. The method is a unique combination of point-source model and recent deep learning technique, showing how to obtain high-quality CGH quickly. HGN is a feed-forward neural network synthesized from different function blocks. The input of the network is a displacement tensor consisting of point clouds and hologram plane coordinates. The output is a holographic matrix whose column vector represents the coordinates of a single point hologram. The RBF network is then trained and tested by the numerical samples in the bounded field, thus the reconstruction quality of the CGH can be guaranteed strictly. Numerical simulation results show that HGN runs faster than the traditional method with high reconstruction accuracy. The optical experiments are performed to demonstrate its feasibility.

Diffraction model-informed neural network for unsupervised layer-based computer-generated holography.

Learning-based computer-generated holography (CGH) has shown remarkable promise to enable real-time holographic displays. Supervised CGH requires creating a large-scale dataset with target images and corresponding holograms. We propose a diffraction model-informed neural network framework (self-holo) for 3D phase-only hologram generation. Due to the angular spectrum propagation being incorporated into the neural network, the self-holo can be trained in an unsupervised manner without the need of a labeled dataset. Utilizing the various representations of a 3D object and randomly reconstructing the hologram to one layer of a 3D object keeps the complexity of the self-holo independent of the number of depth layers. The self-holo takes amplitude and depth map images as input and synthesizes a 3D hologram or a 2D hologram. We demonstrate 3D reconstructions with a good 3D effect and the generalizability of self-holo in numerical and optical experiments.

Dynamic Phase and Polarization Modulation Using Two-Beam Parallel Coding for Optical Storage in Transparent Materials.

In this paper, we propose and experimentally demonstrate a parallel coding and two-beam combining approach for the simultaneous implementation of dynamically generating holographic patterns at their arbitrary linear polarization states. Two orthogonal input beams are parallelly and independently encoded with the same target image information but there is different amplitude information by using two-phase computer-generated holograms (CGH) on two Liquid-Crystal-on-Silicon-Spatial-Light Modulators (LCOS SLMs). Two modulated beams are then considered as two polarization components and are spatially superposed to form the target polarization state. The final linear vector beam is created by the spatial superposition of the two base beams, capable of controlling the vector angle through the phase depth of the phase-only CGHs. Meanwhile, the combined holographic patterns can be freely encoded by the holograms of two vector components. Thus, this allows us to tailor the optical fields endowed with arbitrary holographic patterns and the linear polarization states at the same time. This method provides a more promising approach for laser data writing generation systems in the next-generation optical data storage technology in transparent materials.

Contribution to the Improvement of the Correlation Filter Method for Modal Analysis with a Spatial Light Modulator.

Modal decomposition of light is essential to study its propagation properties in waveguides and photonic devices. Modal analysis can be carried out by implementing a computer-generated hologram acting as a match filter in a spatial light modulator. In this work, a series of aspects to be taken into account in order to get the most out of this method are presented, aiming to provide useful operational procedures. First of all, a method for filter size adjustment based on the standard fiber LP-mode symmetry is presented. The influence of the mode normalization in the complex amplitude encoding-inherent noise is then investigated. Finally, a robust method to measure the phase difference between modes is proposed. These procedures are tested by wavefront reconstruction in a conventional few-mode fiber.

A digital hologram-based encryption and compression method for 3D models

This study proposes a novel method to compress and decompress the 3D models for safe transmission and storage. The 3D models are first extracted to become 3D point clouds, which would be classified by the K-means algorithm. Then, these nearby 3D point clouds are converted into a computer-generated hologram (CGH) by calculating the point distribution on the hologram plane using the optical wavefront propagation method. The computer-generated hologram (CGH) contains the spatial coordinate information on point clouds, which can be decompressed using the convolutional neural network (CNN) method. The decompression accuracy of 3D point clouds is quantitatively assessed by normalized correlation coefficients (NCCs), reflecting the correlation between two points and influenced by the hologram resolution, the convolution kernel, and the diffraction distance. Numerical simulations have shown that the novel method can reconstruct a high-quality 3D point cloud with an accuracy of 0.1 mm.

Implementation of a null test for freeform optics using a high-definition spatial light modulator.

