## Abstract

A tiling integral floating display system is proposed using the optimization of viewing window. The integral floating display, which is a combination of an integral imaging system and a floating lens, has many advantages, but it is hard to realize a large system due to the cost and difficulties in making the large floating device. In this paper, the stackable integral floating display is proposed by modifying the size of the viewing window to be the same as that of the display device, which can be a solution for the large scale autostereoscopic three-dimensional display system.

© 2012 Optical Society of America

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### Equations (8)

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(1)
$$s=\phi \frac{d-g}{d},$$
(2)
$${w}_{i}=\phi \frac{g-d}{g}.$$
(3)
$$m\phi \frac{d-g}{d}=\phi \frac{g-d}{g},$$
(4)
$$g=-\frac{d}{m}=-\frac{F}{m},$$
(5)
$${w}_{i}=\phi (1+m),$$
(6)
$$\theta =2\text{\hspace{0.17em}}\mathrm{arctan}\left|\frac{m\phi}{2d}\right|$$
(7)
$$D=\frac{N{\omega}_{i}}{2\text{\hspace{0.17em}}\mathrm{tan}\left(\frac{\mathrm{\Theta}}{2}\right)}=\frac{N|d|}{m(1+m)}.$$
(8)
$${\mathrm{\Theta}}_{\text{total}}=2\text{\hspace{0.17em}}\mathrm{arctan}\left[\frac{({L}_{o}-D)}{{L}_{o}}\text{\hspace{0.17em}}\mathrm{tan}\left(\frac{\mathrm{\Theta}}{2}\right)\right]\phantom{\rule{0ex}{0ex}}=2\text{\hspace{0.17em}}\mathrm{arctan}[\mathrm{tan}\left(\frac{\mathrm{\Theta}}{2}\right)-\frac{N\phi}{(2{L}_{o})(1+m)}]\phantom{\rule{0ex}{0ex}}=2\text{\hspace{0.17em}}\mathrm{arctan}[\left|\frac{m\phi}{2d}\right|-\frac{N\phi}{(2{L}_{o})(1+m)}].$$