Ultrafast all-polymer electrically tunable silicone lenses

adhesion to the


Introduction
Soft actuators enable many applications and features that are not feasible with conventional approaches based on hard materials. However, most existing soft actuators present serious limitations such as slow response speed, short lifetime, or must be tethered to external bulky controllers that cannot be integrated, as is typically the case of pneumatic actuation.
In this contribution, we present a soft tuneable lens with integrated electrostatic actuation, capable of changing its focal length by more than 20% in less than 175 μs and stable for hundreds of millions of cycles.The concept is based on the bioinspired and DEA-driven design introduced by Carpi et al. in 2011. [4]However, a low-mechanical loss silicone (Nusil CF19-2186) is used here as dielectric membrane, instead of acrylic elastomer.This leads to the world's fastest tuneable lens with the ability to hold a very stable position, and demonstrates the integration of actuation, fast response speed and long lifetime in a soft device.This is a non-trivial performance for a very soft system (1 MPa).For comparison, we fabricated identical lenses made of the more widely-used 3M VHB acrylic elastomer, and obtained a comparable focal length tuning but with a bandwidth about 3 orders of magnitude smaller.
Among the different actuation mechanisms that have been used to drive soft actuators (pneumatic actuation, [1] phase change, [6] etc.), electrostatic actuation presents the advantages of being integrated into the device and consuming very little power, leading to compact, lightweight and energy efficient devices.
However, most of DEAs are based on an acrylic elastomer material with a high mechanical loss factor (VHB from 3M), as this allows for the largest reported strains.Using this acrylic elastomer leads to devices that react slowly to a voltage step input, with a pronounced viscoelastic creep, which causes the strain to keep increasing over several minutes. [9]In addition, DEAs require compliant electrodes, i.e. electrodes that can stretch as much as the device itself. [7]Although different approaches have been developed for the stretchable electrodes, many of today's devices use carbon grease or loose carbon powder electrodes, as they can easily be manually applied. [10]wever, such electrodes are sensitive to mechanical abrasion and subject to wear, leading to devices with a short lifetime, not to mention the difficulty of precisely patterning them on a sub-millimetre level.
The compliant electrodes we use consist of a mixture of carbon black and silicone, and are precisely patterned by pad-printing with subsequent crosslinking in an oven.The process forms solid electrodes with a strong adhesion to the dielectric membrane (Figure S1) and an excellent resistance to mechanical abrasion and wear, leading to reproducible devices with long lifetime.
Because of their large actuation strain, DEAs are particularly interesting in the field of adaptive optics. [5]Deformable optical lenses with electrically controllable focus present numerous advantages over the traditional approach consisting in translating rigid lenses.They have a much reduced mass and footprint, and can potentially be much faster due to the lower inertia of the system.The new DEAbased tuneable lens presented here provides the advantages of being extremely fast, energy-efficient and compact, and having a drift-free actuation.The extremely high speed and low level of visco-elastic drift demonstrated here are important requirements for tuneable lenses, which have never been obtained with any other polymer so far.
The following sections present the lens design and the characterization of its electromechanical response .

