## Abstract

A new method for synthesizing a full-color computer-generated hologram (CGH) of real-existing objects has been proposed. In this method, the synthesizing process of CGHs and the adjustments of magnifications for each wavelength are considered based on parabolic sampling of three-dimensional (3-D) Fourier spectra. Our method requires only one-dimensional (1-D) azimuth scanning of objects, does not require any approximations in the synthesizing process, and can perform efficient magnification adjustments required for color reconstruction. Experimental results have been presented to verify the principle and validity of this method.

© 2004 Optical Society of America

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### Equations (7)

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(1)
$$g({x}_{0},{y}_{0})=\iiint O(x,y,z)\mathrm{exp}\left\{-\frac{i2\pi}{\lambda}\left[\frac{{x}_{0}x+{y}_{0}y}{f}-\frac{\left({x}_{0}^{2}+{y}_{0}^{2}\right)z}{2{f}^{2}}\right]\right\}\mathit{dxdydz},$$
(2)
$$g(u,v)=\iiint O(x,y,z)\mathrm{exp}\left\{-i2\pi \left[ux+vy-\frac{\lambda}{2}\left({u}^{2}+{v}^{2}\right)z\right]\right\}\mathit{dxdydz}$$
(3)
$$=\left\{\iiint O(x,y,z)\mathrm{exp}[-i2\pi (ux+\mathit{vy}+wz)]\mathit{dxdydz}\right\}{\mid}_{w=-\lambda \left({u}^{2}+{v}^{2}\right)\u20442}$$
(4)
$$=\ud4d5\left[O(x,y,z)\right]{\mid}_{w=-\lambda \left({u}^{2}+{v}^{2}\right)\u20442},$$
(5)
$$w\phantom{\rule{.2em}{0ex}}\mathrm{cos}\phantom{\rule{.2em}{0ex}}\theta +u\phantom{\rule{.2em}{0ex}}\mathrm{sin}\phantom{\rule{.2em}{0ex}}\theta =0$$
(6)
$$w=-\frac{\lambda}{2}\left({u}^{2}+{v}^{2}\right).$$
(7)
$${\left(u-\frac{\mathrm{tan}\phantom{\rule{.2em}{0ex}}\theta}{\lambda}\right)}^{2}+{v}^{2}={\left(\frac{\mathrm{tan}\phantom{\rule{.2em}{0ex}}\theta}{\lambda}\right)}^{2},\phantom{\rule{.5em}{0ex}}w=-u\phantom{\rule{.2em}{0ex}}\mathrm{tan}\phantom{\rule{.2em}{0ex}}\theta .$$