# Variable-focus liquid lens for miniature cameras

Original entry: Scott Tsai, APPHY 226, Spring 2009

"Variable-focus liquid lens for miniature cameras"

S. Kuiper, and B.H.W. Hendriks

Applied Physics Letters, Volume 85, Number 7, pp.1128-1130 (16 August 2004)

## Soft Matter Keywords

Electrowetting, lens, contact angle, laplace pressure, curvature.

## Overview

Refer to paper abstract

## Soft Matter Examples

The authors of this paper developed a miniturized lens using the curvature between two imiscible liquids. The authors house the two fluids in a glass cylinder and use electrowetting to control the curvature of the lens, and thus control the focus of the lens. One of the liquids inside the cylinder has to be electrically conducting, and the other is insulating. (Fig. 1a and Fig. 1b)

The bottom part of the housing is coated with transparent indium tin oxide (ITO), and act as electrodes. ITO is also coated on the sides fo the cylinder housing to act as ground. The inside of the cylinder is then coated with a hydrophobic coating so that the equilibrium contact angle will be high before voltage is turned on.

When voltage is applied across the electrodes, and electric field is produced that reduces the interfacial tension between the two fluids and causes a change in contact angle (Fig. 1c to 1e). The contact angle change is described by the following equation.

<math> cos \theta = \frac {\gamma_{wi} - \gamma_{wc}} {\gamma_{ci}} + \frac {\epsilon} {2 \gamma_{ci} d_{f}} V^2 </math>

<math> \epsilon </math> is the dielectric constant of the insulating film, and ,<math> d_{f} </math> is its thickness. By applying voltage a system with a 3 mm diameter lens, the authors were able to produce dioptic power between -100 and +50.

The lens is driven by DC or AC voltage, and the authors used 50V to actuate the lens. When the voltage is applied, and the lens curvature is changed, the speed at which the lens stabilizes from oscillation is critical if the lens is to be adapted for a camera. Therefore, the authors did tests comparing the damping time with variables <math> d, \gamma_{ci}, \rho, \tau </math>. They plotted a dimensionless damping time versus a dimensionless lens parameter (Fig 2) and found that the system was underdamped up to a critical point, at which it became overdamped. When the system is underdamped, the meniscus continues to oscillate. As the dimensionless lens parameter (<math> \nu^2\rho/\gamma_{ci}d </math>) is increased, the systems becomes overdamped at a critical dimensionless time. At that point, the system is critically damped and results in the fastest curvature change without oscillations. They obtain results that show:

<math> \tau_{crit} = 0.3 \sqrt {\rho d^3/\gamma_{ci}} </math>, and <math> \nu_{crit} = 0.02 \sqrt {d \gamma_{ci}/\rho} </math>