## Abstract

An application of varifocal mirror autostereoscopic imaging to 3-D computer-generated movies is described. A high speed movie projector and oscillating varifocal mirror project moving autostereoscopic images at 15 volumetric images per second. In order lo distribute evenly the component images along the depth axis, linear time scans of the image volume are required. However, the image position is a nonlinear function of the mirror displacement, which, in turn, has a nonlinear frequency response to the mirror driving voltage. Analytical and experimental investigations are reported in which approximately linear scans for duty cycles approaching 90% were attained.

© 1968 Optical Society of America

Full Article |

PDF Article
### Equations (10)

Equations on this page are rendered with MathJax. Learn more.

(1)
$${{s}_{f}}^{\prime}=\frac{(-{s}_{f}+\mathrm{\Delta})(1+{\mathrm{\Delta}}^{2}/{R}^{2})}{1+(4{s}_{f}/{R}^{2})\mathrm{\Delta}-(3/{R}^{2}){\mathrm{\Delta}}^{2}}+\mathrm{\Delta}.$$
(2)
$${\sigma}^{\prime}=\frac{(-\sigma +\delta )(1+{\delta}^{2})}{(1+4\sigma \delta -3{\delta}^{2})}+\delta .$$
(3)
$${\sigma}^{\prime}=-\sigma /(1+4\sigma \delta ).$$
(4)
$$\mathrm{\Sigma}=1/(1-\mathrm{\Phi}).$$
(5)
$${m}^{-1}=(1+4\sigma \delta -3{\delta}^{2})/(1+{\delta}^{2}).$$
(6)
$$\mathrm{\Sigma}(t)=1/[1-\mathrm{\Phi}(t)]=1+D(t),$$
(7)
$$\mathrm{\Phi}(t)=D(t)/[1+D(t)],$$
(8)
$$\mathrm{\Phi}(t)=D(t)-{D}^{2}(t)+{D}^{3}(t)-\dots .$$
(9)
$${\mathrm{\Phi}}_{2}(t)\equiv D(t)-{D}^{2}(t)={A}_{0}+\sum _{1}^{\infty}({A}_{m}\hspace{0.17em}\text{cos}m\omega t+{B}_{m}\hspace{0.17em}\text{sin}m\omega t),$$
(10)
$$\begin{array}{c}{A}_{0}=-{\alpha}^{2}/3,\\ {B}_{m}={(-1)}^{m-1}(2\alpha /m\pi ),\\ {A}_{m}={(-1)}^{m-1}(4{\alpha}^{2}/{m}^{2}{\pi}^{2})={(-1)}^{m-1}{{B}_{m}}^{2}.\end{array}$$