Electrically tunable all-polymer solid-body lens

UNIVERSITÀ DI PISA

FACOLTÀ DI INGEGNERIA

Tesi di Laurea Magistrale

Electrically tunable all-polymer solid-body lens

Relatori: Candidata:

Prof. Danilo De Rossi Clara Lagomarsini

Prof. Federico Carpi Dott. Ing. Michael Pieroni

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Index of contents

Chapter 1:

Chapter 2:

2.1 Introduction ... 6

2.2 Simple lens: definitions ... 6

2.3 Spherical and aspherical lenses ... 9

2.4 Thin lens approximation ... 11

2.5 A compound lens ... 12 2.6 Aberrations ... 13 2.6.1 Spherical aberrations ... 14 2.6.2 Coma ... 15 2.6.3 Astigmatism ... 16 2.6.4 Distortion ... 17

2.7 Evaluation of the optical system performance ... 18

2.7.1 Point spread function (PSF) ... 18

2.7.2 Optical transfer function (OTF) ... 19

2.7.3 Modulation transfer function (MTF) ... 20

Chapter 3:

3.1 Introduction ... 24

3.2 The anatomy of the eye ... 24

3.3 The optics of the eye ... 25

3.4 Human eye parameters ... 27

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Chapter 4:

4.1 Introduction ... 32

4.2 State of the art ... 33

4.2.1 Liquid lenses ... 33

4.2.1.1 Pneumatic tuning ... 33

4.2.1.2 Electrowetting tuning ... 35

4.2.1.3 Tuning with stimuli responsive hydrogels ... 37

4.2.1.4 Thermal tuning ... 38

4.2.1.5 Piezoelectric tuning ... 39

4.2.1.6 Artificial muscles tuning ... 40

4.2.2 Solid lenses ... 41

4.2.2.1 Thermal tuning ... 41

4.2.2.2 Mechanical tuning ... 42

Chapter 5:

5.1 Introduction ... 46

5.2 Electroactive polymers actuators ... 46

5.3 Dielectric elastomers actuators (DEAs) ... 49

5.4 Bioinspired tunable lens with electroactive elastomers (previous version) ... 51

5.5 Bioinspired tunable lens with electroactive elastomers (new version) ... 53

Chapter 6:

6.1 Introduction ... 55

6.2 System design ... 55

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6.4 Lens manufacturing ... 62

6.4.1 Selection of the material ... 62

6.4.2 Lens fabrication ... 65

6.5 Device characterization ... 69

6.5.1 Quantitative measurements ... 69

6.5.2 Qualitative characterization ... 76

Chapter 7:

7.1 Quantitative measurements ... 83

7.2 Qualitative characterization... 111

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Chapter 1

Introduction

The work carried out during this research project consists in the realization of an electrically tunable solid body lens, integrated with an annular dielectric elastomer actuator (DEA) working as an artificial muscle. This type of actuator was chosen because it can develop large strains (up to 380%) while having a fast response time (few milliseconds). Besides, even if high voltages are required for the actuation of the elastomeric membrane, low currents are involved in the charging process, resulting in low power consumption.

In chapter 2, the basic properties of conventional optical lenses are described, along with the standard methods used to evaluate the performances of these optical systems.

In chapter 3, the basic principles of human eye optics, in particular the principle of eye accommodation, are illustrated. The working principle of tunable lenses is in fact inspired to the accommodation of human eye: the focusing power of the optical imaging system is varied by changing the lens shape, similarly to that of a human eye crystalline lens during the eye accommodation.

Chapter 4 describes the state-of-the-art types of bio-inspired tunable lenses, covering different mechanisms for tuning. The review allows classifying the designs already present in the literature, and highlighting their specific advantages and limitations.

In particular, the bio-inspired device developed by Carpi et al., from which the present research project takes inspiration, is fully described in chapter 5.

In fact, the tunable lens realized in this project intended to exploit the working principle as well as the advantages of compactness, fast operation and shock tolerance introduced by the tunable lens based on DEAs, as described in [1]. On the other hand, the fluid-filled elastomeric lens produced by Carpi et al. was substituted with a solid- body lens, which is less susceptible to fluctuations in gravity, vibrations, and temperature than liquid-based lenses and constitutes a more robust approach to tunable optical systems.

