End-to-end learning of 3D phase-only holograms for holographic display

Direct amplitude-only hologram realized by broken symmetry

Holographic displays have been a long-standing ambition for decades to realize true-to-life reconstruction. However, their practical adoption is hindered by their subpar image quality compared to two-dimensional displays, which is fundamentally limited by restricted spatial frequency bandwidth and artifacts. We address the limitation by using a symmetry-broken amplitude-only spatial light modulator, demonstrating image quality comparable to that of two-dimensional displays. The broken conjugate symmetry induced by phase noise of modulators eliminates conjugate image that causes issues in amplitude-only holograms and allows direct reconstruction without additional optical elements. The proposed method provides enhanced robustness against artifacts caused by sub-pixel structures of modulators, enabling experimental reconstruction of high-quality holograms. The full bandwidth and the robustness result in a 5-decibel improvement in peak signal-to-noise ratio compared to state-of-the-art holograms. Furthermore, the hologram has 24 times higher optical efficiency and a smaller volume than the traditional amplitude-only holograms while real-time synthesis is enabled by using a neural network.

Holo-U2Net for High-Fidelity 3D Hologram Generation

Traditional methods of hologram generation, such as point-, polygon-, and layer-based physical simulation approaches, suffer from substantial computational overhead and generate low-fidelity holograms. Deep learning-based computer-generated holography demonstrates effective performance in terms of speed and hologram fidelity. There is potential to enhance the network's capacity for fitting and modeling in the context of computer-generated holography utilizing deep learning methods. Specifically, the ability of the proposed network to simulate Fresnel diffraction based on the provided hologram dataset requires further improvement to meet expectations for high-fidelity holograms. We propose a neural architecture called Holo-U2Net to address the challenge of generating a high-fidelity hologram within an acceptable time frame. Holo-U2Net shows notable performance in hologram evaluation metrics, including an average structural similarity of 0.9988, an average peak signal-to-noise ratio of 46.75 dB, an enhanced correlation coefficient of 0.9996, and a learned perceptual image patch similarity of 0.0008 on the MIT-CGH-4K large-scale hologram dataset.

Non-convex optimization for inverse problem solving in computer-generated holography

Computer-generated holography is a promising technique that modulates user-defined wavefronts with digital holograms. Computing appropriate holograms with faithful reconstructions is not only a problem closely related to the fundamental basis of holography but also a long-standing challenge for researchers in general fields of optics. Finding the exact solution of a desired hologram to reconstruct an accurate target object constitutes an ill-posed inverse problem. The general practice of single-diffraction computation for synthesizing holograms can only provide an approximate answer, which is subject to limitations in numerical implementation. Various non-convex optimization algorithms are thus designed to seek an optimal solution by introducing different constraints, frameworks, and initializations. Herein, we overview the optimization algorithms applied to computer-generated holography, incorporating principles of hologram synthesis based on alternative projections and gradient descent methods. This is aimed to provide an underlying basis for optimized hologram generation, as well as insights into the cutting-edge developments of this rapidly evolving field for potential applications in virtual reality, augmented reality, head-up display, data encryption, laser fabrication, and metasurface design.

Generating Multi-Depth 3D Holograms Using a Fully Convolutional Neural Network

Efficiently generating 3D holograms is one of the most challenging research topics in the field of holography. This work introduces a method for generating multi-depth phase-only holograms using a fully convolutional neural network (FCN). The method primarily involves a forward-backward-diffraction framework to compute multi-depth diffraction fields, along with a layer-by-layer replacement method (L2RM) to handle occlusion relationships. The diffraction fields computed by the former are fed into the carefully designed FCN, which leverages its powerful non-linear fitting capability to generate multi-depth holograms of 3D scenes. The latter can smooth the boundaries of different layers in scene reconstruction by complementing information of occluded objects, thus enhancing the reconstruction quality of holograms. The proposed method can generate a multi-depth 3D hologram with a PSNR of 31.8 dB in just 90 ms for a resolution of 2160 × 3840 on the NVIDIA Tesla A100 40G tensor core GPU. Additionally, numerical and experimental results indicate that the generated holograms accurately reconstruct clear 3D scenes with correct occlusion relationships and provide excellent depth focusing.

