Study On Polygon-based Methods In Computer-generated Holography For Dynamic Holographic Three-dimensional Display

Display technology as one of cornerstones of our national industry founds and propels developments of various fields, inlcuding medical, culture, entertainment, manufacturing, military etc. Traditional two-dimensional display technologies and current three-dimensional(3D) display such as autostereoscopic and light field technologies cannot provide all depth cues of a 3D scene, which brings visual fatigue and inconvenience when people watch those 3D images. Holographic 3D display can physically reconstruct all information of a 3D image. As it provides all depth cues of 3D scenes, it is one of the most promising 3D display technologies in the future. Traditional optical holography only conducts with static and real instead of dynamic and virtual object, and it has to physically interference object wave and reference light. Computer-generated holography(CGH) is the digital version of the optical holography, which intersects various of different fields, including high speed computation, advanced optoelectronic devices etc. It digitally models 3D object and numerically computes interference pattern. CGH techniquies heavily determines the quality and the dynamic performance of the holographic 3D display. As the complicated 3D scene contains huge information capcity, speeding up CGH computation and adding vivid render information are the top hot-spot of the CGH research.In dynamic holographic 3D display, for the purpose of accelerating and correctly adding illumiations to polygon-based method of computer-generated holography, my research investigates the fundamental theory of the holographic display, and studied the physical model of polygon-baesd methods. Several accelerating methods and shading approaches for polygon-based method was proposed. The research and achievements are:1. I briefly summarized the current state-of-art development of the holographic 3D display, studied mathematical and physical theories of the holographic 3D display, introduced scalar diffraction theory and holography, and studied and analyized the approaches of numerical computation of wave diffraction.2. I corrected basic theory and fomulas of traditional polygon-based method: I fully derived the theory of the traditional polygon-based method, analyized and concluded the physical basis of this method was the computation of spectral 3D roation bringing by spatial 3D rotation. Correspondingly, I corrected the derivation of Jacob determination in variable replacement of integration, and eliminated requirement of paraxial condition.3. I proposed a brightness compenstation method for adding ambient light illumination in the traditional polygon-based method where hologram synthesis was separated from manufacturing procedure: I studied Lambert surface and defined a surface function of it in accordance with theory of computer graphics. I analyzed that brightnesss difference of reconstructed images was brought by two dimensional linear interpolation of the traditional polygon-based method and proposed a brightness compensation method by the use of unit power spectrum properties of a random signal and the limited geometrical relationship between original and new spectrum domain.4. I proposed an affine formed traditional polygon-baesd method which accelerated computational speed of hologram synthesis. I defined a unique primitive triangle and calculated its corresponding primitive spectrum. Taking advantages of affine transformation theory of multiview geometory, I established a direct relationship between spectrum of an arbitrary triangle and that of the primitive triangle. Then, I calculated the critical parameter of the affine transformation matrix by the use of pseudo-inversion matrix theory. I optically proved the correctness of the proposed method and discussed its acceleration performance and approximation.5. I propoed an affine formed full anlayitical polygon-based method which improved the computational effiency of the polygon approach. A specific primitive triangle was defined, and its spectrum was analytically expressed. Using the affine transformation, I calculated the value of each frequency point of spectrum of an aribrary polygon. In addition, I proposed a full matrix operating method to add random phase to each arbitrary polygon. Optical experiments were conducted to prove the effiency of the proposed method.