5 Based on these purposes, the realization and characterization of a bio-inspired solid-body lens actuated with DEA is fully expounded in chapter 6. The project phases are divided as follow:

 Selection of the material and fabrication of the solid-body lens with two different techniques. The material selected for the lens fabrication was a water clear encapsulation rubber produced by Smooth-on: Encapso® K;

 Setup of the final design of the lens, which is actuated by an annular dielectric elastomer actuator connected with thin alluminium striped to a high voltage source. The membrane was covered with four different areas of electrode, in order to evaluate how the deformation of the lens varies in the different configurations;  Quantitative and qualitative characterization of the device. The quantitative

evaluation is based on the calculation of the geometrical parameters of the lens with two different methods (laser beam displacement and image acquisition and processing of the lens profile). Both methods were used to derive the radius of curvature of the lens and consequently its focal length as a function of the voltage applied to the lens.

The qualitative measurements are aimed to the evaluation of the optical performances of the lens. For this purpose, the lens was integrated on the same optical axis of a Color Industrial Camera (Imaging source DFK 23GM021). With this experimental setup, several acquisitions with different voltage applied to the membrane could be performed to acquire different types of objects. The images are then analyzed to evaluate the optical performances of the device.

Finally, the main results obtained from these assessments are described in chapter 7.

In particular, it has been found that the deformation of the solid body lens was comparable with the deformation of the liquid lens produced by Carpi et al. [1]. This is a promising result because the solid body lens could overcome the limitations related to the liquid lens, while maintaining the same performances.

REFERENCE

[1] Carpi F., et al. "Bioinspired Tunable Lens with Muscle‐Like Electroactive Elastomers." Advanced Functional Materials 21.21, 4152-4158 (2011)

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Chapter 2

Conventional Optical Lenses

2.1 Introduction

In this chapter we will consider the geometric (or refractive) domain, which relies on the refraction of light and assumes the light propagating in form of rays. In particular, the focus will be put on the geometrical parameters of the different types of lenses and on their optical performances.

2.2 Simple lens: definitions

A lens consists of one or more curved surfaces of a material, optically transparent at the wavelength at which it is used. Thanks to the difference in refractive index between the lens and the surrounding medium, the light ray that strikes the surface of the lens is bent in a controlled manner. According to the curvature of the surfaces, lenses can be classified into five basic types: plano-convex, bi-convex, plano-concave, bi-concave, and convex–concave (meniscus), as shown in Figure 2.1.

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Figure 2.1: Various combinations of convex and concave surfaces for different lenses types. R1 and R2 are radii of curvature of the left and right interfaces, respectively [1]

Plano-convex and bi-convex lenses have positive optical power: they converge a parallel input beam into a real focal point at some distance behind the lens. Plano-concave and bi-concave elements have negative power: they diverge a parallel input beam from a virtual point in front of the lens element.

The device developed in this research project has a plano-convex shape.

All the different type of lenses can be described by means of a set of cardinal points and surfaces, described as follow:

 Optical axis: the optical axis is the main axis of the optics, usually denoted as z-direction and it usually coincides with the main z-direction of light propagation. All the points that are located on the optical axis and all the elements centered around it are called on-axis; otherwise they are denoted as off-axis.

 Cardinal or principal Planes: the principal planes are two hypothetical planes in a lens system at which all the refraction can be considered to occur.

Extended towards the lens interior, the incoming and the outgoing rays intersect at a point on the principal surface of the lens. The projection of the intersection point onto the optical axis is called the corresponding principal point (H2 in figure 2.2). In paraxial approximation, the principal surface becomes flat, forming the principal plane. As a result, all principal points merge into a single one.

The principal planes allow for the graphical construction of ray paths and they are not necessarily located within the lens itself.

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Figure 2.2: Cardinal points and principal planes

Figure 2.3: Position of principal planes for different lens types [1]

 Focal Length: within the paraxial domain, all incident rays entering parallel to the optical axis intersect it behind the lens, in a point called the back focal point (BFP) Due to the reversibility of the ray paths, rays emerging from the front focal point (FFP) run parallel to the axis after passing the lens. When rays emerge from off-axis points on the focal plane, they still form a parallel ray bundle, but are non-parallel to the optical axis. The distance from the FFP to the front principal plane gives the effective focal length (EFL) of the lens. If there is no change in refractive index inside the lens, the front EFL is equal to the back EFL. When the refractive index changes from n1 in front of the lens to n2 behind the lens the back EFL changes to

. Therefore, the EFL in air is often referred to as the focal length of the lens. Additionally, the distance between the focal points and the lens vertices are called

9 the front focal length (FFL) and back focal length (BFL), respectively. In case of symmetric lenses, they equal each other.