We report the implementation of an interferometric null test using a high-definition spatial light modulator (SLM) as a reconfigurable alternative to a computer-generated hologram. We detail the alignment process chain, including novel techniques using the SLM to project alignment fiducials on the test part. To validate the alignment protocol, we measure a mild off-axis conic with the SLM-based system and cross-validate with conventional interferometry within 30 nm root-mean-square (RMS) surface figure. Finally, we report the null test of a 65 mm clear aperture concave freeform with 91 μm peak-valley sag departure from the base sphere. The measured surface figure of the freeform is within 40 nm RMS compared to the measurement with a commercial metrology instrument.

Visual perception of noise in a simulated holographic display—A user study

This work explores ways to bypass the fundamental image quality limitations of displays using Computer Generated Holograms (CGHs) and, specifically, the high-frequency noise associated with phase-only holograms. Although there is a wealth of literature on building experimental holographic systems, there are no user studies to assess the performance of a holographic system projecting a dynamic two-dimensional image. In this study, 18 participants blindly compared three groups of images displayed on a conventional monitor. The first group contained the original image, the second the simulated holographic reconstruction of the original image, and the third group had the foveated reconstruction of the original image, based on the pupil position. Holograms in the second group were computed using the Fienup algorithm and the third group using the Fienup with Perceptual Don’t Care Areas (FiPDoC) algorithm, a novel algorithm that uses eye tracking to optimize image quality in CGHs. The aim of the study was to find out if the holographic display, assuming an ideal hardware, can be as good as a conventional display and whether eye tracking can help this goal. Most participants distinguished between the original image and the un-foveated simulated reconstruction. However, the participants could not differentiate between the original image and the foveated reconstruction. Thus, foveation may be essential in designing and building the first commercial holographic displays.

On nonlinear effects in holographic-modulated ultrasound

Holographic acoustic lenses (HALs), also known as acoustic holograms, are used for generating unprecedented complex focused ultrasound (FU) fields. HALs store the phase profile of the desired wavefront, which is used to reconstruct the acoustic pressure field when illuminated by a single acoustic source. Nonlinear effects occur as the sound intensity increases, leading to distorted and asymmetric waveforms. Here, the k-space pseudospectral method is used to perform homogeneous three-dimensional nonlinear acoustic simulations with power law absorption. An in-depth analysis is performed to study the evolution of holographic-modulated FU fields produced by HALs as the excitation amplitude increases. It is shown that nonlinear waveform distortion significantly affects the reconstruction of the pressure pattern when compared to the linear condition. Diffraction and nonlinear effects result in an asymmetric waveform with distinct positive and negative pressure patterns at the target plane. Peak positive pressure distribution becomes more localized around the areas with the highest nonlinear distortion. The peak signal-to-distortion ratio (PSDR) at the target plane falls while the nonuniformity index (NUI) rises. As a result of harmonic generation, the heat deposition distribution becomes highly localized with a significant increase in the NUI. Nonlinear effects have also been shown to flatten the peak negative pressure distribution while having minimal effect on the PSDR or NUI. However, nonlinear effects are shown to be critical for accurately predicting cavitation zones. Findings will pave the way for HALs implementation in high-intensity applications and prompt the incorporation of nonlinear acoustics into the notion of computer-generated holography.

Method for generating planar computer-generated hologram at free viewpoint from cylindrical object light

Computer-generated holography (CGH) is an ideal three-dimensional (3D) display technology, and head-mounted displays (HMDs) using CGH are expected to become the next-generation display devices without eye strain, which is called holographic HMDs (holo-HMDs). However, the CGH computational load is too much for a holo-HMD, which has limited processing power. We have devised a method that calculates the cylindrical object light on a sender, broadcasts the object light data to multiple holo-HMDs, and generates holograms matched to the planar display device on the holo-HMD. The cylindrical object light calculations, which take up most of the computational load, are performed on a high-performance computer with sufficient computational power. The cylindrical object light is transformed into an object light on the plane in accordance with the motion of the holo-HMD. The phase difference information between the complex amplitude distribution of the cylindrical object light and the object light on the plane corresponding to a free viewpoint position must be corrected. Using this method, objects placed near the center of the cylinder can be observed from a wide area, making it possible to support 3D image observation with multiple holo-HMDs. Experiments using an actual optical system demonstrated that planar transform was performed and that the computational load on a holo-HMD side was very small.

