Abstract
A texturing method for the semi-analytic polygon computer-generated hologram synthesis algorithm is studied. Through this, the full-potential and development direction of the semi-analytic polygon computer-generated holograms are discussed and compared to that of the conventional numerical algorithm of polygon computer-generated hologram generation based on the fast Fourier transform and bilinear interpolation. The theoretical hurdle of the semi-analytic texturing algorithm is manifested and an approach to resolve this problen. A key mathematical approximation in the angular spectrum computer-generated hologram computation, as well as the trade-offs between texturing effects and computational efficiencies are analyzed through numerical simulation. In this fundamental study, theoretical potential of the semi-analytic polygon computer-generated hologram algorithm is revealed and the ultimate goal of research into the algorithm clarified.
Highlights
The computational algorithms of computer-generated holograms (CGHs) have been actively researched
In the field of CGH algorithms, most research effort is directed towards the development of fast computation algorithms using parallel computing devices such as GPUs [9,10,11,12,13,14,15] and representation theories such as those about texturing [16,17,18,19,20], shading [21, 22], and the creation of hybrid scenes from 2D and 3D images [16, 17]
The analytic result ∆G shows faster computation since the coordinate transformation process IL→G can be carried out directly in the analytic formula ∆G, so the angular spectrum CGH (ASCGH) is a mathematically rigorous form which does not include any distortion unlike the fast Fourier transform (FFT)-based method IL→G (∆L )
Summary
The computational algorithms of computer-generated holograms (CGHs) have been actively researched. The motivation for the development of the semi-analytic polygon CGH algorithm [26] was the efficient computation of the required non-uniform Fourier transform using the de facto standard mathematical formula From this respect, the research contrasts that recently carried out on the conventional fully numerical FFT-based method. The semianalytic polygon CGH algorithm seems to have been successful for 3D objects that are composed of bare triangle facets and has increased the possibility of achieving substantial improvements in computational efficiency and accuracy Regarding expressiveness such as texturing that is a fundamental element for the realistic rendering of reconstructed holographic 3D objects, the FFT-based method has an advantage of that its computational complexity is constant regardless of whether the 3D objects are textured or bare. This fundamental study on semi-analytic CGH paves the way to novel semi-analytic fast textured CGH algorithm, allows an understanding of their theoretical potential, and clarifies the research direction necessary to achieve the ultimate goal of real-time photorealistic CGH generation
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