## Abstract

We have designed and built an electrostatically deformable membrane
mirror with simple bias and driver electronics to evaluate its
suitability for a curvature-sensing adaptive optics system. It has
a 100-mm-diameter aluminized nitrocellulose membrane, with 31 actuators
arranged concentrically. The unit operates at atmospheric pressure
with a high bias voltage applied to the membrane. The high-voltage
electronics are contained within the mirror housing for safety
reasons. An entrance window reduces the effects of air-coupled
vibration. Details of the device and design rationale are
presented. With a proper bias, the unit can provide low-order
(including tip–tilt) wave-front correction.

© 1998 Optical Society of America

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### Equations (6)

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(1)
$${\nabla}^{2}z=\frac{{\mathrm{\u220a}}_{0}}{\mathit{Tl}_{0}{}^{2}}{V}^{2},$$
(2)
$${\nabla}^{2}z=\frac{{\mathrm{\u220a}}_{0}}{\mathit{Tl}_{0}{}^{2}}\xb7\left(V_{0}{}^{2}+2{V}_{0}\mathrm{\Delta}V\right),$$
(3)
$$z\left(r\right)=\left\{\begin{array}{cc}\frac{{\mathrm{\u220a}}_{0}}{4\mathit{Tl}_{0}{}^{2}}\left\{{V}^{2}{r}^{2}-V_{0}{}^{2}r_{a}{}^{2}\left[1-2ln\left(\frac{{r}_{a}}{{r}_{f}}\right)\right]-\left({V}^{2}-V_{0}{}^{2}\right)r_{p}{}^{2}\left[1-2ln\left(\frac{{r}_{p}}{{r}_{f}}\right)\right]\right\}& r{r}_{p}\\ \frac{{\mathrm{\u220a}}_{0}}{4\mathit{Tl}_{0}{}^{2}}\left\{V_{0}{}^{2}{r}^{2}+2\left({V}^{2}-V_{0}{}^{2}\right)r_{p}{}^{2}ln\left(\frac{r}{{r}_{f}}\right)-V_{0}{}^{2}r_{a}{}^{2}\left[1-2ln\left(\frac{{r}_{a}}{{r}_{f}}\right)\right]\right.& {r}_{p}r{r}_{a},\\ \frac{{\mathrm{\u220a}}_{0}}{2\mathit{Tl}_{0}{}^{2}}\left[\left({V}^{2}-V_{0}{}^{2}\right)r_{p}{}^{2}+V_{0}{}^{2}r_{a}{}^{2}\right]ln\left(\frac{r}{{r}_{f}}\right)& {r}_{a}r{r}_{f}\end{array}\right\},$$
(4)
$$f=\frac{\mathit{Tl}_{0}{}^{2}}{{\mathrm{\u220a}}_{0}V_{0}{}^{2}},$$
(5)
$$\frac{{\nabla}^{2}z}{\mathrm{\Delta}V}=\frac{2{\mathrm{\u220a}}_{0}{V}_{0}}{\mathit{Tl}_{0}{}^{2}},$$
(6)
$$\frac{\mathrm{\Delta}{z}_{p}}{\mathrm{\Delta}V}=\frac{{\mathrm{\u220a}}_{0}{V}_{0}}{2\mathit{Tl}_{0}{}^{2}}r_{p}{}^{2}\left[1-2ln\left(\frac{{r}_{p}}{{r}_{f}}\right)\right],$$