Correction of the wavelength error in transmission of a full-color holographic 3D image

When a digital holographic image represented by a sampled wavefield is transmitted and the wavelength used in the three-dimensional (3D) display devices does not agree exactly with the wavelength of the original image data, the reconstructed 3D image will differ slightly from the original. This slight change is particularly problematic for full-color 3D images reconstructed using three wavelengths. A method is proposed here to correct the holographic image data and reduce the problems caused by wavelength mismatch. The effectiveness of the method is confirmed via theoretical analysis and numerical experiments that evaluate the reconstructed images using several image indices.

Full-colour 3D holographic augmented-reality displays with metasurface waveguides

Emerging spatial computing systems seamlessly superimpose digital information on the physical environment observed by a user, enabling transformative experiences across various domains, such as entertainment, education, communication and training1-3. However, the widespread adoption of augmented-reality (AR) displays has been limited due to the bulky projection optics of their light engines and their inability to accurately portray three-dimensional (3D) depth cues for virtual content, among other factors4,5. Here we introduce a holographic AR system that overcomes these challenges using a unique combination of inverse-designed full-colour metasurface gratings, a compact dispersion-compensating waveguide geometry and artificial-intelligence-driven holography algorithms. These elements are co-designed to eliminate the need for bulky collimation optics between the spatial light modulator and the waveguide and to present vibrant, full-colour, 3D AR content in a compact device form factor. To deliver unprecedented visual quality with our prototype, we develop an innovative image formation model that combines a physically accurate waveguide model with learned components that are automatically calibrated using camera feedback. Our unique co-design of a nanophotonic metasurface waveguide and artificial-intelligence-driven holographic algorithms represents a significant advancement in creating visually compelling 3D AR experiences in a compact wearable device.

Vision transformer empowered physics-driven deep learning for omnidirectional three-dimensional holography

The inter-plane crosstalk and limited axial resolution are two key points that hinder the performance of three-dimensional (3D) holograms. The state-of-the-art methods rely on increasing the orthogonality of the cross-sections of a 3D object at different depths to lower the impact of inter-plane crosstalk. Such strategy either produces unidirectional 3D hologram or induces speckle noise. Recently, learning-based methods provide a new way to solve this problem. However, most related works rely on convolution neural networks and the reconstructed 3D holograms have limited axial resolution and display quality. In this work, we propose a vision transformer (ViT) empowered physics-driven deep neural network which can realize the generation of omnidirectional 3D holograms. Owing to the global attention mechanism of ViT, our 3D CGH has small inter-plane crosstalk and high axial resolution. We believe our work not only promotes high-quality 3D holographic display, but also opens a new avenue for complex inverse design in photonics.

Experimental realization of a transmissive microwave metasurface for dual vector vortex beams generation

This work presents a theoretical design and experimental demonstration of a transmissive microwave metasurface for generating dual-vector vortex beams (VVBs). The proposed metasurface consists of an array of pixelated dartboard discretization meta-atoms. By rotating the meta-atoms from 0° to 180°, a Pancharatnam-Barry (P-B) phase covering the full 360° range is achieved, with a transmittance exceeding 90% over the frequency range from 9.7 to 10.2 GHz. The measured results demonstrate that when a linearly polarized microwave normally impinges on the metasurface, the transmitted beams correspond to the dual VVBs with different directions. A good agreement among Poincaré sphere theory, full-wave simulation, and experimental measurement is observed. This proposed transmissive microwave metasurface for VVBs may offer promising applications in communications and radar detection.

Deep learning based coherence holography reconstruction of 3D objects

We propose a reconstruction method for coherence holography using deep neural networks. cGAN and U-NET models were developed to reconstruct 3D complex objects from recorded interferograms. Our proposed methods, dubbed deep coherence holography (DCH), predict the non-diffracted fields or the sub-objects included in the 3D object from the captured interferograms, yielding better reconstructed objects than the traditional analytical imaging methods in terms of accuracy, resolution, and time. The DCH needs one image per sub-object as opposed to N images for the traditional sin-fit algorithm, and hence the total reconstruction time is reduced by N×. Furthermore, with noisy interferograms the DCH amplitude mean square reconstruction error (MSE) is 5×104× and 104× and phase MSE is 102× and 3×103× better than Fourier fringe and sin-fit algorithms, respectively. The amplitude peak signal to noise ratio (PSNR) is 3× and 2× and phase PSNR is 5× and 3× better than Fourier fringe and sin-fit algorithms, respectively. The reconstruction resolution is the same as sin-fit but 2× better than the Fourier fringe analysis technique.

