## 2 DEA Lens
### Free Constrained Boundary  
To simplify the fabrication procedure, one DEA film can be used to actuate a liquid lens [47]. The lens structure is shown in Figure 3. The center area of the DEA film is drilled with a through hole. Figure 3a shows the film in a relaxed state (left) and stressed state (right). In the relaxed state, the diameter of the hole is at its maximum. In a stressed state, the DEA film expands, and the diameter of the hole decreases. Then, a small liquid droplet is used to fill the hole, as shown in Figure 3b. In the relaxed state (left), the droplet partially wets its border with a biconvex shape. The radius of curvature of the droplet is at its maximum (left). On the other hand, in a stressed state, the diminished hole squeezes the droplet, leading its surface profile to change (right). Similar to the lens shown in Figure 2, the focal length of the droplet can be tuned.  
Figure 2: A liquid lens actuated using DEA films: (**a**) voltage-off state and (**b**) voltage-on state.  
To make a demo, we drilled a hole on a \(\sim\)0.2-mm thick DEA film. The diameter of the hole is \(\sim\)1.85 mm and it was filled with glycerol (glycerol, no \(\sim\)1.47). The volume of glycerol is \(\sim\)0.6 mm\({}^{3}\). To observe the image property, a tiny object (Kitty) was placed at \(\sim\)6 cm under the lens. Figure 4 shows the observed image at V = 0 (left) and V = 2.6 kV (right). The right image is shrunk greatly, indicating that the focal length of the droplet is tunable.  
As the voltage increases from 0 to 2.6 kV, the focal length decreases from \(\sim\)5.5 mm to \(\sim\)3 mm. The measured resolution is \(\sim\)143 lp/mm at V = 2.6 kV, and the total (rise + decay) response time is \(\sim\)0.8 s. The major advantages of such a lens are the: simple fabrication process, miniature size, and high optical performance. However, the lens should be placed in a horizontal position in order to avoid a gravitational effect because of free-constrained boundaries. To increase the stability of the lens in case of shocking, shaking, and vibrating, the diameter of the hole should be kept at a micro-sized scale.  
Using the DEA film with a through hole, a solid lens can be shifted in a transverse direction [48]. Figure 5 shows the structure and operation method of such a solid lens. A DEA film is stretched by a rigid frame. A solid lens is trapped in the hole (Figure 5a). Only the surfaces of the left DEA film have electrodes. The solid lens can be prepared by curing an optical adhesive droplet in the hole. By applying a voltage across the electrodes (Figure 5b), the left DEA film is stretched, while the right DEA film shrinks. As a result, the lens shifts toward the right. The lens can conduct a reciprocating motion if the voltage is removed. When this lens system integrates with other lenses, a variable focal  
Figure 4: Images of the object observed through the liquid lens at different voltages. The figures are adapted from Ref. [47] with permission.  
Figure 3: The DEA film with a through hole for actuating a liquid droplet: (**a**) no droplet in the hole. Left is the relaxed state and right is the stressed state, (**b**) with a droplet in the hole. Left: relaxing state and right: stressing state.  
length can be obtained. This lens system has potential applications in imaging and beam steering, as well as optical switching, without the concern of a gravitational effect.