Lens design and principle
The lens, based on the biomimetic principle presented by Carpi et al, [4] consists of two pre-stretched elastomeric membranes bonded together and encapsulating a small amount (2 to 8 μl) of transparent fluid at the centre, forming a lens.An annular compliant electrode is patterned by pad printing a conductive mixture of carbon black and silicone on both sides of the device, which is clamped between two rigid or flexible PCBs (Figure 1).The rigid PCB in figure 1b   The fluid used to fill the lens must be chosen carefully, as it must fulfil optical criteria (high optical transmittance, low scattering, high index of refraction, thermal stability, durability, etc.), and at the same time be compatible with the elastomeric membrane (i.e. the fluid should not penetrate or interact with the membrane), and not evaporate though the membrane.Because of the design of the lens, the same membrane is used as dielectric for the actuator and as membrane encapsulating the liquid.In order to increase the device's tuning speed, we choose silicone membranes for the actuator, [11] and hence also for the lens.However, silicone elastomers are gas permeable, and swell when in contact with many non-polar liquids.Polar solvents, such as water, glycerol and ethylene glycol, are generally considered to be compatible with PDMS because they don't induce swelling of the material. [12]However, they are not suitable for this lens because they would evaporate or diffuse through the membrane.We found that the Sylgard 184 silicone pre-polymer, used by Carpi et al. for a tuneable lens based on a VHB acrylic elastomer membrane, [4] was also the best choice for silicone membranes. [13]The index of refraction was measured to be 1.41.Lenses made by encapsulating Sylgard 184 pre-polymer have shown no volume decrease and no droplet formation on the surface of the membrane more than two years after fabrication.
We used oxygen plasma activation to bond the two silicone membranes together without the need for an adhesive or glue, to ensure the fastest possible response.
Exposing silicone surfaces to low-power oxygen plasma renders them rich in O-H groups, leading to strong, irreversible covalent bonding when two treated surfaces are placed in contact. [14]This approach has enabled us to reliably and reproducibly encapsulate the liquid between two thin silicone membranes.Details about the fabrication process of the lens are given in the experimental section.
The change in focal length is driven by a dielectric elastomer actuator (DEA) located around the lens (Figure 1).When a voltage is applied between the electrodes of a DEA, it generates a compressive stress (Maxwell pressure) in the dielectric elastomer, which compresses the structure and reduces the membrane thickness while increasing the surface area of the electrodes.The relation between the applied voltage V and the Maxwell pressure p is given by: [7]  =  0    2  2 (1) where ε0 and εr are respectively the vacuum permittivity and the relative permittivity of the dielectric, and d the thickness of the membrane.To a first approximation, assuming that the elastomer behaves as a linear elastic body, the relation between the electrostatic pressure and the strain of the electrode is inversely proportional to the Young's Modulus of the elastomer.More complete models exist, which include the non-linear mechanical behaviour of elastomers [15] .A detailed analytical analysis of the relation between the applied voltage and the steady-state radius of curvature of the lens for the device geometry we are considering here was recently published [16] and can serve as a design tool in order to optimize the lens.
The focal length and tuning range depend on the initial filling of the lens, and on the different failure modes of the DEA.To show this graphically, we plot the focal length vs. initial lens volume and diameter in Figure 2.For illustration, we plot up to 10% radial compression of the lens due to an applied voltage (i.e., the initial radius roff of 2.5mm is reduced to ron=2.25mmdue to an applied voltage).
We compute the focal length f for different volumes of encapsulated liquid using the thin lens equation: where R1 and R2 are the radius of curvature of the two sides of the lens.For the initial calculations, we set R1=-R2=R, as the two membranes have identical

Static Focal Length
The measured steady-state (DC) focal length as a function of the applied voltage is shown in Figure 3 for six different lenses (5 with a silicone membrane, and 1 with a VHB acrylic elastomer membrane), each with a different amount of liquid encapsulated between the membranes, i.e., a different initial focal length.In accordance with the theory (Figure 2), the lens with the highest initial focal length presents the highest absolute tuning range (7.1 mm), which decreases for lenses filled with more liquid.The relative tuning range of the five silicone lenses is between -26% and -19%.For comparison, we also characterized the static focal length of an acrylic elastomer-based lens of identical geometry and have obtained a maximal change of focal length of -37%.The increased tuning range compared to the silicone lenses is mainly due to the higher electric field that could be applied before breakdown, as shown on Figure 3.The white light interferometry measurement of the surface of the lens shows a non-negligible difference in the curvature radius between the top and bottom membranes.This is due to the fabrication process (c.f.section 8), and more precisely during the liquid encapsulation step, when one of the two membranes is pulled by vacuum into a spherical cavity.Because of the stretch-induced softening (Mullins effect), [17] this membrane ends up being softer than the other, thus leading to a smaller radius of curvature when the lens is inflated with the fluid.Any deformation of the membrane during the fabrication process can have a detrimental influence on the lens quality, particularly if the deformation is not axi-symmetric, as it can lead to serious astigmatism, the lens taking the shape of an ellipsoid instead of a spherical cap.The deformation induced during the liquid encapsulation is axi-symmetric and therefore does not cause astigmatism.
However, undesired non-symmetric stretching of the membranes can be induced during their fabrication, when they are separated from the substrate on which they were casted.Indeed, pulling the membrane leads to very directional stretching during the release process.To avoid such an undesired mechanical deformation during this step, we cast our membranes on substrates which were previously coated with a sacrificial layer, thus allowing for a stress-free separation of the membrane from its casting substrate by dissolution of the sacrificial layer.
The optical quality of silicone lenses is measured by phase shift interferometry at different driving electric fields.The Zernike coefficient and Strehl ratio are extracted from the data (Figure S2), and show a very good optical quality up to a field of 100 V/μm (less than 0.1 µm deviation), above which the first order astigmatism quickly increases, probably due to loss of tension in the material.As a general trend, aberrations tend to increase with increasing voltage.For driving fields smaller than 100 V/ μm, the Strehl ratio is higher than 0.8, which is usually regarded as good for high quality optical systems, making these soft tuneable lenses suitable for imaging applications.The ability to electrically control the focal point of the soft lens is further demonstrated by mounting a tuneable lens in front of a 5 MP CCD imaging sensor; the tuneable lens being the only optical element in front of the CCD.The spacing between the CCD and the lens is chosen so that objects far away from the lens appear in focus when no voltage is applied to the device.A 10x3 mm 2 EPFL logo is positioned at 120 mm in front of the lens, and a building located about 70 m away from the lens is also visible in the field of view (Figure 4).An applied voltage of 2.8 kV allows bringing the EPFL logo in focus, the background appearing blurry.When no voltage is applied, the situation is reversed with the background being in focus, and the logo being out of focus.At 3.5 kV, objects as close as 80 mm could be brought in focus.

