## Abstract

A fast calculation method for computer-generated holograms for hidden surface removal is proposed. In this method, a three-dimensional object is considered as a set of point light sources emitting light rays. To achieve the hidden surface removal, only appropriate light rays are selected according to their geometrical position, which are then converted into a Fourier spectrum of the wavefront. After the Fourier spectrum on the spherical surface is obtained, diffraction in arbitrary directions is calculated. Numerical simulation of a series of diffracted wavefronts onto arbitrary observation planes has been demonstrated to verify the effectiveness of our proposal.

© 2013 Optical Society of America

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### Equations (6)

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(1)
$$F(u,v)=\frac{i}{4\pi}\frac{O(u,v,\sqrt{1/{\lambda}^{2}-{u}^{2}-{v}^{2}})}{\sqrt{1/{\lambda}^{2}-{u}^{2}-{v}^{2}}}\phantom{\rule{0ex}{0ex}}\times \mathrm{exp}\left(i2\pi R\sqrt{1/{\lambda}^{2}-{u}^{2}-{v}^{2}}\right),$$
(2)
$$O(u,v,\sqrt{1/{\lambda}^{2}-{u}^{2}-{v}^{2}})={{O}_{p}(1/\lambda ,\theta ,\varphi )|}_{0\le \theta \pi ,-\pi /2\le \varphi \pi /2}.$$
(3)
$$g(\mathrm{\Theta},\mathrm{\Phi})=\iiint o(x,y,z)\mathrm{exp}(-\frac{i2\pi Z}{\lambda})\mathrm{d}X\mathrm{d}Y\mathrm{d}Z\mathrm{.}$$
(4)
$$g(\mathrm{\Theta},\mathrm{\Phi})=\iiint o(x,y,z)\mathrm{exp}[-\frac{i2\pi}{\lambda}(\mathrm{sin}\text{\hspace{0.17em}}\mathrm{\Theta}\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\mathrm{\Phi}x+\mathrm{sin}\text{\hspace{0.17em}}\mathrm{\Theta}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\mathrm{\Phi}y+\mathrm{cos}\text{\hspace{0.17em}}\mathrm{\Theta}z)]\mathrm{d}x\mathrm{d}y\mathrm{d}z=\iiint o(x,y,z)\times \mathrm{exp}[-i2\pi (Ux+Vy+Wz)]\mathrm{d}x\mathrm{d}y\mathrm{d}z=O(U,V,W),$$
(5)
$$U=\mathrm{sin}\text{\hspace{0.17em}}\mathrm{\Theta}\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\mathrm{\Phi}/\lambda ,\phantom{\rule[-0.0ex]{2em}{0.0ex}}V=\mathrm{sin}\text{\hspace{0.17em}}\mathrm{\Theta}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\mathrm{\Phi}/\lambda ,\phantom{\rule[-0.0ex]{2em}{0.0ex}}W=\mathrm{cos}\text{\hspace{0.17em}}\mathrm{\Theta}/\lambda .$$
(6)
$$g(\mathrm{\Theta},\mathrm{\Phi})={O}_{p}(1/\lambda ,\mathrm{\Theta},\mathrm{\Phi}).$$