Rendering of specular curved objects in polygon-based computer holography

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.

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.

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

In this review paper, we first provide comprehensive tutorials on two classical methods of polygon-based computer-generated holography: the traditional method (also called the fast-Fourier-transform-based method) and the analytical method. Indeed, other modern polygon-based methods build on the idea of the two methods. We will then present some selective methods with recent developments and progress and compare their computational reconstructions in terms of calculation speed and image quality, among other things. Finally, we discuss and propose a fast analytical method called the fast 3D affine transformation method, and based on the method, we present a numerical reconstruction of a computer-generated hologram (CGH) of a 3D surface consisting of 49,272 processed polygons of the face of a real person without the use of graphic processing units; to the best of our knowledge, this represents a state-of-the-art numerical result in polygon-based computed-generated holography. Finally, we also show optical reconstructions of such a CGH and another CGH of the Stanford bunny of 59,996 polygons with 31,724 processed polygons after back-face culling. We hope that this paper will bring out some of the essence of polygon-based computer-generated holography and provide some insights for future research.

Real-Time Computation of 3D Wireframes in Computer-Generated Holography

Computer-Generated Holography (CGH) algorithms simulate numerical diffraction, being applied in particular for holographic display technology. Due to the wave-based nature of diffraction, CGH is highly computationally intensive, making it especially challenging for driving high-resolution displays in real-time. To this end, we propose a technique for efficiently calculating holograms of 3D line segments. We express the solutions analytically and devise an efficiently computable approximation suitable for massively parallel computing architectures. The algorithms are implemented on a GPU (with CUDA), and we obtain a 70-fold speedup over the reference point-wise algorithm with almost imperceptible quality loss. We report real-time frame rates for CGH of complex 3D line-drawn objects, and validate the algorithm in both a simulation environment as well as on a holographic display setup.

Photorealistic computer generated holography with global illumination and path tracing

Computer generated holography (CGH) algorithms come in many forms, with different trade-offs in terms of visual quality and calculation speed. However, no CGH algorithm to date can accurately account for all 3D visual cues simultaneously, such as occlusion, shadows, continuous parallax, and precise focal cues, without view discretization. The aim is to create photorealistic CGH content, not only for display purposes but also to create reference data for comparing and testing CGH and compression algorithms. We propose a novel algorithm combining the precision of point-based CGH with the accurate shading and flexibility of ray-tracing algorithms. We demonstrate this by creating a scene with global illumination, soft shadows, and precise occlusion cues, implemented with OptiX and CUDA.

Fast calculation of high-definition depth-added computer-generated holographic stereogram by spectrum-domain look-up table [Invited]

High-definition depth-added computer-generated holographic stereogram (DA-CGHS) is superior in its high quality, easy realization, and auto-shading effect. However, its computing cost is extremely high because numerous scenes together with depth information must be calculated. Here, we proposed a fast calculation scheme of DA-CGHS by the spectrum-domain look-up table (SDLUT) method. In SDLUT, diffraction fields on the hogel plane of selected reference points in the object space are calculated. Subsequently, the fields are Fourier transformed to the spectrum domain. Because the signal energy always concentrates in a small spectrum region, these regions are cropped as the elemental tables. In the computing of the hogels, the field superposition is conducted in the spectrum domain by using the elemental tables. In our demonstration, the table size of SDLUT is only 0.44% that of the look-up table (LUT). Because the table size is very small, the computing time of SDLUT method can be nearly 80 times faster than that of conventional LUTs in the spatial domain, while the image quality is comparable.

Analytic computation of line-drawn objects in computer generated holography

Digital holography is a promising display technology that can account for all human visual cues, with many potential applications i.a. in AR and VR. However, one of the main challenges in computer generated holography (CGH) needed for driving these displays are the high computational requirements. In this work, we propose a new CGH technique for the efficient analytical computation of lines and arc primitives. We express the solutions analytically by means of incomplete cylindrical functions, and devise an efficiently computable approximation suitable for massively parallel computing architectures. We implement the algorithm on a GPU (with CUDA), provide an error analysis and report real-time frame rates for CGH of complex 3D scenes of line-drawn objects, and validate the algorithm in an optical setup.

Image quality improvement of holographic 3-D images based on a wavefront recording plane method with a limiting diffraction region

This study aims to improve the image quality of holographic three-dimensional (3-D) images based on the wavefront recording plane (WRP) method. In this method, we place a WRP close to the 3-D objects to reduce the propagation distance of light from the objects to the WRP. The conventional WRP method has been implemented only under conditions that did not cause aliasing noise. This study proposes a WRP method with a limiting diffraction region from the WRP to the hologram such that we can perform the WRP method under any condition. As a result, we succeeded in improving the image quality of the 3-D images based on the WRP method.

