## Abstract

Electrical address circuits developed for driving fast-switching ferroelectric liquid-crystal spatial light modulators (SLM) can be programmed to increase the speed of much slower responding nematic liquid-crystal SLMs. Using an addressing circuit that can switch as fast as
$0.164\text{\hspace{0.17em} ms}$, voltages are programmed for values of phase that exceed the desired phase, and when the phase reaches the desired value, the voltage is switched to the required steady-state voltage. For a SLM that has a phase range of
$3.5\text{\pi}$ and that is programmed over a
$2\text{\pi}$ range, switching speed is reduced from
$400\text{\hspace{0.17em} ms}$ to between 71 and
$\text{77\hspace{0.17em} ms}$. The speedup algorithm is applied to each pixel of the SLM together with a digital correction for a spatially nonuniform phase.

© 2006 Optical Society of America

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### Equations (3)

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(1)
$$I\left(t\right)={I}_{0}\left[1+\mathrm{cos}\text{\hspace{0.17em}}\phi \left(t\right)\right]/2,$$
(2)
$$\phi \left(t\right)={\phi}_{0}+\left({\phi}_{1}-{\phi}_{0}\right)\left[1-\mathrm{exp}\left(-\frac{t-{t}_{0}}{\Delta t}\right)\right],$$
(3)
$$\phi \left(t\right)=\{\begin{array}{l}{\phi}_{0}+\left({\phi}_{H}-{\phi}_{0}\right){\left(\frac{t-{t}_{0}}{\Delta {t}_{1}}\right)}^{2},\text{\hspace{1em}}{t}_{0}<t\le {t}_{0}+\Delta {t}_{1},\\ {\phi}_{H}+\left({\phi}_{M}-{\phi}_{H}\right)\left(\frac{t-{t}_{0}-\Delta {t}_{1}}{\Delta {t}_{2}}\right),\text{\hspace{0.17em}}{t}_{0}+\Delta {t}_{1}<t\le {t}_{0}+\Delta {t}_{1}+\Delta {t}_{2},\\ {\phi}_{M}+\left({\phi}_{1}-{\phi}_{M}\right)\left[1-\mathrm{exp}\left(-\frac{t-{t}_{0}-\Delta {t}_{1}-\Delta {t}_{2}}{\Delta {t}_{3}}\right)\right],\text{\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}}t>{t}_{0}+\Delta {t}_{1}+\Delta {t}_{2},\end{array}$$