Dynamic response
To assess the response speed of the device to a voltage step, we characterize both the mechanical displacement of the electrodes, and the change of focal length of the lens.Since the response speed depends not only on mechanical parameters (displaced mass, stiffness, damping, viscoelasticity) but also on electrical parameters, we first measure the time required to transfer the electrical charges to the electrodes (electrical response time for kV signals).
We apply a 3.5 V amplitude square wave signal from a function generator with a rise time of less than 13 ns to a high-voltage amplifier (max output 4 kV) that has a slew rate faster than 150 V/μs and a gain of 1000.If we neglect the leakage current across the dielectric membrane, the DEA actuator can be represented as a lumped series RC circuit, and the speed at which it can be charged is limited by the capacitance as well as by the series resistance of the electrodes.Our highvoltage amplifier provides a current monitoring output, and we integrate this signal i(t) to determine the effective voltage Vl applied to the DEA capacitive component as a function of time: The constant of proportionality between Vl and the integral of the current is in principle equal to the inverse of the device capacitance.However, as the capacitance has not been precisely measured and depends on the electrode strain (and is therefore time-dependent), we set the constant of proportionality so that Vl(t→∞)=3.5kV,i.e. the output voltage of the amplifier (Figure S3).The effective voltage applied to the capacitor, the associated displacement of the edge of the electrodes, as well as the focal length signal measured by a photodiode (c.f.experimental section) are reported on Figure 5 for a 3.5 kV signal with the low-voltage step applied at t=0 µs.The voltage on the electrodes takes 125 μs to reach 90% of its steady-state value.There is a 50 μs delay between the beginning of the voltage ramp and the onset of the electrode edge displacement.The optical signal shows stronger oscillations than the in-plane displacement of the electrodes.This is due to the shockwave sent through the liquid by the rapid expansion of the electrodes and which causes the lens to vibrate, as we observed by filming a side view of the lens with a high-speed camera.Despite these oscillations, the system is sufficiently damped so that less than 175 μs after the start of the voltage step, the optical signal lies within ±10% of its final value.This makes this soft device the fastest reported tuneable lens capable of holding a stable focal position.To highlight the importance of the elastomer material on the dynamic performance, we also characterize the optical response to a voltage step of a acrylic elastomer-based tuneable lens of identical dimensions.The response is strongly overdamped, shows no oscillations, and has a viscoelastic drift of at least several minutes.The response clearly shows different time constants and is fitted with a 5-terms Prony series. [9]The fastest time constant is 23 ms, but has a relative amplitude of 43% of the total response.
It takes 16 seconds to reach 90% of the full response, which is almost five orders of magnitude slower than the settling time of the silicone-based lens.
The speed at which the focal length can be shifted between two positions has also been observed directly by shining a collimated laser beam through the lens, and inside a colloidal liquid.A high-speed camera was positioned above the bath, acquiring images at 40k frames per seconds (c.f.supplemental information).The shift of the focal point as observed on the movie is in agreement with the signal from the photodiode, and a stable position is reached within 400 μs of the voltage step.
The response speed of the device can be limited by two main factors: 1) the viscoelastic properties of the electrode-elastomer-electrode sandwich that forms the actuator, and 2) the damping induced by the lens through the displacement of the liquid.To assess the importance of these two contributions, we fabricated a dummy device similar to the tuneable lens, except that we did not fill the central part with the optical liquid.We measured the electro-mechanical displacement of the electrode edge in response to a voltage step input and obtained a rise time identical to that of the full functional lens.This result shows that the lens itself plays a negligible role in the response speed, which is dominated by the viscoelastic properties of the elastomeric actuator.Therefore, a careful choice of the silicone used as membrane material (in terms of minimization of the viscous component) could therefore lead to even faster devices.