Figure 2.4: Fundamental terms of the paraxial description of lenses [1]

2.3 Spherical and aspherical lenses

A spherical lens can be seen as two spherical surfaces with a constant refractive index medium between them. In order to analyze the formulas that describe the behavior of this type of lens, only a spherical surface will be considered. As illustrated in Fig. 2.5, a ray emerging from an on-axis object point O1 intersects the optical axis at a point O2 behind the spherical surface.

Within the paraxial domain, all rays emerging from an object point intersect in one point in the image space. Thus, the object point is imaged onto its optical conjugate image point. The distances d1 and d2 of object and image points are correlated with the radius of curvature R of the surface and the indices of refraction n1 and n2, as shown in equation (1).

10 The equation (1) can also be expressed in the form:

Equation (1) separates object and image space. Equation (2) is known as Abbe’s invariant.

Figure 2.5: Ray path at a single spherical surface [1]

A single surface separating regions of different refractive index is therefore sufficient to form an imaging optics, and can therefore be seen as the simplest possible lens.

Setting either of the distances d1 or d2 to infinity, it is possible to obtain both focal lengths.

In this case, both principal planes coincide at the location of the vertex V.

Similarly to the case of single surface, the paraxial properties of a lens made of two spherical surfaces can be obtained, using ray calculations similar to those for a single surface.

(2)

(3) (4)

11 Considering the lens placed in air, as usually happens, the refractive indices of the surrounding medium become n1 = n2 = 1. As a result, the lens data can be described by the following relationships:

In the equations, D = V1V2 is the thickness of the lens, is the refractive index of the lens, R1 and R2 are the radii of curvature of the lens surfaces, h = P1P2 is the distance between the principal planes, νi = ViPi is the distance to the corresponding vertices.

As the refractive index is assumed to be identical on both sides of the lens, the front and back focal lengths of the lens coincide with the focal length f.

Unlike conventional lenses with a spherical front surface, aspheric lenses have a more complex front surface that gradually changes in curvature from the center of the lens out of the edge of the lens.

The asphere's more complex surface profile can eliminate spherical aberration and reduce other optical aberrations compared to a simple lens. Nevertheless, because of their unaxial character, aspherical surfaces are much more difficult to fabricate than ordinary spherical surfaces and for this reason they are usually employed in high precision and customed devices.

2.4 Thin lens approximation

The thin lens approximation allows a simplified analysis to derive a relationship between the curvatures of the two lens surfaces and the object and image distances which result. This approximation considers the optical effect of both surfaces of the lens yet ignoring its

(5)

(6)

(7)

12 thickness. Thus the lens can be considered as the sum of refraction at two surfaces, ignoring what happens to the beam as it traverses the bulk of the lens material.

The surface radii of curvature and the refractive indexes of a lens can be related to the positions of object and image by using the Lensmaker’s equation:

In this equation, R1 represents the radius of the left surface, R2 the radius of the right, S0 and S1 are the distances of the object and the image from the lens vertex. Both object and image are considered to be outside the lens, in a region with refractive index , while represents the refractive index of the lens.

In the case of a thin lens, the object and image focal lengths are identical: and the Lensmaker’s equation can be simplified to the following form:

From this expression, that gives a relationship between the radii of curvature of a thin lens and its focal length f, can be derived another important relationship: The Gaussian lens formula:

Given a lens with focal length f, this relationship allows to determine the image position given any object position.

2.5 A compound lens

A compound lens is a collection of at least two simple lenses which are arranged one after another with a common axis. This design is commonly found in cameras and other optical instruments. Figure 2.6 shows a compound lens with two convex lenses separated by a distance d, where F1 is the focal point of lens L1 and F2 is the focal point of lens L2.

(9)

(10)

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Figure 2.6: A compound lens system [2]

Such a compound lens still obeys the law of refraction. If the two lenses are separated in the air by a distance d which is not too much greater than the sum of the two focal lengths, then this combination behaves as a single lens. Thus the system can be converted into a new equivalent lens, with one effective focal length given by:

In the equation, f1 and f2 represent the focal lengths of lens (L1) and lens (L2), respectively. From equation (12) it derives that, when the distance d is varied, the effective focal length f is changed correspondingly. Considering the optical performance of the compound system, the distance d cannot be changed in a wide range. Consequently, the associated change in focal length is rather limited. For practical applications, three or more lenses are necessary to get a wide range of focal length change by adjusting the distances among them.