Liquid lens based holographic camera for real 3D scene hologram acquisition using end-to-end physical model-driven network

With the development of artificial intelligence, neural network provides unique opportunities for holography, such as high fidelity and dynamic calculation. How to obtain real 3D scene and generate high fidelity hologram in real time is an urgent problem. Here, we propose a liquid lens based holographic camera for real 3D scene hologram acquisition using an end-to-end physical model-driven network (EEPMD-Net). As the core component of the liquid camera, the first 10 mm large aperture electrowetting-based liquid lens is proposed by using specially fabricated solution. The design of the liquid camera ensures that the multi-layers of the real 3D scene can be obtained quickly and with great imaging performance. The EEPMD-Net takes the information of real 3D scene as the input, and uses two new structures of encoder and decoder networks to realize low-noise phase generation. By comparing the intensity information between the reconstructed image after depth fusion and the target scene, the composite loss function is constructed for phase optimization, and the high-fidelity training of hologram with true depth of the 3D scene is realized for the first time. The holographic camera achieves the high-fidelity and fast generation of the hologram of the real 3D scene, and the reconstructed experiment proves that the holographic image has the advantage of low noise. The proposed holographic camera is unique and can be used in 3D display, measurement, encryption and other fields.

HoloTile light engine: new digital holographic modalities and applications

HoloTile is a patented computer generated holography approach with the aim of reducing the speckle noise caused by the overlap of the non-trivial physical extent of the point spread function in Fourier holographic systems from adjacent frequency components. By combining tiling of phase-only of rapidly generated sub-holograms with a PSF-shaping phase profile, each frequency component-or output 'pixel'- in the Fourier domain is shaped to a desired non-overlapping profile. In this paper, we show the high-resolution, speckle-reduced reconstructions that can be achieved with HoloTile, as well as present new HoloTile modalities, including an expanded list of PSF options with new key properties. In addition, we discuss numerous applications for which HoloTile, its rapid hologram generation, and the new PSF options may be an ideal fit, including optical trapping and manipulation of particles, volumetric additive printing, information transfer and quantum communication.

Deep-computer-generated holography with temporal-focusing and a digital propagation matrix for rapid 3D multiphoton stimulation

Deep learning-based computer-generated holography (DeepCGH) has the ability to generate three-dimensional multiphoton stimulation nearly 1,000 times faster than conventional CGH approaches such as the Gerchberg-Saxton (GS) iterative algorithm. However, existing DeepCGH methods cannot achieve axial confinement at the several-micron scale. Moreover, they suffer from an extended inference time as the number of stimulation locations at different depths (i.e., the number of input layers in the neural network) increases. Accordingly, this study proposes an unsupervised U-Net DeepCGH model enhanced with temporal focusing (TF), which currently achieves an axial resolution of around 5 µm. The proposed model employs a digital propagation matrix (DPM) in the data preprocessing stage, which enables stimulation at arbitrary depth locations and reduces the computation time by more than 35%. Through physical constraint learning using an improved loss function related to the TF excitation efficiency, the axial resolution and excitation intensity of the proposed TF-DeepCGH with DPM rival that of the optimal GS with TF method but with a greatly increased computational efficiency.

Real-time 4K computer-generated hologram based on encoding conventional neural network with learned layered phase

Learning-based computer-generated hologram (CGH) demonstrates great potential for real-time high-quality holographic displays. However, real-time 4K CGH generation for 3D scenes remains a challenge due to the computational burden. Here, a variant conventional neural network (CNN) is presented for CGH encoding with learned layered initial phases for layered CGH generation. Specifically, the CNN predicts the CGH based on the input complex amplitude on the CGH plane, and the learned initial phases act as a universal phase for any target images at the target depth layer. These phases are generated during the training process of the coding CNN to further optimize the quality. The CNN is trained to learn encoding 3D CGH by randomly selecting the depth layer in the training process, and contains only 938 parameters. The generation time for a 2D 4K CGH is 18 ms, and is increased by 12 ms for each layer in a layered 3D scene. The average Peak Signal to Noise Ratio (PSNR) of each layer is above 30dB in the depth range from 160 to 210 mm. Experiments verify that our method can achieve real-time layered 4K CGH generation.