Frequency response
To further characterize the dynamic behaviour of the lens, we performed a frequency response analysis of silicone-based lenses and acrylic elastomer-based lenses, both of identical geometry and size, and made using the pad-printed carbon-silicone electrodes.A large-signal sinusoidal excitation waveform with peak-to-peak amplitude of 1400 V is used to drive the lens, which is mounted on the same setup used to characterize the dynamic response to a voltage step (c.f.section 4).The normalized amplitude of the photodiode signal is plotted as a function of the excitation frequency (Figure 6).constantly and rapidly decreasing strain amplitude for frequencies ranging from 10 -3 Hz to 1 Hz, [18] an observation also reported by Keplinger et al. between 0.04 Hz and 1000 Hz (displacement roughly 100 times smaller at 1 kHz than at 0.04 Hz). [19]The acrylic elastomer VHB has a very high mechanical loss tangent, increasing from 0.3 to almost 1 in the 1 mHz to 100 Hz frequency range. [18]lberg et al. observed that although at very low frequencies acrylic elastomerbased devices lead to larger strains compared to silicone devices, the strain of their silicone actuators was larger than acrylic elastomer (VHB) actuators for frequencies above 0.1Hz.
To further demonstrate the capability of our silicone-based lens to follow a 1 kHz signal, we drive it with a series of steps of increasing voltage (0, 2.5 kV and down), with holding time of 1 ms at each step.We record the amplitude of the optical signal using the same setup used for the step response (c.f.section 4).Despite the very short holding time, the lens is fast enough to shift its focal length and stabilize within the 1 ms step duration (Figure 7).