2.6 Aberrations

Within the limits of paraxial approximation, a perfect image quality can be achieved. Nevertheless, an optical device never reaches this ideal behavior, but shows degradations of (12)

14 image quality caused by aberrations of the optics. These aberrations are divided into two main classes according to their cause.

The change of refractive index with wavelength causes polychromatic aberrations that even exist in paraxial optics.

Instead, non-paraxial rays, which appear in any real optics, are the cause of monochromatic aberrations. These aberrations are divided into the five primary aberrations (Figure 2.7), also known as Seidel aberrations. Three of them, namely, spherical aberration, coma and astigmatism, cause image degradations by blurring, while field curvature and distortion deform the image. In the following chapters we will describe in particular third-order aberrations.

Figure 2.7: Classification of aberrations [2]

2.6.1 Spherical aberrations

Spherical aberration (SA) is an image imperfection that is due to the spherical lens shape. Outside the paraxial domain, rays that are parallel to the optic axis but at different distances from the optic axis fail to converge to the same point. On the contrary, rays hitting the surface at a greater distance to the axis are focused on a point closer to the surface than rays nearer to the axis, as shown in figure 2.8.

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Figure 2.8: Spherical aberration of a convex lens [3]

For a single, convex lens, light that strikes the lens close to the optical axis is focused at position a (figure 2.8). The light that traverses the margins of the lens comes to a focus at a position b closer to the lens. The difference between the focal points for rays that are close to the axis and for rays that strike the lens near its edge is called spherical aberration.

Since the effective focal point determines the position of the image for any object, if the rays are separated into concentric zones, rays in different zones will have different focal points on its principal axis; thus several images can be formed by the lens. When these images are received in a screen, the images are overlapped and the observed image is blurred. Spherical aberration can be minimized, besides using aspherical surfaces as described in the paragraph 2.4, by limiting the opening of the lens so that only rays in the paraxial region can pass through it.

2.6.2 Coma

Coma is an aberration associated with off-axis object points. It is an image degrading aberration associated with an off-axis point even at a short distance from the axis. When parallel rays pass through a lens at an oblique angle (θ), as shown in Figure 2.9, the rays cannot be focused as a point, but as a comet-shaped image. Coma can be improved by the use of a diaphragm.

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Figure 2.9: Representation of coma [3]

2.6.3 Astigmatism

Astigmatism is an aberration associated with off-axis rays emerging from non-axial source points. When astigmatism is present in a lens system, fans of rays of differing orientations at the lens aperture tend to focus on differing curved surfaces.

In an optical element of axial symmetry, for an on-axis point there is no difference between the meridional plane (which is defined as the plane containing the optical axis and the chief ray) and the sagittal plane (the plan that contains the chief ray and is perpendicular to the meridional plane). On the contrary, an off-axis point will show the lens under different angles, causing the effective focal lengths in the two planes to be different. The difference of the focal length increases with the paraxial focal length of the lens and the skew angle of the rays.

Consequently, the resulting image depends upon the location of the focal plan and thus produces blurry images more or less elongated, which intensity and contrast decrease as the distance from the center increases.

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Figure 2.10: Representation of astigmatism [3]

2.6.4 Distortion

Displacement of image points with respect to their paraxial locations causes distortions of the image geometry without degrading sharpness. In case of optical system of rotational symmetry, the shift of the image points is purely radial and distortion can also be seen as a dependence of the transversal magnification of the distance of the object to the axis.

Usually, the displacement increases with the object height as the rays become more inclined. This effect is caused by variation in magnification of the image across the field of view. When the magnification of a lens differs at the edge of the lens and at the center, the image of a square object will be abnormally curved. Figure 2.11 illustrates two kinds of distortion. In Figure 2.11 (a), the lens has too much magnification at its edges, causing a surfeit of magnification of the square at the corners. This is commonly called pincushion distortion, or positive distortion. In Figure 2.11 (b), the lens has too little power at its edges, causing a barrel, or negative distortion.

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Figure 2.11: Two types of distortion. (a) Pincushion and (b) barrel [3]

Distortion is influenced by the thickness of the lens and by the position of the aperture stop. However, stopping down the aperture does not reduce distortion but it reduces the other aberrations. Therefore, positioning the stop at an appropriate position is often done to correct for distortion.