Comparison of double-phase hologram and binary amplitude encoding: holographic projection and vortex beam generation

Utilizing computer-generated holograms is a promising technique because these holograms can theoretically generate arbitrary waves with high light efficiency. In phase-only spatial light modulators, encoding complex amplitudes into phase-only holograms is a significant issue, and double-phase holograms have been a popular encoding technique. However, they reduce the light efficiency. In this study, our complex amplitude encoding, called binary amplitude encoding (BAE), and conventional methods including double-phase hologram, iterative algorithm, and error diffusion methods were compared in terms of the fidelity of reproduced light waves and light efficiency, considering the applications of lensless zoomable holographic projection and vortex beam generation. This study also proposes a noise reduction method for BAE holograms that is effective when the holograms have different aspect ratios. BAE is a non-iterative method, which allows holograms to be obtained more than 2 orders of magnitude faster than iterative holograms; BAE has about 3 times higher light efficiency with comparable image quality compared to double-phase holograms.

Crosstalk-free for multi-plane holographic display using double-constraint stochastic gradient descent

Multi-plane crosstalk is a key issue affecting the quality of holographic three-dimensional (3D) displays. The time-multiplexing stochastic gradient descent (TM-SGD) method has been applied to solve the inter-plane crosstalk problem in multi-plane reconstruction. However, the inter-plane crosstalk increases greatly as the inter-plane interval decreases, and the optimization time increases greatly as the number of planes increases. In this paper, we propose a double-constraint stochastic gradient descent method to suppress inter-plane crosstalk in multi-plane reconstruction. In the proposed method, we use the mask to make the optimization process focus more on the signal region and improve the reconstruction quality. Meanwhile, we adopt a constraint strategy of phase regularization to reduce the phase randomness of the signal region and suppress inter-plane crosstalk. Numerical simulation and optical experiment results confirm that our method can effectively suppress the inter-plane crosstalk and improve the quality of the reconstructed planes at a lower inter-plane interval. Moreover, the optimization time of our method is almost 4 times faster than that of TM-SGD. The proposed method can contribute to the realization of tomographic 3D visualization in the biomedical field, which requires the reconstruction of multiple tomographic images without inter-plane crosstalk.

Fast Hologram Calculation Method Based on Wavefront Precise Diffraction

In this paper, a fast hologram calculation method based on wavefront precise diffraction is proposed. By analyzing the diffraction characteristics of the object point on the 3D object, the effective viewing area of the reproduced image is analyzed. Based on the effective viewing area, the effective hologram size of the object point is obtained, and then the accurate diffraction calculation from the object point to the wavefront recording plane (WRP) is performed. By calculating all the object points on the recorded object, the optimized WRP of the whole 3D object can be obtained. The final hologram is obtained by calculating the diffraction light field from the WRP to the holographic plane. Compared with the traditional method, the proposed method can improve the calculation speed by more than 55%, while the image quality of the holographic 3D display is not affected. The proposed calculation method provides an idea for fast calculation of holograms and is expected to contribute to the development of dynamic holographic displays.

DGE-CNN: 2D-to-3D holographic display based on a depth gradient extracting module and ZCNN network

Holography is a crucial technique for the ultimate three-dimensional (3D) display, because it renders all optical cues from the human visual system. However, the shortage of 3D contents strictly restricts the extensive application of holographic 3D displays. In this paper, a 2D-to-3D-display system by deep learning-based monocular depth estimation is proposed. By feeding a single RGB image of a 3D scene into our designed DGE-CNN network, a corresponding display-oriented 3D depth map can be accurately generated for layer-based computer-generated holography. With simple parameter adjustment, our system can adapt the distance range of holographic display according to specific requirements. The high-quality and flexible holographic 3D display can be achieved based on a single RGB image without 3D rendering devices, permitting potential human-display interactive applications such as remote education, navigation, and medical treatment.