Discussion
The very short settling time of the lens (<175 μs) is mainly due to two important factors: 1) the use of silicone as a dielectric membrane for the actuator, and 2) the overall design of the lens, which minimizes the damping and inertia of the moving masses.
The response speed of the actuator is mainly dominated by the properties of the elastomer used as membrane.In this work, we have used a commercial silicone (CF19-2186 from Nusil) amongst many available products with different properties in terms of Young's modulus, mechanical loss factor, and dielectric breakdown field, which have a direct influence on the behaviour of the actuator.
Silicones with a higher Young's modulus generally have a lower mechanical loss tangent, but being stiffer, have lower actuation strain.The Young's modulus of the silicone used for the lens was determined from a uniaxial pull-test on a 30 μm-thick test sample.The data was fitted with a Yeoh hyperelastic model, and the Young's modulus calculated from the parameter C1 was 0.78 MPa.The hardness of this silicone places it at the higher end of silicones typically used for DEAs (Young's modulus between 0.1 and 1 MPa), and it therefore enters into the category of harder silicones with lower mechanical loss tangent.Despite its relatively high Young's modulus for a PDMS, the lenses made with this material exhibit the same tuning range shown by similar devices made by Carpi et al. with the acrylic elastomer VHB, [4] a finding which is confirmed by our own characterization of acrylic elstomer-based lenses.This shows that the use of silicone allows for gaining several orders of magnitude in response speed, without sacrificing much tuning range.The response speed of the actuator can also be influenced by the electrodes, which can contribute to the viscoelasticity of the device.For example, Rosset et al. have shown that the rise time of actuators made with 3 different silicones (with hardness between Shore A 24 and A 5) and 3 different types of electrodes (metal ion implantation, conductive rubber, and carbon grease) is mainly influenced by the type of electrode, and not the hardness of the silicone used as dielectric. [11]Consequently an optimization of the carbon black mixture used in this work for the compliant electrodes could further increase the response speed of the device.
One particularly interesting feature of this lens design is the very small amount of liquid that needs to be displaced upon actuation: only a small shell of fluid close to the membrane is moved during actuation, while the bulk of the fluid remains still at the centre of the lens.Consequently, the contribution of the fluid to the response speed of the device is negligible, and the DEA remains the dominant part, as observed in the dynamic measurement with a full lens and a dummy device without liquid (c.f.section 4).
In addition to the remarkable achieved response speed, the implemented fabrication process leads to the efficient fabrication of reproducible devices, which exhibit long lifetime.Unlike the widely used technique of manually smearing carbon grease over the membrane, the automated stamping method used here allows us to precisely and reproducibly pattern a mixture of carbon black and silicone on thin silicone membranes without damaging them.After the patterning step, the conductive ink is crosslinked in an oven, which provides strong adhesion of the electrode on the dielectric membrane, thus producing electrodes which are resilient, resistant to wear, and extremely stable over time.
Silicone lenses were actuated at 1kHz for more than 400 million cycles with no change in performance, and devices made more than 2 year ago are still working without performance degradation in the actuator or in the lens (no loss of optical fluid).
One drawback of the lens design used in this work is the limited achievable tuning range, which is due to the fact that the expansion of the electrodes compresses the lens radially, which increases the curvature of an already curved lens.As shown in Figure 2, the absolute achievable tuning range becomes smaller when the amount of encapsulated liquid becomes larger (i.e.larger initial curvature), thus limiting the tuning range to 19-26% for silicone lenses and 26.4-37% for acrylic elastomer lenses.Other DEA-based tuneable lenses approaches have demonstrated a much larger tuning range.For example, Wei et al. recently reported on a lens in which an optical liquid is moved back and forth from the central lens to an annular DEA surrounding it and acting like a pump. [20]In that design, upon activation of the DEA, the curvature of a central membrane, which serves as the lens, decreases and could in principle reach a completely flat state and therefore an infinite focal length.A tuning range of 300% has been demonstrated for that geometry.However, as the displaced fluid is forced through a channel, the fluidic impedance of this design slows down the overall response speed of the device: indeed, although the lens is also made with a silicone membrane, a response speed of a few hundred of miliseconds is reported. [20]So, the large tuning range comes at the cost of a slow response time.
In another configuration, Shian et al. have demonstrated a liquid lens formed by two back-to-back membranes of different diameters enclosing an optical liquid.
One of the membranes is coated with transparent compliant electrodes and expands upon actuation, leading to a reduced curvature in the second membrane.When the diameter of the active membrane is larger, then the reduction of curvature of the passive membrane dominates, and a large positive tuning range up to 100% can be obtained. [5]The response speed of that lens is in the range of hundreds of millisecond, [5] probably mostly due to the use of acrylic elastomer as dielectric membrane rather than to the effect of inertia or fluidic impedance.In that device, the mass of the displaced volume of liquid upon actuation is rather small, and consequently, it is expected that a combination of that design with low-loss silicone elastomer as dielectric would lead to considerable improvement in response speed and large tuning range.
Because of DEAs are electrostatically actuated actuation and are typically made from dielectric membranes 10 to 100 µm in thickness, they generally require voltages in the range of 1-10 kV for maximum displacement (about 3 kV for the devices presented in this article).Nevertheless, the mean driving currents are very small (since only a small capacitance needs to be charged), and -neglecting the leakage through the dielectric membrane -no power is necessary to hold a static position.However, the high driving voltage can be an issue, because it makes the drive electronics more complex, and often bulky and expensive especially when high slew rates are required, as is the case to drive fast devices.
One possibility to reduce the driving voltage consists in decreasing the thickness of the elastomeric membrane.However, this would reduce the lateral actuation force exerted on the central lens by its surrounding annular actuating membrane, thus also reducing the deformation of the lens and the associated change of focal length too.Stacking several membranes, one on top of each other, can compensate this effect, as it would increase the total lateral force applied to the lens.Since the actuator of our device consists of two membranes bonded together (c.f.section 8), the driving voltage could straightforwardly be divided by two by patterning an electrode at the interface between them.