Phase added sub-stereograms for accelerating computer generated holography

Phase-added stereograms are a form of sparse computer generated holograms, subdividing the hologram in small Fourier transformed blocks and updating a single coefficient per block and per point-spread function. Unfortunately, these algorithms' computational performance is often bottlenecked by the relatively high memory requirements. We propose a technique to partition the 3D point cloud into cells using time-frequency analysis, grouping the affected coefficients into subsets that improve caching and minimize memory requirements. This results in significant acceleration of phase added stereogram algorithms without affecting render quality, enabling real-time CGH for driving holographic displays for more complex and detailed scenes than previously possible. We report a 30-fold speedup over the base implementation, achieving real-time speeds of 80ms per million points per megapixel on a single GPU.

Acceleration of computer-generated hologram using wavefront-recording plane and look-up table in three-dimensional holographic display

In this paper, we propose a fast calculation method using look-up table and wavefront-recording plane. Wavefront-recording plane method consists of two steps: the first step is the calculation of a wavefront-recording plane which is placed between the object and the hologram. In the second step, we obtain the hologram by executing diffraction calculation from the wavefront-recording plane to the hologram plane. The first step of the previous wavefront-recording plane method is time consuming. In order to obtain further acceleration to the first step, we propose high compressed look-up table method based on wavefront-recording plane. We perform numerical simulations and optical experiments to verify the proposed method. Numerical simulation results show that the calculation time reduces dramatically in comparison with previous wavefront-recording plane method and the memory usage is very small. The optical experimental results are in accord with the numerical simulation results. It is expected that proposed method can greatly reduce the computational complexity and could be widely applied in the holographic field in the future.

High-quality full-parallax full-color three-dimensional image reconstructed by stacking large-scale computer-generated volume holograms

A novel technique is presented for the full-color reconstruction of large-scale computer-generated holograms (CGHs). In this method, three printed CGHs are transferred to three volume holograms at the wavelengths corresponding to red-green-blue (RGB) colors and then stacked to superimpose the RGB color images. The developed CGHs are compact and portable. The reconstructed image is sharp and vivid as compared with that developed using RGB color filters. A technique for correcting the original CGHs is proposed to compensate for the aberration caused by the thick glass substrate because the RGB images exhibit a considerable position shift owing to the aberration. Fabricated large-scale full-color CGHs are demonstrated to verify the techniques.

Reducing the memory usage of computer-generated hologram calculation using accurate high-compressed look-up-table method in color 3D holographic display

In this paper, we propose an accurate high-compressed look-up-table method that uses less memory to generate the hologram. In precomputation, we separate the longitudinal modulation factors and only calculate the basic horizontal and vertical factors. Therefore, we obtain other horizontal and vertical modulation factors of object points by simply shifting the basic horizontal and vertical modulation factors while computing holograms. We perform numerical simulations and optical experiments to verify the proposed method. Numerical simulation results show that the proposed method has the least memory usage, the fastest computation time and no distortion. The optical experimental results are in accord with the numerical simulation results. The proposed method is simple and effective to calculate computer-generated holograms for color dynamic holographic display with high speed, less memory usage and high accuracy that could be applied in the holographic field in the future.

Direct calculation of computer-generated holograms in sparse bases

Computer-generated holography is computationally intensive, making it especially challenging for holographic displays where high-resolutions and video rates are needed. To this end, we propose a technique for directly calculating short-time Fourier transform coefficients without the need for a look-up table. Because point spread functions are sparse in this transform domain, only a small fraction of the coefficients need to be updated, enabling significant speed gains. Twenty-fold accelerations are reported over the reference implementation. This approach generalizes the notion of the phase-added stereogram, allowing for the calculatiion of an arbitrary number of Fourier coefficients per block, enabling high calculation speed with holograms of good visual quality, targeting minimal memory requirements.

Enhanced direct binary search algorithm for binary computer-generated Fresnel holograms

The direct binary search (DBS) algorithm was originally invented for the synthesis of a binary Fourier hologram, and was applied for the generation of a binary Fresnel hologram recently. DBS performs quality evaluation on every pixel. Therefore, both the quality and diffraction efficiency of the generated binary hologram are better among various algorithms of the binary hologram. However, DBS is a time-consuming algorithm and thus is impractical for the generation of high-definition computer-generated holograms. In this paper, we proposed an enhanced DBS (E-DBS) method to speed up the hologram computation. E-DBS is based on the same pixelwise evaluation strategy of DBS, but the diffraction field of a single pixel is precomputed as a lookup table. In evaluating any pixel value, only a small area in the region of interest affected by the diffraction field of single pixel is calculated. In addition, it is also found that qualified results can be obtained by using only 4% of the area of the diffraction field. As a result, the computing complexity of E-DBS can be reduced by at least 2 orders of magnitude in contrast to conventional DBS.