2.7 Evaluation of the optical system performance

In order to evaluate the quality of an optical system, in the literature are usually employed the following parameters: point spread function (PSF), optical transfer function (OTF) and modulation transfer function (MTF).

2.7.1 Point spread function (PSF)

The point spread function describes the response of an imaging system to a point source or point object. A more general term for the PSF is a system's impulse response.

The image of an object is seen as the superposition of the images of all object points. The degree of spreading (blurring) of the point object is a measure for the quality of an imaging system. An ideal aberration-free optics would image every object point onto its conjugate point in the image plane. In the case of defocus, the rays emerging from the object point no longer intersect at the image plane but at the plane conjugate to the actual object plane.

19 The image of the object point is therefore an intensity distribution at the image plane, which is called the point spread function (PSF) of the lens.

Figure 2.12: PSF of an image

Assuming that the PSF does not change for various object points, the effect of blurring can be described as a convolution of the well-focused image, as it would be achieved by a pinhole camera, with the PSF:

It is important to note that the description by a convolution is only valid in case of a linear, shift-invariant system.

2.7.2 Optical transfer function (OTF)

The optical transfer function (OTF) is used to describe how the optical device projects light from the object or scene onto a screen. The function specifies the translation and contrast reduction of a periodic sine pattern after passing through the lens system, as a function of its periodicity and orientation. Formally, the optical transfer function can be defined as the Fourier transform of the PSF. Its values give the transfer coefficient for spatial structures of different wavelength through the optical system. A value of zero indicates that this particular wavelength cannot be seen by the optics.

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Spatial domain:

Fourier domain:

A typical OTF will act as a low-pass filter, eliminating higher spatial frequencies, that is, high resolution details.

2.7.3 Modulation transfer function (MTF)

The resolution of an imaging lens or lens system is defined by the dimension of the smallest feature which can be distinguished. The resolution is typically characterized by the modulation transfer function (MTF). Since MTF is a direct measure of how well the various details in the object are produced in the image, MTF has become the most widely accepted criterion for specifying and judging an image quality, that will be used also for the performances evaluation of the device developed in this research project.

To define MTF, rectangular black and white bars with specified frequency are chosen, as shown in figure 2.13. The frequency content is measured in line pairs/mm, thus containing one black line and one white line for each cycle.

Figure 2.13: Image consisting in black and white lines, with different frequencies, whose acquisition is tested to evaluate the optical performance of an optical device

It is possible to measure the amount of light coming from each one: the maximum amount of light will come from the white bars, and the minimum amount will come from the black bars. If the light is measured in terms of radiances, the modulation (or contrast) M of a spatial frequency (ν) is given by:

(14) (15)

21 In the equation (16), Imax [W/m2] and Imin [W/m2] represent the maximum (white bar) and minimum (black bar) intensities of the image, respectively.

When a stimulus made of square-wave grating of a specific frequency (v) and modulation passes through a lens, the modulation of the image can be measured. Thus, the MTF is defined as the ratio of image modulation to object modulation, or:

Mimage and Mobject are calculated for each spatial frequency by Equation (16).

When describing the performance of a lens, a plot of MTF against spatial frequency is typically used. Figure 2.13 shows MTF as a function of spatial frequency at three different cases. In an ideal case, the MTF of the lens does not change even though the spatial frequency increases, as straight line a shows; in the case without any aberration, diffraction limit is the only reason to cause the MTF to decrease, as shown by line b; and in a normal case, MTF decreases quickly because of lens aberrations and diffraction limit, as line c depicts. In comparison with the diffraction-limited case, the MTF of the normal case drops much faster. The point at which any variation in the image can be no longer seen is the point at which the MTF is zero, and that is the definition of the “resolution” of the lens. A lens or lens system with less aberration always gives a higher resolution.