Conclusions
Our tuneable lens with a settling time shorter than 175 μs demonstrates that soft and compliant systems, and particularly dielectric elastomer actuators, can combine high strain and stretchability with a fast response time, when materials with low mechanical loss factors are used.Our silicone-based lens has the ability to change its focal length extremely rapidly, but equally importantly, it does not exhibit viscoelastic drift, thus allowing to accurately hold a stable focal position.
This position stability is very important for many applications involving tuneable lenses, where it is desirable to rapidly switch between different focal length, and to remain at a constant focal length during image acquisition.Such ultrafast tuneable lenses can be used for high-frequency varifocal applications such as 3D and ultra-depth-of-field imaging techniques (light sheet microscopy, [21] quasisimultaneous imaging of multiple focal planes, [22] depth from focus [23] ) or advanced laser machining techniques. [24]Imaging applications that require a fast change of focal point would particularly suited for this lens design, because they only require a small change of focal length (the 20-25% change of focal length that we obtained is sufficient to vary the focusing distance between 80mm and infinity when the lens is simply mounted in front of a CCD sensor, Figure 4).
In addition, the lens exhibits a good optical quality (Figure S2).This is made possible by smooth surfaces, a well-controlled geometry and the absence of light-scattering particles in the light path (clear optical liquid, membrane with low filler content, and no compliant electrode on the lens itself).Optical quality characterization of soft DEA-based tuneable lenses has not been reported prior to this work, and this is an essential parameter for any practical imaging application.
Fast (>kHz) speed and drift-free compliant dielectric elastomer actuators are expected to find applications in many fields when compliance and speed are needed, for example in tuneable gratings for spectroscopy or telecommunication, flexible grippers, [25] tuneable mm-wave phase shifters, [26] and many aspects of soft robotics in general.
serves as a mounting frame and to route the actuation voltage to the electrodes.The flexible frame demonstrated in figure1dallows the lens to be folded, and provides a support on which to bond contact wires.The diameter of the optical lens at the centre is 5 mm, and the outer diameter of the annular electrode is 19 mm.When a voltage is applied between the electrodes, their in-plane expansion compresses the lens.Because the volume of the encapsulated liquid remains constant, this causes a decrease of the radius of curvature of the lens, and hence a decrease of its focal length.The initial focal length of the device depends on the volume of liquid encapsulated between the two membranes, with more liquid leading to a shorter initial focal length due to the larger initial curvature of the lens.

Figure 1 :
Figure 1: A) schematic of the fast tuneable DEA-driven lens, consisting of two prestretched elastomer membranes bonded together and encapsulating a transparent fluid, forming a biconvex lens.An annular compliant electrode is patterned around the lens.Upon applying a voltage, the expansion of the electrode due to Maxwell pressure compresses the lens in-plane, thus decreasing its radius of curvature and hence focal length.B) Picture of the device showing the lens at the centre, the annular electrode (black) and the outer frame.C) The resilience of the actuator is shown by an extreme deformation of the lens over a needle head.D) Flexible version of the lens revealing the white knight of a chess set hidden behind (left).The inset shows a blown-up image of the lens.The details of the knight are clearly visible.In this flexible configuration, the lens can be folded by over 180° without damage (right).
thickness and are equally prestretched.The relation between the radius of the lens r and the radius of curvature of the membrane R is obtained by solving the equation describing the volume of a spherical cap for a fixed total volume, representing the amount of liquid enclosed in the lens.The dashed red line in Figure2at a constant lens radius of 2.5 mm shows the initial focal length with no actuation.It decreases for an increasing amount of liquid, i.e. for increasingly bulged lenses.The effect of voltage can be observed by recalling that the electrostatic actuation squeezes the lens and reduces its size: following a line with a constant volume of liquid, from the initial radius of 2.5 mm towards 2.25 mm (in this simplified case where we assume only up to 10% electrostatic compression), one sees clearly the decrease in focal length induced by actuation.The tuning range of the focal length depends strongly on the amount of liquid: it is larger for lenses filled with a smaller amount of liquid (i.e. with a large initial radius of curvature).The focal length changes nearly linearly with the lens diameter, and per (1) we therefore expect a quadratic relationship between the focal length and the applied voltage.