Point-polygon hybrid method for generating holograms

Computer-generated holograms (CGHs) are usually calculated from point clouds or polygon meshes. Point-based holograms are good at depicting details of objects, such as continuous depth cues, while polygon-based holograms tend to efficiently render high-density surfaces with accurate occlusions. Herein, we propose a novel point-polygon hybrid method (PPHM) to compute CGHs for the first time (to the best of our knowledge), which takes advantage of both point-based and polygon-based methods, and thus performs better than each of them separately. Reconstructions of 3D object holograms confirm that the proposed PPHM can present continuous depth cues with fewer triangles, implying high computational efficiency without losing quality.

Computer holography using deep neural network with Fourier basis

The use of a deep neural network is a promising technique for rapid hologram generation, where a suitable training dataset is vital for the reconstruct quality as well as the generalization of the model. In this Letter, we propose a deep neural network for phase hologram generation with a physics-informed training strategy based on Fourier basis functions, leading to orthonormal representations of the spatial signals. The spatial frequency characteristics of the reconstructed diffraction fields can be regulated by recombining the Fourier basis functions in the frequency domain. Numerical and optical results demonstrate that the proposed method can effectively improve the generalization of the model with high-quality reconstructions.

End-to-end real-time holographic display based on real-time capture of real scenes

Holographic display is considered as a promising three-dimensional (3D) display technology and has been widely studied. However, to date, the real-time holographic display for real scenes is still far from being incorporated in our life. The speed and quality of information extraction and holographic computing need to be further improved. In this paper, we propose an end-to-end real-time holographic display based on real-time capture of real scenes, where the parallax images are collected from the scene and a convolutional neural network (CNN) builds the mapping from the parallax images to the hologram. Parallax images are acquired in real time by a binocular camera, and contain depth information and amplitude information needed for 3D hologram calculation. The CNN, which can transform parallax images into 3D holograms, is trained by datasets consisting of parallax images and high-quality 3D holograms. The static colorful reconstruction and speckle-free real-time holographic display based on real-time capture of real scenes have been verified by the optical experiments. With simple system composition and affordable hardware requirements, the proposed technique will break the dilemma of the existing real-scene holographic display, and open up a new direction for the application of real-scene holographic 3D display such as holographic live video and solving vergence-accommodation conflict (VAC) problems for head-mounted display devices.

Reducing crosstalk of a multi-plane holographic display by the time-multiplexing stochastic gradient descent

Multi-plane reconstruction is essential for realizing a holographic three-dimensional (3D) display. One fundamental issue in conventional multi-plane Gerchberg-Saxton (GS) algorithm is the inter-plane crosstalk, mainly caused by the neglect of other planes' interference in the process of amplitude replacement at each object plane. In this paper, we proposed the time-multiplexing stochastic gradient descent (TM-SGD) optimization algorithm to reduce the multi-plane reconstruction crosstalk. First, the global optimization feature of stochastic gradient descent (SGD) was utilized to reduce the inter-plane crosstalk. However, the crosstalk optimization effect would degrade as the number of object planes increases, due to the imbalance between input and output information. Thus, we further introduced the time-multiplexing strategy into both the iteration and reconstruction process of multi-plane SGD to increase input information. In TM-SGD, multiple sub-holograms are obtained through multi-loop iteration and then sequentially refreshed on spatial light modulator (SLM). The optimization condition between the holograms and the object planes converts from one-to-many to many-to-many, improving the optimization of inter-plane crosstalk. During the persistence of vision, multiple sub-hologram jointly reconstruct the crosstalk-free multi-plane images. Through simulation and experiment, we confirmed that TM-SGD could effectively reduce the inter-plane crosstalk and improve image quality.The proposed TM-SGD-based holographic display has wide applications in tomographic 3D visualization for biology, medical science, and engineering design, which need to reconstruct multiple independent tomographic images without inter-plane crosstalk.