22 Figure 2.14: MTF function as a function of spatial frequency for three different functions [2]

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REFERENCES

[1] Hans Zappe , Fundamentals of Micro-Optics, Cambridge University Press (2010) [2] H. Ren, S. T. Wu, Introduction to Adaptive Lenses, Wiley (2012)

[3] B. Jähne, H. Haußecker ,P. Geißler , Handbook of computer vision and applications, Volume 1, Sensors and Imaging, Editors Bernd Jähne (1999)

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Chapter 3

Biological Optical system

3.1 Introduction

Light is a component of the electromagnetic spectrum and the human eye responds to radiation with wavelengths between about 380 nm (deep violet) to 800 nm (deep red). This is a relatively narrow part of the total spectrum and other animals have a slightly different range of sensitivities. Like all electromagnetic radiation, light has the properties of both wave and particle but for many purposes, it may be considered to travel in straight lines. The

eye is structurally designed to detect and process light. In this chapter, it will be described the structure of the eye and its working principle, as the

human eye is an important starting point for the development of optical systems and imaging technologies. In the latter part of the chapter eye-inspired technologies will be mentioned, in particular the working principle of different types of bio-inspired tunable lenses will be developed.

3.2 The anatomy of the eye

The eyes are protected by their location in the bony cavities of the orbits. Only about a third of the eyeball is unprotected by bone. The eyeball itself is roughly spherical and its wall consists of three layers (figure 3.1): the sclera, which is the outer white and fibrous coat; a pigmented layer called the choroid, which is highly vascular and the retina, which contains the photoreceptors (rods and cones) together with an extensive network of nerve cells. The retinal ganglion cells are the output cells of the retina and they send axons to the brain via the optic nerves.

At the front of the eye, the sclera gives way to the transparent cornea, which consists of a special kind of connective tissue that lacks blood vessels. The transparency of the cornea is

25 maintained by the tear fluid secreted by the lacrimal glands and by the aqueous humor that is secreted by the ciliary body within the eye itself. The pigmented iris covers much of the transparent opening of the eye formed by the cornea leaving a central opening, the pupil, to admit light to the photoreceptors of the retina.

The pupil diameter is controlled by two muscles, the circular sphincter papillae and the radial dilator pupillae of the iris, both of which are innerved by the autonomic nervous system. The sphincter papillae receive parasympathetic innervations via the ciliary ganglion

while the dilator papillae receive sympathetic innervations via the superior cervical ganglion. Behind the iris, it lies the ciliar body, which contains smooth muscle fibers.

The lens of the eye is attached to the ciliary body by a circular array of fibers called the zonule of Zinn or the suspensory ligament. The lens is formed as a series of cell layers, which arise from the cuboidal epithelial cells that covers its anterior surface. The cells of the lens synthesize proteins known as crystallins that are important for maintaining its transparency. Like the cornea, the lens has no blood vessels and depends on the diffusion of nutrients from the aqueous humor and its nourishment.

Figure 3.1: Cross-sectional view of the human eye [1]

3.3 The optics of the eye

When the light enters through the pupil, it is focused by the cornea and lens onto the retina. The eye behavior is similar to a pinhole camera. The image is inverted so that light falling on the retina nearest to the nose (nasal retina) comes from the lateral part of the visual field

26 (the temporal field), while the more lateral part of the retina (the temporal retina) receives light from the central region of the visual field (the nasal field).

Since objects may lie at different distances from the eye, the optical elements of eye must be able to vary its focus in order to form a clear image on the retina. The optical power of the eye is at its minimum when distant objects are bought into focus while it is at its maximum when it is focused on the nearest point. This variation in the optical power is achieved by the lens, which is suspended from the ciliary muscle by the zonula fibres. The lens itself is elastic and can change its shape according to the tension placed on it by the zonal fibers. The ability of the lens to change its shape is an essential part of the mechanism by which the eye can bring images into focus on the retina.

This process is controlled by the ciliary muscle and is called accommodation: when the ciliary muscles are relaxed, there is a constant tension on the zonula fibers exerted by the effect of the intraocular pressure on the sclera. This tension stretches the lens and minimizes its curvature. When the eye switches its focus from a distant object to a near object, the ciliary muscle, innervated by the parasympathetic fibers from the ciliary ganglion, contracts and this opposes the tension in the sclera. As a result, the tension on the zonula fibres decreases and the lens is able to assume a more spheroidal shape due to its inherent elasticity: the more spheroidal the lens, the greater its optical power.

27 As for any lens system, the optical power of the eye is measured in diopters. The dioptric power of a lens is the reciprocal of the focal length measured in meters.

For a normal relaxed eye, the total optical power is about 58 diopters. Most of the optical power of the eye is provided by the refractive power of the cornea, while the lens contributes a further 15 diopters when the eye is focused on a distant object and about 30 diopters when it is focused on the near point [3].