The recovery scheme of computer-generated holography encryption–hiding images based on deep learning

In order to improve the security of ciphertext images in transmission, a scheme of using neural network is proposed to restore the encryption–hiding images based on chaotic iris phase mask and computer-generated holography (CGH), which solve the great difficulty of illegal attacks in the symmetric–asymmetric hybrid encryption system. Firstly, the ciphertext image based on CGH and chaotic iris phase mask is generated, and the ciphertext image is hidden into a carrier image. A large number of hidden image and plaintext image pairs are produced as a dataset. Next, the neural network is built by continuous training and testing. Finally, the established neural network can fit the mapping relationship between the hidden image and the plaintext image. It is not necessary to extract the ciphertext image from the hidden image before decrypting. We compare the image recovered by the neural network with the plaintext image. The experimental results show that the average cross-correlation coefficient (CC) is 0.994, the average peak signal-to-noise ratio (PSNR) is 70.2 dB, and the average structural similarity (SSIM) is 0.929. This scheme can directly realize the decryption of the hidden image. The scheme (encryption–decryption–hiding) are elaborated in detail. The simulation experiments show that the scheme is feasible and has good robustness.

Wavefront optical spacing of freeform surfaces and its measurement using CGH interferometry

For optical surfaces, the distance between the wavefront at ideal design position and that at real surface testing position along the wavefront propagation direction is an important parameter. It determines the on-axis curvature deviation and best-fit sphere radius of the surface under testing, and thus, affects the optical distance, effective focal length, and tolerance design of the optical system. We define the distance as wavefront optical spacing (WOS or spacing d). The analytical form of the WOS can be utilised in critical tolerance balancing, and its test results can aid in optical system redesign. Aiming at a computer-generated hologram (CGH) interferometric test, in this study, we propose the WOS concept and deduce the coupling relation between the surface error and spacing d, particularly in freeform surface conditions. A cat-eye CGH interferometric method was presented to test the spacing error within a precision of several microns. The simulation and error budget demonstrate that this method can measure the WOS of freeform surfaces. The experimental results indicate that the metrology accuracy is 10.2 ± 4.3 μm (P = 95%) (absolute accuracy), 4.5 μm (repeatability), and 2.1 ppm (relative accuracy).

Modeling and suppressing the wavefront degeneration in a CGH interferometric null test.

The computer-generated hologram (CGH) enables the ultra-high accuracy of surface measurement but causes the wavefront degeneration in the optical system. In this article, we give a high-accuracy analytical simulation of the wavefront degeneration in null test by the elliptical Gaussian model. We propose an analytical expression of instrumental transfer function (ITF) for the CGH null test without knowing the phase distribution of CGH, which gives an efficient instruction to suppress the wavefront degeneration. The ITF of the interferometric null test for a ∅3m aspheric mirror can be optimized from 0 to 0.65 at 0.4 Nyquist frequency.

A region based random multi-pixel search algorithm to improve the binary hologram reconstruction quality

Direct binary search (DBS) is an effective method for the generation of binary computer-generated holograms (CGHs), which has been widely used in wavefront synthesis, optical tweezers and 3D display. However, the correlation of pixels in holograms is neglected in DBS, resulting the algorithm easily converging to local minimum and leading to an unsatisfactory reconstruction quality. To ameliorate this disadvantage, we proposed a new algorithm by randomly selecting multiple related pixels in the same region to generate hologram. Compared with DBS, the mean square error (MSE) of reconstructed image in simulation has declined from 844.85 to 445.74, the peak signal to noise ratio (PSNR) has increased from 18.86 to 21.64 and structural similarity (SSIM) has increased from 0.336 to 0.459. The reconstructed image in experiment shows fewer noise points and clearer outline. Both the numerical and experimental results demonstrate that the reconstruction quality can be improved by this algorithm, which will exhibit great applications in the fields of data storage, microscopy, and true sense dynamic 3D display.