Traditional holography records light on photosensitive materials to reconstruct a 3D image. Unlike stereoscopic 3D displays, holographic images do not conflict with sensations of depth. However, this technology can only create 3D images from physical objects. The analog technology used to create the images also prevents them from being archived or transmitted using digital media. Computer holography (CH)—using computer graphics (CG) to create a hologram—combines the image completeness of traditional holography with the flexibility of creating a virtual image from a numerical model. This technology also resolves the digital storage problems of analog holography. However, CH suffers from long computation times and no technique to render the numerical models. We have developed a technique, called wave-field rendering, to address the drawbacks of CH and create photorealistic computer-generated 3D images.1–3 Our newest hologram4—called ‘Brothers’—is currently on display at the Massachusetts Institute of Technology (MIT) Museum (see Figure 1).
Figure 1. A computer-generated hologram, named ‘Brothers,’ using our new technique is on display at the Massachusetts Institute of Technology (MIT) Museum.
The long computation time for creating CH comes from the point-based model—see Figure 2(a)—commonly used to produce the image. In this model, an object is expressed by a set of point sources and the light is then computed for each point. However, the computation is time-consuming, especially for high-definition holograms like ‘Brothers’ because a tremendous number of point sources are necessary for forming the object. To resolve this problem, we model object surfaces as the composition of many polygons, similar to traditional CG: see Figure 2(b). The light is computed for each polygon and then summed to form the object. This procedure can drastically reduce the computation time of CHs.
Figure 2. Schematic comparison of (a) the point-based method and (b) the polygon-based method for modeling the light reflected off objects in a computer-generated hologram.
The computation of the light from each polygon is based on wave optics and executed with a fast Fourier transform. Figure 3 shows the basic wave-field rendering procedure. Polygons are expressed as a 2D distribution of complex amplitudes called the surface function: see Figure 3(b). While the phase distribution of the surface function describes the light diffusion, the amplitude distribution represents the shape, brightness, and texture of the polygon.
Figure 3. Procedure for producing the object field of a triangular prism by wave-field rendering.
One advantage of wave-field rendering is its similarity to conventional CG techniques. Figure 4 shows a comparison between surface functions for flat and Gouraud shading. The amplitude distribution is a constant for flat shading, whereas there is a gradation for Gouraud shading. The phase distribution is almost random and thus has a nearly flat spatial spectrum in both cases because diffuse surfaces are rendered. When a texture is mapped on to the polygon, the amplitude distribution is simply modulated by the mapped image.3
Figure 4. Examples of the surface function for (a) flat shading and (b) Gouraud shading. CG: Computer graphics.
Specular surfaces can also be modeled with wave-field rendering.5 In this case, the phase distribution spatial spectrum for each polygon is peaked rather than flat. In addition, the frequency peak is shifted depending on the reflection direction. Flat specular surfaces can be rendered by providing these properties to the phase distribution, whereas smooth specular surfaces use a segmented phase distribution technique (see Figure 5).6
Figure 5. Examples of specular reflection: (a) specular flat shading and (b) specular smooth shading.
Figure 6 shows the 3D scene of ‘Brothers’ exhibited at the MIT Museum. The process for making this image is shown in a short video that is available online.7 For this hologram, the main subjects are live faces measured with a Konica Minolta Vivid 910 3D laser scanner. The total number of polygons for the two faces is 6519 with only 5339 visible. The hologram is composed of nearly 25 billion (196, 608×131, 072) pixels, and each pixel is 0.64×0.8μm2. The maximum viewing angles are approximately 60 and 45° in the horizontal and vertical directions, respectively. The fringe pattern, calculated with wave-field rendering, is printed on a glass plate as a binary pattern with chromium thin film using a laser lithography system made by Heidelberg Instruments GmbH.
Figure 6. The 3D scene of ‘Brothers’ exhibited at the MIT Museum.
In summary, we have developed a technique called wave-field rendering to create high-definition, photorealistic computer-generated holograms whose optical reconstruction is comparable to conventional analog holography. One of the newest holograms, ‘Brothers,’ is currently on display at the MIT Museum and is considered a milestone in 3D imagery. While current video display devices cannot reproduce these holograms' high definition, our technique demonstrates the potential of future 3D imaging systems. These holograms are also limited to monochromatic images. Creating full-color 3D images is the next target in computer holography.
The authors thank Ichiroh Kanaya of Osaka University for his assistance in the 3D scan of live faces. This work was supported in part by the Japan Society for the Promotion of Science through a KAKENHI grant (21500114, 24500133) and Kansai University (Grant-in-Aid for Joint Research 2011–2012).
Department of Electrical and Electronic Engineering
Kyoji Matsushima received his PhD in applied physics from Osaka City University. He is currently a professor. His research interests include computer-generated holograms, digital holography, and numerical simulations of wave optics.
Department of Mechanical Engineering
Sumio Nakahara received his PhD from Osaka University in 1987. He was an adjunct professor at Washington State University in 1993–1994. His current research interests are in the development of laser direct-write lithography technology for computer-generated holograms, laser microprocessing, and microelectromechanical systems technology. He is currently an associate professor.
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21(2), p. 023002, 2012. doi:10.1117/1.JEI.21.2.023002
5. H. Nishi, K. Matsushima, S. Nakahara, Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography, Proc. SPIE
8281, p. 828110, 2012. doi:10.1117/12.908871