## Abstract

We propose a fast method for generating digital Fresnel holograms based on an interpolated wavefront-recording plane (IWRP) approach. Our method can be divided into two stages. First, a small, virtual IWRP is derived in a computational-free manner. Second, the IWRP is expanded into a Fresnel hologram with a pair of fast Fourier transform processes, which are realized with the graphic processing unit (GPU). We demonstrate state-of-the-art experimental results, capable of generating a 2048x2048 Fresnel hologram of around $4\times {10}^{6}$object points at a rate of over 40 frames per second.

© 2011 OSA

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### Equations (9)

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(1)
$$D\left(x,y\right)={\displaystyle \sum _{j=0}^{N-1}\frac{{a}_{j}}{{r}_{j}}}\mathrm{exp}\left(ik{r}_{j}\right)={\displaystyle \sum _{j=0}^{N-1}\left[\frac{{a}_{j}}{{r}_{j}}\mathrm{cos}\left(k{r}_{j}\right)+i\frac{{a}_{j}}{{r}_{j}}\mathrm{sin}\left(k{r}_{j}\right)\right]},$$
(2)
$${u}_{w}\left(x,y\right)={\displaystyle \sum _{j=0}^{N-1}\left({A}_{j}/{R}_{wj}\left(x-{x}_{j},y-{y}_{j}\right)\right)\mathrm{exp}\left(i\frac{2\pi}{\lambda}{R}_{wj}\left(x-{x}_{j},y-{y}_{j}\right)\right)},$$
(3)
$${u}_{w}\left(x,y\right)={\displaystyle \sum _{j=0}^{N-1}{f}_{j}},$$
(4)
$$u\left(x,y\right)=K{F}^{-1}\left[F\left[{u}_{w}\left(x,y\right)\right]\cdot F\left[h\left(x,y\right)\right]\right],$$
(5)
$${u}_{w}\left(x,y\right)|{}_{{l}_{m}\le x<{r}_{m},{b}_{n}\le y<{t}_{n}}=I\left(m,n\right)\mathrm{exp}\left(i2\pi {R}_{d\left(m,n\right)}\left(x-{x}_{m},y-{y}_{n}\right)/\lambda \right),$$
(6)
$${u}_{w}\left(x,y\right)=I\left(m,n\right)\mathrm{exp}\left(i2\pi {R}_{d\left(m,n\right)}\left(x-{x}_{m},y-{y}_{n}\right)/\lambda \right)=G\left(x-{x}_{m},y-{y}_{n},I\left(m,n\right),d\left(m,n\right)\right)$$
(7)
$${u}_{w}\left(x,y\right)|{}_{{l}_{m}\le x<{r}_{m},{t}_{n}\le y<{b}_{n}}=I\left(m,n\right){\displaystyle \sum _{{\tau}_{x}=-{\scriptscriptstyle \frac{M}{2}}}^{{\scriptscriptstyle \frac{M}{2}}-1}}{\displaystyle \sum _{{\tau}_{y}=-{\scriptscriptstyle \frac{M}{2}}}^{{\scriptscriptstyle \frac{M}{2}}-1}\mathrm{exp}\left(i2\pi {R}_{d\left(m,n\right)}\left(x-{x}_{m}+{\tau}_{x}p,y-{y}_{n}+{\tau}_{y}p\right)/\lambda \right)}$$
(8)
$$={G}_{A}\left(x-{x}_{m},y-{y}_{n},I\left(m,n\right),d\left(m,n\right)\right)$$
(9)
$$H\left(x,y\right)=RE\left[u\left(x,y\right)\cdot R\left(y\right)\right],$$