3.4 Human eye parameters

A healthy human eye presents the following characteristics:

 Crystalline lens: the crystalline lens is a biconvex structure where the anterior surface is less curved than the posterior. The rest diameter is of about 9 mm and the rest thickness is 3.6 mm [4]. The distribution of the refractive index ranges from about 1.406 in the central part to about 1.386 in outer layers, making it a gradient index (GRIN) lenses. This allows the eye to image with good resolution and low aberration at both short and long distances.

Figure 3.3: Distribution of the refractive index in the human eye: higher in the center (red) and lower in the periphery (blue)

28  Broadband: a typical human eye responds to wavelengths from about 390 to 750 nm. In terms of frequency, this corresponds to a band in the proximity of 400–790 THz. A light-adapted eye generally has a relatively high light transmittance in the 500- to 700-nm range [5].

 Accommodation: the ability of the eye to adjust its focal length is known with the term of accommodation, as described in the previous chapter. In the eyeball, light rays passing through the cornea are bent by its curvature toward the pupil. The lens, by changing its curvature, finishes the focusing process. When an object is located at infinity, the focal length, or the distance from the lens to the retina, is about 24 mm. When the distance between the object and the eye is shorter than 25 cm, the focal length cannot be adjusted and a clear image on the retina cannot be formed. This distance is known as the least distance of clear vision. In this case, the focal length of the lens is about 22 mm [6].

 Resolution: the angular resolution, which is often measured in cycles per degree, is an indicator of how much an eye can differentiate one object from another in terms of visual angles. Resolution in CPD can be measured by bar charts of different numbers of white/black stripe cycles. For a human eye with excellent acuity, the maximum theoretical resolution would be 1.2 arc-minute per line pair, or a 0.35 mm/line pair, at 1 m [6].

 Response Time: the response time is the reaction time of accommodation responding to sudden changes in focus. Research results show that the average values obtained for movement time are 0.64 seconds for far-to-near accommodation and 0.56 seconds for near-to-far accommodation [6].

 Efficiency: when a human eye moves its focus from one object to another, the adjusted focal length is very accurate without obvious defocus. In comparison with a conventional lens system which is operated mechanically, such as a camera lens system, the focal length adjustment exhibits high efficiency.

In addition to the above mentioned properties, the human eye has some other unique properties, such as multiple axes, rotatable movement, and wide field of vision angle (greater than 90◦ in the temporal field) [7].

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3.5 The eye-inspired lenses

As described in the previous chapter, a healthy human eye can arbitrarily vary its focal length by changing the lens shape, as well as exhibiting many advantages over a conventional solid lens.

Such an optical device has inspired the development of different types of eye-like adaptive lenses, which can be divided in two main categories: surface profile change and refractive index change lenses.

 Refractive Index Change: this types of lenses exhibit a variable focal length due to the change of refractive index inside the volume. Figure 3.4 depicts the variation of the refractive index of the lens material across the lens aperture: in the original state (black line), the material refractive index distribution is uniform across the lens aperture; when an external force is applied to the material, it causes a gradient redistribution of the refractive index across the lens aperture, as shown in the curved line in Figure 3.4 (red line).

The material which is usually used to obtain such a refractive index distribution is liquid crystal (LC) [8, 9].

Figure 3.4: Basic principle of change of the refractive index of an eye-inspired lens [6]

 Surface Profile Change: in this type of devices an actuation force is usually applied to the lens, causing its shape deformation. To do so, two different approaches are usually found in literature, as shown in Figure 3.5.

In the first method (Figure. 3.5a), the volume of the lens is kept constant, while the diameter and the radius of curvature of the lens both change after deformation applied by an external force. In particular, both the aperture diameter and the radius of curvature of the lens decrease in the deformed state, in order to increase the focal

30 length of the lens. Among these types of tunable lenses, it is possible to finf: elastomeric solid lens [10, 11], electrowetting lens [12], and dielectric liquid lens [13, 14]. As many of these devices are made of soft elastomer, the device shape can be easily tuned by the application of a driving force.

In the other type of Surface Profile Change lenses (Figure. 3.5b), instead, the aperture of the lens does not varies but the volume of the lens increases or decreases, changing accordingly the shape of the lens surface.

For instance, the conventional elastic membrane lenses belong to this category.

These types of tunable lenses will be better described in the following chapter.