High Resolution Computer-Generated Rainbow Hologram

We have developed an output device for a computer-generated hologram (CGH) named a fringe printer, which can output a 0.35- μ m plane-type hologram. We also proposed several CGH with a fringe printer. A computer-generated rainbow hologram (CGRH), which can reconstruct a full color 3D image, is one of our proposed CGH. The resolution of CGRH becomes huge (over 50 Gpixels) due to improvement of the fringe printer. In the calculation, it is difficult to calculate the whole fringe pattern of CGRH at the same time by a general PC. Furthermore, since the fine pixel pitch provides a wide viewing angle in CGRH, object data, which are used in fringe calculation, should be created from many viewpoints to provide a proper hidden surface removal process. The fringe pattern of CGRH is calculated in each horizontal block. Therefore, the object data from several view points should be organized for efficient computation. This paper describes the calculation algorithm for huge resolution CGRH and its output results.

Efficient tiled calculation of over-10-gigapixel holograms using ray-wavefront conversion

In the calculation of large-scale computer-generated holograms, an approach called "tiling," which divides the hologram plane into small rectangles, is often employed due to limitations on computational memory. However, the total amount of computational complexity severely increases with the number of divisions. In this paper, we propose an efficient method for calculating tiled large-scale holograms using ray-wavefront conversion. In experiments, the effectiveness of the proposed method was verified by comparing its calculation cost with that using the previous method. Additionally, a hologram of 128K × 128K pixels was calculated and fabricated by a laser-lithography system, and a high-quality 105 mm × 105 mm 3D image including complicated reflection and translucency was optically reconstructed.

Colour computer-generated holography for point clouds utilizing the Phong illumination model

A technique integrating the bidirectional reflectance distribution function (BRDF) is proposed to generate realistic high-quality colour computer-generated holograms (CGHs). We build on prior work, namely a fast computer-generated holography method for point clouds that handles occlusions. We extend the method by integrating the Phong illumination model so that the properties of the objects' surfaces are taken into account to achieve natural light phenomena such as reflections and shadows. Our experiments show that rendering holograms with the proposed algorithm provides realistic looking objects without any noteworthy increase to the computational cost.

Full-color digitized holography for large-scale holographic 3D imaging of physical and nonphysical objects

Digitized holography techniques are used to reconstruct three-dimensional (3D) images of physical objects using large-scale computer-generated holograms (CGHs). The object field is captured at three wavelengths over a wide area at high densities. Synthetic aperture techniques using single sensors are used for image capture in phase-shifting digital holography. The captured object field is incorporated into a virtual 3D scene that includes nonphysical objects, e.g., polygon-meshed CG models. The synthetic object field is optically reconstructed as a large-scale full-color CGH using red-green-blue color filters. The CGH has a wide full-parallax viewing zone and reconstructs a deep 3D scene with natural motion parallax.

Fast occlusion processing for a polygon-based computer-generated hologram using the slice-by-slice silhouette method

In a polygon-based computer-generated hologram (CGH), the three-dimensional (3D) model is represented as a polygon, which consists of numerous small facets. Lighting effect, material texture, and surface property can be included in the polygonal model, which enables polygon-based CGH to realize high-fidelity 3D display. On the other hand, the occlusion effect is an important depth cue for 3D display. In polygon-based CGH, however, occlusion processing is difficult and time-consuming work. In this paper, we proposed a simple and fast occlusion processing method, the slice-by-slice silhouette (S³) method, for generating the occlusion effect in polygon-based CGH. In the S³ method, the polygonal model is sliced into multiple thin segments. For each segment, a silhouette mask is generated and located at the backside of the segment. The incident light is first shaded by the mask and superimposes on the light emitted from the facets of the evaluated segment. In this way, every segment can be processed sequentially to get the resulting object light. Our experimental result demonstrates that the S³ method can generate a high-definition hologram with qualified occlusion effect. The computing complexity of the S³ method is lower than that of previous methods. In addition, the S³ method can be parallelized easily, and thus can be further speeded up by applying a parallel computing framework, such as multi-core CPU or GPU.

Digital Holography and 3D Imaging: introduction to the joint feature issue in Applied Optics and Journal of the Optical Society of America B

The OSA Topical Meeting on Digital Holography and 3D Imaging (DH) was held 25-28 July 2016 in Heidelberg, Germany, as part of the Imaging Congress. Feature issues based on the DH meeting series have been released by Applied Optics (AO) since 2007. This year, AO and the Journal of the Optical Society of America B (JOSA B) jointly decided to have one such feature issue in each journal. This feature issue includes 31 papers in AO and 11 in JOSA B, and covers a large range of topics, reflecting the rapidly expanding techniques and applications of digital holography and 3D imaging. The upcoming DH meeting (DH 2017) will be held from 29 May to 1 June in Jeju Island, South Korea.