## Abstract

In this paper, a fast method for displaying a digital, real and off-axis Fresnel hologram on a lower resolution device is reported. Preserving the original resolution of the hologram upon display is one of the important attributes of the proposed method. Our method can be divided into 3 stages. First, a digital hologram representing a given three dimensional (3D) object is down-sampled based on a fix, jitter down-sampling lattice. Second, the down-sampled hologram is interpolated, through pixel duplication, into a low resolution hologram that can be displayed with a low-resolution spatial light modulator (SLM). Third, the SLM is overlaid with a grating which is generated based on the same jitter down-sampling lattice that samples the hologram. The integration of the grating and the low-resolution hologram results in, to a good approximation, the resolution of the original hologram. As such, our proposed method enables digital holograms to be displayed with lower resolution SLMs, paving the way for the development of low-cost holographic video display.

©2013 Optical Society of America

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### Equations (7)

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(1)
$${H}_{C}\left(x,y\right)={\displaystyle \sum _{j=0}^{P-1}{a}_{j}}\mathrm{exp}\left(\frac{i2\pi}{\lambda}\sqrt{{\left(x-{x}_{j}\right)}^{2}{\delta}^{2}+{\left(y-{y}_{j}\right)}^{2}{\delta}^{2}+{z}_{j}^{2}}\right),$$
(2)
$$H\left(x,y\right)=\text{Real}\left[{H}_{C}\left(x,y\right)R\left(y\right)\right].$$
(3)
$${s}_{d}\left(x\right)=\{\begin{array}{cc}s\left(x\right)(s\text{ample}\text{point})& x=km+{\tau}_{1}\\ 0& otherwise\end{array},$$
(4)
$$\begin{array}{l}{S}_{d}(\omega )=S\left(\omega \right)\ast \varphi (\omega )=S\left(\omega \right)\ast \left[\frac{1}{k}\left(1-\mathrm{sin}{c}^{2}\left(\omega /2k\right)\right)\right]+\frac{2\pi}{{k}^{2}}S\left(\omega \right)\\ =S\left(\omega \right)\ast \frac{{N}_{j}\left(\omega \right)}{k}+\frac{2\pi}{{k}^{2}}S\left(\omega \right),\end{array}$$
(5)
$$G\left(x,y\right)=\{\begin{array}{cc}1(s\text{ample}\text{point})& x=mk+{\tau}_{1}\text{and}y=nk+{\tau}_{2}\\ 0& otherwise\end{array},$$
(6)
$${H}_{J}\left(x,y\right)=H\left(x,y\right)G\left(x,y\right).$$
(7)
$${H}_{J}\left(x,y\right)=M\left(x,y\right)G\left(x,y\right).$$