## Abstract

We describe various techniques to synthesize three types of computer-generated hologram (CGH): the Fresnel–Fourier CGH, the Fresnel CGH, and the image CGH.
These holograms are synthesized by fusing multiple perspective views of a computer-generated scene. An initial hologram is generated in the computer as a Fourier hologram. Then it can be converted to either a Fresnel or an image hologram by computing the desired wave propagation and imitating an interference process of optical holography. By illuminating the CGH, a 3D image of the objects is constructed. Computer simulations and experimental results underline the performance of the suggested techniques.

© 2006 Optical Society of America

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### Equations (11)

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(1)
$$s\left(m,n\right)={\displaystyle \int {\displaystyle \int {p}_{mn}\left({x}_{p},{y}_{p}\right)\times \text{exp}\left[-i2\pi b\left({x}_{p}\text{\hspace{0.17em} sin \hspace{0.17em}}{\phi}_{m}+{y}_{p}\text{\hspace{0.17em} sin \hspace{0.17em}}{\theta}_{n}\right)\right]}\times \mathrm{d}{x}_{p}\mathrm{d}{y}_{p},}$$
(2)
$$s\left(u,v\right)\propto {\displaystyle \int {\displaystyle \int {\displaystyle \int t\left({x}_{s},{y}_{s},{z}_{s}\right)\times \text{exp}\left\{-i2\pi \alpha \left[u{x}_{s}+v{y}_{s}\text{\hspace{0.17em}}+\sigma {z}_{s}\left({u}^{2}+{v}^{2}\right)\right]\right\}\times \mathrm{d}{x}_{s}\mathrm{d}{y}_{s}\mathrm{d}{z}_{s},}}}$$
(3)
$${H}_{\text{FF}}\left(u,v\right)=\Re \left\{s\left(u,v\right)\text{exp}\left(\frac{-i\pi {r}^{2}}{\lambda {z}_{\text{\U0001d50d}}}\right)\times \text{exp}\left(\frac{i2\pi \text{\hspace{0.17em} sin \hspace{0.17em}}\psi}{\lambda}\text{\hspace{0.17em}}v\right)\right\}+c,$$
(4)
$${{H}_{\text{FF}}}^{\prime}\left(u,v\right)=\Re \left\{\text{exp}\left[-i\text{8}\pi \gamma {\left(\frac{r}{dN}\right)}^{2}+i4\pi \beta \text{\hspace{0.17em}}\frac{v}{dN}\right]\right\},$$
(5)
$${Z}_{\U0001d50d}=\frac{{\left(dN\right)}^{2}}{8\lambda \gamma},$$
(6)
$$\text{sin \hspace{0.17em}}\psi =\frac{2\lambda \beta}{dN}.$$
(7)
$${\left[2\pi \gamma {\left(\frac{2r}{dN}\right)}^{2}+2\pi \beta \text{\hspace{0.17em}}\frac{2v}{dN}\right]}_{v\text{,}r=\mathit{dN}/2}-{\left[2\pi \gamma {\left(\frac{2r}{dN}\right)}^{2}\text{\hspace{0.17em}}+2\pi \beta \text{\hspace{0.17em}}\frac{2v}{dN}\right]}_{v\text{,}r=(\mathit{dN}/2)-2d}\le 2\pi .$$
(8)
$${z}_{\U0001d50d}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\frac{d}{\lambda}\text{\hspace{0.17em}}\left(Nd+2{r}_{o}\right),$$
(9)
$${H}_{\text{Fr}}\left(x,y\right)=\Re \left\{{\U0001d50d}^{-1}\left\{s\left(u,v\right)\right\}\text{\hspace{0.17em}}\ast \text{\hspace{0.17em} exp}[\frac{i\pi}{\lambda {z}_{F}}\text{\hspace{0.17em}}\left({x}^{2}+{y}^{2}\right)]\times \text{exp}\left(i2\pi \text{\hspace{0.17em}}\frac{\text{sin \hspace{0.17em}}\psi}{\lambda}\text{\hspace{0.17em}}y\right)\right\}+c,$$
(10)
$${z}_{F}\hspace{0.17em}\ge \hspace{0.17em}\frac{{d}^{2}N}{\lambda}.$$
(11)
$${H}_{I}\left(x,y\right)=\Re \left\{{\U0001d50d}^{-1}\left\{s\left(u,v\right)\right\}\text{exp}\left(i2\pi \text{\hspace{0.17em}}\frac{\mathrm{sin}\text{\hspace{0.17em}}\psi}{\lambda}\text{\hspace{0.17em}}y\right)\right\}+c.$$