Polygon-based computer-generated holography: a review of fundamentals and recent progress [Invited]

Real-time calculation of Fresnel holograms using the split-Lohmann method

Holography is often considered as the most promising technology to enable high fidelity 3D perception in augmented and virtual reality applications. However, the computation of holograms in real time is still a challenging process especially for a 3D scene with a complex geometry. To overcome this limitation, we propose a one-step technique to compute the Fresnel diffraction integral for several propagation distances. Our approach is based on the split-Lohmann method that consists of successive operations in both space and frequency domains. We demonstrate that our technique can compute Fresnel holograms of complex geometry scenes in real time with a GPU implementation up to 18.1 times faster than layer-based approaches. Optical experiments are also conducted on a 4K full-color holographic display to show the high fidelity 3D perception provided by Fresnel split-Lohmann holograms.

Viewpoint-dependent lighting on polygonal holograms using bump mapping

Holograms can be observed from different viewpoints, because light waves can be encoded to propagate in multiple directions. Thus, accurate holograms for 3D display should model viewpoint-dependent light reflections. We proposed a new, to the best of our knowledge, hologram generation method for objects represented by polygonal meshes, whose lighting changes as the viewer moves, all while rendering smooth shading using low-poly objects. The proposed method leverages bump mapping and converts it into a bump-phase map encoding the propagation frequency and then spreads the reflected light wave so that only a specific viewpoint can receive them. Simulation experiments with small pixel pitches confirm the method's high computational performance.

Fast view-specific generation of high-definition holograms with enhanced quality

Holography is often considered as the most promising immersive technology because it provides all the depth cues of the human visual system. Some limitations still need to be overcome such as the huge computational load of high-definition holograms and the noise introduced in the reconstructed scene during the quantization process. In this paper, we propose what we believe is a novel view-specific layer-based stereogram approach combined with a view-dependent error diffusion algorithm that aims to solve those limitations. This method selects the light waves of the 3D scene that reach a specific viewing area and leverages this particular configuration to apply an error diffusion algorithm. Two additional quality enhancement features are observed: the reduction of the conjugate order perceptibility and the increased brightness of the reconstructed scene. Numerical and optical experiments demonstrate the time savings and quality enhancements of our approach.

An FEM Study on Minimizing Electrostatic Cross-Talk in a Comb Drive Micro Mirror Array

We are developing a phase-modulating micro mirror-array spatial light modulator to be used for real holography within the EU-funded project REALHOLO, featuring millions of pixels that can be individually positioned in a piston mode at a large frame rate. We found earlier that an electrostatic comb-drive array offers the best performance for the actuators: sufficient yoke forces for fast switching even at low voltages compatible with the CMOS addressing backplane. In our first design, the well-known electrostatic cross-talk issue had already been much smaller than would have been possible for parallel-plate actuators, but it was still larger than the precision requirements for high-image-quality holography. In this paper, we report on our analysis of the crucial regions for the electrostatic cross-talk and ways to reduce it while observing manufacturing constraints as well as avoiding excessively high field strengths that might lead to electrical breakdown. Finally, we present a solution that, in FEM simulations, reduces the remaining cross-talk to well below the required specification limit. This solution can be manufactured without any additional processing steps and suffers only a very small reduction of the yoke forces.

Optical versus radiographic imaging and tomography: introduction to the ROADS feature issue

Optical imaging is an ancient branch of imaging dating back to thousands of years. Radiographic imaging and tomography (RadIT), including the first use of X-rays by Wilhelm Röntgen, and then, γ-rays, energetic charged particles, neutrons, etc. are about 130 years young. The synergies between optical and radiographic imaging can be cast in the framework of these building blocks: Physics, Sources, Detectors, Methods, and Data Science, as described in Appl. Opt.61, RDS1 (2022)APOPAI0003-693510.1364/AO.455628. Optical imaging has expanded to include three-dimensional (3D) tomography (including holography), due in to part the invention of optical (including infrared) lasers. RadIT are intrinsically 3D because of the penetrating power of ionizing radiation. Both optical imaging and tomography (OIT) and RadIT are evolving into even higher dimensional regimes, such as time-resolved tomography (4D) and temporarily and spectroscopically resolved tomography (4D +). Further advances in OIT and RadIT will continue to be driven by desires for higher information yield, higher resolutions, and higher probability models with reduced uncertainties. Synergies in quantum physics, laser-driven sources, low-cost detectors, data-driven methods, automated processing of data, and artificially intelligent data acquisition protocols will be beneficial to both branches of imaging in many applications. These topics, along with an overview of the Radiography, Applied Optics, and Data Science virtual feature issue, are discussed here.

