In this review paper, we first provide comprehensive tutorials on two classical methods of polygon-based computergenerated 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.
Bragg processing using a volume hologram offers an alternative in optical image processing in contrast to Fourier-plane processing. By placing a volume hologram near the object in an optical imaging setup, we achieve Bragg processing. In this review, we discuss various image processing methods achievable with acousto-optic modulators as dynamic and programmable volume holograms. In particular, we concentrate on the discussion of various differentiation operations leading to edge extraction capabilities.
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.
We study the use of two dynamic thick holograms to realize isotropic two-dimensional (2D) differentiation under Bragg diffraction. Acousto-optic modulators (AOMs) are used as dynamic volume holograms. Using a single volume hologram, we can accomplish a first-order derivative operation, corresponding to selective edge extraction of an image. Since the AOM is a 1D spatial light modulator, filtering of the image only occurs along the direction of the sound propagation. To achieve 2D image processing, two AOMs are used within a Mach–Zehnder interferometer (MZI). By aligning one AOM along the x-direction on the upper arm of the interferometer and another AOM along the y-direction on the lower arm, we accomplish the sum of two first-derivative operations, leading to isotropic edge extraction. We have performed both computer simulations and optical experiments to verify the proposed idea. The system provides additional operations in optical computing using AOMs as dynamic holograms.
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