Light field displays with computational vision correction for astigmatism and high-order aberrations with real-time implementation

Vision-correcting near-eye displays are necessary concerning the large population with refractive errors. However, varifocal optics cannot effectively address astigmatism (AST) and high-order aberration (HOAs); freeform optics has little prescription flexibility. Thus, a computational solution is desired to correct AST and HOA with high prescription flexibility and no increase in volume and hardware complexity. In addition, the computational complexity should support real-time rendering. We propose that the light field display can achieve such computational vision correction by manipulating sampling rays so that rays forming a voxel are re-focused on the retina. The ray manipulation merely requires updating the elemental image array (EIA), being a fully computational solution. The correction is first calculated based on an eye's wavefront map and then refined by a simulator performing iterative optimization with a schematic eye model. Using examples of HOA and AST, we demonstrate that corrected EIAs make sampling rays distributed within ±1 arcmin on the retina. Correspondingly, the synthesized image is recovered to nearly as clear as normal vision. We also propose a new voxel-based EIA generation method considering the computational complexity. All voxel positions and the mapping between voxels and their homogeneous pixels are acquired in advance and stored as a lookup table, bringing about an ultra-fast rendering speed of 10 ms per frame with no cost in computing hardware and rendering accuracy. Finally, experimental verification is carried out by introducing the HOA and AST with customized lenses in front of a camera. As a result, significantly recovered images are reported.

Wavefront recording plane-like method for polygon-based holograms

The wavefront recording plane (WRP) method is an algorithm for computer-generated holograms, which has significantly promoted the accelerated computation of point-based holograms. Similarly, in this paper, we propose a WRP-like method for polygon-based holograms. A WRP is placed near the object, and the diffracted fields of all polygons are aggregated in the WRP so that the fields propagating from the polygonal mesh affect only a small region of the plane rather than the full region. Unlike the conventional WRP method used in point-based holograms, the proposed WRP-like method utilizes sparse sampling in the frequency domain to significantly reduce the practical computational kernel size. The proposed WRP-like method and the analytical shading model are used to generate polygon-based holograms of multiple three-dimensional (3D) objects, which are then reproduced to confirm 3D perception. The results indicate that the proposed WRP-like method based on an analytical algorithm is hundreds of times faster than the reference full region sampling case; a hologram with tens of thousands of triangles can be computed in seconds even on a CPU, whereas previous methods required a graphics processing unit to achieve these speeds.

High Resolution Multiview Holographic Display Based on the Holographic Optical Element

Limited by the low space-bandwidth product of the spatial light modulator (SLM), it is difficult to realize multiview holographic three-dimensional (3D) display. To conquer the problem, a method based on the holographic optical element (HOE), which is regarded as a controlled light element, is proposed in the study. The SLM is employed to upload the synthetic phase-only hologram generated by the angular spectrum diffraction theory. Digital grating is introduced in the generation process of the hologram to achieve the splicing of the reconstructions and adjust the position of the reconstructions. The HOE fabricated by the computer-generated hologram printing can redirect the reconstructed images of multiview into multiple viewing zones. Thus, the modulation function of the HOE should be well-designed to avoid crosstalk between perspectives. The experimental results show that the proposed system can achieve multiview holographic augmented reality (AR) 3D display without crosstalk. The resolution of each perspective is 4K, which is higher than that of the existing multiview 3D display system.

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.

Neural compression for hologram images and videos

Holographic near-eye displays can deliver high-quality three-dimensional (3D) imagery with focus cues. However, the content resolution required to simultaneously support a wide field of view and a sufficiently large eyebox is enormous. The consequent data storage and streaming overheads pose a big challenge for practical virtual and augmented reality (VR/AR) applications. We present a deep-learning-based method for efficiently compressing complex-valued hologram images and videos. We demonstrate superior performance over the conventional image and video codecs.

Accelerating hologram generation using oriented-separable convolution and wavefront recording planes

Recently, holographic displays have gained attention owing to their natural presentation of three-dimensional (3D) images; however, the enormous amount of computation has hindered their applicability. This study proposes an oriented-separable convolution accelerated using the wavefront-recording plane (WRP) method and recurrence formulas. We discuss the orientation of 3D objects that affects computational efficiency, which is overcome by reconsidering the orientation, and the suitability of the proposed method for hardware implementations.