## Abstract

A three-dimensional (3D) digital holographic display system with image processing is presented. By use of phase-shifting digital holography, we obtain the complex amplitude of a 3D object at a recording plane. Image processing techniques are introduced to improve the quality of the reconstructed 3D object or manipulate 3D objects for elimination and addition of information by modifying the complex amplitude. The results show that the information processing is effective in such manipulations of 3D objects. We also show a fast recording system of 3D objects based on phase-shifting digital holography for display with image processing. The acquisition of 3D object information at 500 Hz is demonstrated experimentally.

© 2006 Optical Society of America

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### Equations (8)

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(1)
$$f(x,y)={\displaystyle \int \int {o}_{z}(\xi ,\eta ){g}_{z}(x-\xi ,y-\eta )\mathrm{d\xi d\eta}}$$
(2)
$$={o}_{z}(x,y)\otimes {g}_{z}(x,y)$$
(3)
$$={f}_{a}(x,y)\mathrm{exp}\left[i{f}_{p}(x,y)\right],$$
(4)
$${g}_{z}(x,y)=\mathrm{exp}\left[\frac{i\pi}{\lambda z}\left({x}^{2}+{y}^{2}\right)\right],$$
(5)
$$\begin{array}{c}{I}_{\mathrm{\Delta}}(x,y)={\left|f(x,y)+{r}_{\mathrm{\Delta}}(x,y)\right|}^{2}\end{array}={\left|{f}_{a}(x,y)\right|}^{2}+{\left|{r}_{a}(x,y)\right|}^{2}+2{f}_{a}(x,y){r}_{a}(x,y)\mathrm{cos}[{f}_{p}(x,y)-{r}_{p}(x,y)-\mathrm{\Delta}]\text{,}$$
(6)
$${r}_{\mathrm{\Delta}}(x,y)={r}_{a}(x,y)\mathrm{exp}\left\{i\left[{r}_{p}(x,y)+\mathrm{\Delta}\right]\right\},$$
(7)
$${f}_{r}(x,y)=\frac{1}{4{r}_{r}(x,y)}\left\{{[{I}_{0}(x,y)-{I}_{\pi}(x,y)]}^{2}+{[{I}_{\pi /2}(x,y)-{I}_{3\pi /2}(x,y)]}^{2}\right\},$$
(8)
$${f}_{i}(x,y)={\text{tan}}^{-1}\left[\frac{{I}_{\pi /2}(x,y)-{I}_{3\pi /2}(x,y)}{{I}_{0}(x,y)-{I}_{\pi}(x,y)}\right]\mathrm{.}$$