## Abstract

We report the generation of a real-time large computer generated hologram (CGH) using the wavefront recording plane (WRP) method with the aid of a graphics processing unit (GPU). The WRP method consists of two steps: the first step calculates a complex amplitude on a WRP that is placed between a 3D object and a CGH, from a three-dimensional (3D) object. The second step obtains a CGH by calculating diffraction from the WRP to the CGH. The disadvantages of the previous WRP method include the inability to record a large three-dimensional object that exceeds the size of the CGH, and the difficulty in implementing to all the steps on a GPU. We improved the WRP method using Shifted-Fresnel diffraction to solve the former problem, and all the steps could be implemented on a GPU. We show optical reconstructions from a 1,980 × 1,080 phase only CGH generated by about 3 × 10^{4} object points over 90 frames per second. In other words, the improved method obtained a large CGH with about 6 mega pixels (1,980 × 1,080 × 3) from the object points at the video rate.

© 2012 OSA

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### Equations (4)

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(1)
$${u}_{w}\left({x}_{w},{y}_{w}\right)=\sum _{j}^{N}{A}_{j}\text{exp}\left(i\frac{2\pi}{\lambda}{r}_{wj}\right),$$
(2)
$$u\left(x,y\right)=\frac{\text{exp}\left(i\frac{2\pi}{\lambda}z\right)}{i\lambda z}\iint {u}_{w}\left({x}_{w},{y}_{w}\right)\text{exp}\left(i\frac{\pi}{\lambda z}\left({\left(x-{x}_{w}\right)}^{2}+{\left(y-{y}_{w}\right)}^{2}\right)\right)d{x}_{w}d{y}_{w}$$
(3)
$$=\frac{\text{exp}\left(i\frac{2\pi}{\lambda}z\right)}{i\lambda z}{\mathcal{F}}^{-1}\left[\mathcal{F}\left[{u}_{w}\left(x,y\right)\right]\cdot \mathcal{F}\left[h\left(x,y\right)\right]\right]$$
(4)
$$\begin{array}{l}u\left(x,y\right)=\frac{\text{exp}\left(i\frac{2\pi}{\lambda}z\right)}{i\lambda z}\iint {u}_{w}\left({x}_{w},{y}_{w}\right)\text{exp}\left(i\frac{\pi}{\lambda z}\left({\left(x-m{x}_{w}\right)}^{2}+{\left(y-m{y}_{w}\right)}^{2}\right)\right)d{x}_{w}d{y}_{w}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\frac{\text{exp}\left(i\frac{2\pi}{\lambda}\left(z+\frac{\left(1-m\right)\left({x}^{2}+{y}^{2}\right)}{2z}\right)\right)}{i\lambda z}{\mathcal{F}}^{-1}\left[\mathcal{F}\left[{u}_{n}\left(x,y\right)\right]\cdot \mathcal{F}\left[{h}_{n}\left(x,y\right)\right]\right],\end{array}$$