Digital holographic content manipulation for wide-angle holographic near-eye displays

In recent years, the development of holographic near-eye displays (HNED) has surpassed the progress of digital hologram recording systems, especially in terms of wide-angle viewing capabilities. Thus, there is capture-display parameters incompatibility, which makes it impossible to reconstruct recorded objects in wide-angle display. This paper presents a complete imaging chain extending the available content for wide-angle HNED of pupil and non-pupil configuration with narrow-angle digital holograms of real objects. To this end, a new framework based on the phase-space approach is proposed that includes a set of affine transformations required to account for all differences in capture-display cases. The developed method allows free manipulation of the geometry of reconstructed objects, including axial and lateral positioning and size scaling. At the same time, it has a low computational effort. The presented work is supported with non-paraxial formulas developed using the phase-space approach, enabling accurate tracing of the holographic signal, its reconstruction, and measuring appearing deformations. The applicability of the proposed hologram manipulation method is proven with experimental results of digital hologram reconstruction in wide-angle HNED.

Adaptive layer-based computer-generated holograms

We propose a novel, to the best of our knowledge, and fast adaptive layer-based (ALB) method for generating a computer-generated hologram (CGH) with accurate depth information. A complex three-dimensional (3D) object is adaptively divided into layers along the depth direction according to its own non-uniformly distributed depth coordinates, which reduces the depth error caused by the conventional layer-based method. Each adaptive layer generates a single-layer hologram using the angular spectrum method for diffraction, and the final hologram of a complex three-dimensional object is obtained by superimposing all the adaptive layer holograms. A hologram derived with the proposed method is referred to as an adaptive layer-based hologram (ALBH). Our demonstration shows that the desired reconstruction can be achieved with 52 adaptive layers in 8.7 s, whereas the conventional method requires 397 layers in 74.9 s.

Rendering of 3D scenes in analytical polygon-based computer holography with texture mapping

A computer-generated hologram (CGH) is a technique that generates an object light field by superimposing elementary holograms. Unlike traditional holography, this technique does not require the generation of an additional reference light to interfere with the calculated object light field. Texture mapping is a method that enhances the realism of 3D scenes. A fast method is presented that allows users to render holograms of 3D scenes consisting of triangular meshes with texture mapping. All calculations are performed with analytical expressions to ensure that the holograms generated by this method are fast and can reconstruct three-dimensional scenes with high quality. Using this method, a hologram of a three-dimensional scene consisting of thousands of triangles is generated. Our algorithm generates the same reconstruction results as those of Kim et al. [Appl. Opt.47, D117 (2008)APOPAI0003-693510.1364/AO.47.00D117], but significantly reduces the computation time (the computation time of our algorithm is only one-third of that of Kim et al.'s algorithm). The results show that the proposed method is computationally efficient as compared to a previous work. The proposed method is verified by simulations and optical experiments.

End-to-end compression-aware computer-generated holography

Joint photographic experts group (JPEG) compression standard is widely adopted for digital images. However, as JPEG encoding is not designed for holograms, applying it typically leads to severe distortions in holographic projections. In this work, we overcome this problem by taking into account the influence of JPEG compression on hologram generation in an end-to-end fashion. To this end, we introduce a novel approach to merge the process of hologram generation and JPEG compression with one differentiable model, enabling joint optimization via efficient first-order solvers. Our JPEG-aware end-to-end optimized holograms show significant improvements compared to conventional holograms compressed using JPEG standard both in simulation and on experimental display prototype. Specifically, the proposed algorithm shows improvements of 4 dB in peak signal-to-noise ratio (PSNR) and 0.27 in structural similarity (SSIM) metrics, under the same compression rate. When maintained with the same reconstruction quality, our method reduces the size of compressed holograms by about 35% compared to conventional JPEG-compressed holograms. Consistent with simulations, the experimental results further demonstrate that our method is robust to JPEG compression loss. Moreover, our method generates holograms compatible with the JPEG standard, making it friendly to a wide range of commercial software and edge devices.