Figure 2 :
Figure 2: Computed focal length as a function of volume of liquid encapsulated in the lens, and the lens radius, which is controlled by the DEA.Because the electrostatic actuation reduces the radius of the lens, its effect on the focal length can be determined by following a line with a constant volume of liquid.The biggest voltageinduced variation of the focal length occurs for lenses with a small amount of liquid.

Figure 3 :
Figure 3: Measured focal length of the tuneable lens as a function of electric field for different volumes of encapsulated liquid.Less liquid leads to a higher initial focal length and a larger absolute tuning range.All the tested lenses were made with silicone elastomer, except for one acrylic elastomer-based lens used as comparison (dashed line).The relative tuning ranges at the maximal voltage are indicated on the graph and lie between -26% and -19% for silicone lenses, 37% for the acrylic elastomer lens.A quadratic relationship between the electric field and the focal length has been fitted to the data points.The focal length values that we measured directly (as described in the

Figure 4 :
Figure 4: The tuneable lens is placed directly in front of a 5 MP CCD sensor with no other optical elements, and used to image objects at different distances.Top: schematic representation of the setup with a 10x3 mm 2 EPFL logo positioned at 120 mm in front of the lens as well as trees and buildings approximately 70 m away.Bottom: resulting images captured by the sensor for 2 different driving voltages (2.8 kV, and 0V), showing the focal plane can be placed on the logo and the background.

Figure 5 :
Figure 5: Electro-mechanical and optical response of the silicone DEA lens to a 3.5 kV voltage step input.The voltage on the electrodes takes 125 μs to reach 90% of its final value, and the optical settling time of the system is shorter than 175 μs.

Figure 6 :
Figure 6: Frequency response of the tuneable lens to large drive signals (1.4 kV), comparing silicone-based (blue triangles) and acrylic elastomer-based (red squares) lenses of identical geometry and size.The relative amplitude of the optical signal recorded on the photodiode is plotted vs. frequency for excitation signals from 5 mHz to 20 kHz.The response is normalized to 1 at 5 for both lenses.For the silicone lens, the response is nearly flat until the resonance peak with maximum amplitude at 4.7 kHz, allowing full tuning up to 1 kHz.For acrylic elastomer, the response drops off very quickly with frequency, limiting the acrylic elastomer lens to applications below a few Hz.For the silicone-based lens, the frequency response shows an almost flat

Figure 7 :
Figure 7: Optical response of the silicone lens to voltage steps of increasing amplitude with 1 ms of holding time per step.The lens is able to follow the step and stabilise during the short holding time, allowing thousands of different stable focal lengths to be generated per second.

Figure S1 :
FigureS1: The compliant electrodes are patterned by pad-printing a mixture of carbon black powder dispersed in a silicone matrix.This leads to precisely-defined electrodes that present excellent adhesion to the elastomer membrane, as demonstrated here by applying a polyimide tape with silicone adhesive directly on the electrode of one of the lens devices.When the tape is pulled, the electrode remains perfectly bonded to the membrane and the whole device deforms.This cannot be achieved with loose carbon powders or carbon grease, which are typically used for compliant electrodes.Robust and wear-resistant compliant electrodes are the key for reliability and long lifetime of DEAs.

Figure S2 :
Figure S2: Optical quality of the lens as measured by phase shift interferometry on a silicone lens showing the Zernike coefficient deviations as a function of applied electric field.The Strehl ratio is plotted as a function of the applied electric field andshows that the lens quality decreases with increasing electrically-induced deformation.However, with an initial Strehl ratio of 0.92 at 0 V/μm decreasing to 0.8 at 100V/μm, the lens quality is suitable for high quality optical systems such as for imaging.

Figure S3 :
Figure S3: Top: Schematic representation of the electrical equivalent circuit for the step response.The high voltage amplifier charges the capacitance (CDEA) through 2 series resistor Rs which represent the electrodes.Bottom: measured voltage from the amplifier used as input for the device (blue), measured current outputted from the amplifier (green), and calculated voltage applied to the actuator (red), obtained by integration of the measured current.