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.

Efficient rendering by parallelogram-approximation for full analytical polygon-based computer-generated holography using planar texture mapping

We have developed a full analytical method with texture mapping for polygon-based computer-generated holography. A parallel planar projection mapping for holographic rendering along with affine transformation and self-similar segmentation is derived. Based on this method, we further propose a parallelogram-approximation to reduce the number of polygons used in the polygon-based technique. We demonstrate that the overall method can reduce the computational effort by 50% as compared to an existing method without sacrificing the reconstruction quality based on high precision rendering of complex textures. Numerical and optical reconstructions have shown the effectiveness of the overall scheme.

Real-time computing for a holographic 3D display based on the sparse distribution of a 3D object and requisite Fourier spectrum

In holographic three-dimensional (3D) displays, the surface structures of 3D objects are reconstructed without their internal parts. In diffraction calculations using 3D fast Fourier transform (FFT), this sparse distribution of 3D objects can reduce the calculation time as the Fourier transform can be analytically solved in the depth direction and the 3D FFT can be resolved into multiple two-dimensional (2D) FFTs. Moreover, the Fourier spectrum required for hologram generation is not the entire 3D spectrum but a partial 2D spectrum located on the hemispherical surface. This sparsity of the required Fourier spectrum also reduces the number of 2D FFTs and improves the acceleration. In this study, a fast calculation algorithm based on two sparsities is derived theoretically and explained in detail. Our proposed algorithm demonstrated a 24-times acceleration improvement compared with a conventional algorithm and realized real-time hologram computing at a rate of 170 Hz.

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.

Fast shadow casting algorithm in analytical polygon-based computer-generated holography

Shadow casting is essential in computer graphics, which can significantly enhance the reality of rendered images. However, shadow casting is rarely studied in polygon-based computer-generated holography (CGH) because state-of-art triangle-based occlusion handling methods are too complicated for shadow casting and unfeasible for complex mutual occlusion handling. We proposed a novel drawing method based on the analytical polygon-based CGH framework and achieved Z-buffer-based occlusion handling instead of the traditional Painter's algorithm. We also achieved shadow casting for parallel and point light sources. Our framework can be generalized to N-edge polygon (N-gon) rendering and accelerated using CUDA hardware, by which the rendering speed can be significantly enhanced.

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.

Review of computer-generated hologram algorithms for color dynamic holographic three-dimensional display

Holographic three-dimensional display is an important display technique because it can provide all depth information of a real or virtual scene without any special eyewear. In recent years, with the development of computer and optoelectronic technology, computer-generated holograms have attracted extensive attention and developed as the most promising method to realize holographic display. However, some bottlenecks still restrict the development of computer-generated holograms, such as heavy computation burden, low image quality, and the complicated system of color holographic display. To overcome these problems, numerous algorithms have been investigated with the aim of color dynamic holographic three-dimensional display. In this review, we will explain the essence of various computer-generated hologram algorithms and provide some insights for future research.

Fast 3D Analytical Affine Transformation for Polygon-Based Computer-Generated Holograms

We present a fast 3D analytical affine transformation (F3DAAT) method to obtain polygon-based computer-generated holograms (CGHs). CGHs consisting of tens of thousands of triangles from 3D objects are obtained by this method. We have attempted a revised method based on previous 3D affine transformation methods. In order to improve computational efficiency, we have derived and analyzed our proposed affine transformation matrix. We show that we have further increased the computational efficiency compared with previous affine methods. We also have added flat shading to improve the reconstructed image quality. A 3D object from a 3D camera is reconstructed holographically by numerical and optical experiments.