31

REFERENCES

[1] http://www.mastereyeassociates.com/eye-anatomy (accessed August 2014)

[2]http://projects.cbe.ab.ca/Diefenbaker/Biology/Bio%20Website%20Final/notes/nervous_system/8 _eye_note%20s.html (accessed August 2014)

[3] Gillian Pocock, Christopher D. Richards, David A. Richards, Human Physiology, 199-205 (2013) [4] F. Carpi, G. Frediani, S. Turco, and D. De Rossi, Bioinspired tunable lens with muscle-like electroactive elastomers, Adv. Funct. Mater. 21, 4152–4158 (2011)

[5] S. J. Williamson and H. Z. Cummins, Light and Color in Nature and Art, Wiley, New York (1983) [6] Introduction to Adaptive Lenses, Hongwen Ren, Shin-Tson Wu (2012)

[7] D. D. Atchison and G. Smith, Optics of the Human Eye, Oxford University Press, New York (2000) [8] S. Sato, Liquid-crystal lens-cells with variable focal length, Jpn. J. Appl. Phys. 18, 1679 (1979) [9] D. K. Yang and S. T. Wu, Fundamentals of Liquid Crystal Devices, Wiley, Hoboken, NJ (2006) [10] H. Oku, K. Hashimoto and M. Ishikawa, Variable-focus lens with 1-kHz bandwidth, Opt. Express 12, 2138–2149 (2004)

[11] H. Ren and S. T. Wu, Variable-focus liquid lens, Opt. Express 15, 5931–5936 (2007) [12] F. Schneider, J. Draheim, C. Muller, and U. Wallrabe, Optimization of an adaptive

PDMS-membrane lens with an integrated actuator, Sensors and Actuators A: Physical 154, 316–321 (2009) [13] S. Xu, H. Ren, Y. J. Lin, M. G. Jim Moharam, S. T. Wu, and N. Tabiryan, Adaptive liquid lens actuated by photo-polymer, Opt. Express 17, 17590–17595 (2009)

[14] C. S. Liu and P. D. Lin, Miniaturized auto-focusing VCM actuator with zero holding current, Opt.

32

Chapter 4

Tunable lenses

4.1 Introduction

In conventional active optical systems, the focus and the zoom are usually obtained by the movement of solid or plastic lenses with constant focus.

Alternatively, different types of eye-inspired lenses can be used in order to vary the focusing power of the optical imaging system by changing either the refractive index of the material or by changing the lens shape, as described in the previous chapter.

In this chapter it will be described how the lenses can be tuned by changing their shape, since the device realized in the present project belongs to this category. The dynamic change of the lens shape, in particular of the radius of curvature, allows the optical system to focus on a range of positions. This change can have the same optical effect as moving the entire lens, without the need of expensive mechanical actuators.

For this reason, optical system can be designed in a more compact way, with few lenses and usually with shorter or no translational movement. These features lead to the possibility of realizing a more robust and compact design. Moreover, the materials used to produce tunable lenses are generally lightweight compared to glass, leading to a reduction of the overall weight and to a faster response time of the optical system. The possible applications in which they could be integrated include consumer electronics (e.g. cameras, mobile phones etc.), medical diagnostics (e.g. video endoscopes and optical instrumentations) and optical communications (e.g. optical fiber components).

33

4.2 State of the art

Because of the advantages described in the previous chapter, a wide range of tunable shape lenses have been studied and realized, using a wide number of actuation concepts. Among these, there are devices in which the body of the lens is liquid and others in which the lens is solid.

4.2.1 Liquid lenses

Liquid lenses have been developed using a wide range of actuation technologies. Among these, the most important ones are:

 Pneumatic tuning;  Electrowetting tuning;

 Tuning with stimuli responsive hydrogels;  Thermal tuning;

 Electromechanical tuning;  Piezoelectric tuning;  Artificial muscles tuning.

4.2.1.1 Pneumatic tuning

Devices that use a pneumatic tuning of the lens shape commonly include a circular chamber covered by a deformable elastic membrane with a liquid (the most commonly-used being water), which is introduced into the chamber through an integrated micro-channel network acting as the lens medium.

The application of a pressure to the liquid lens can deform the membrane and consequently adjust the lens surface contour, thereby altering its optical properties such as the focal length. The pressure is usually generated by an external precise pressure controller or a syringe.

One of the first example of pneumatic tuning was introduced by Ahn and Kim [1], who realized a pneumatic device made with conventional micromachining technology based on silicon and glass. Their design was later improved by Werber and Zappe [2], who replaced the glass membrane with a layer of PDMS in order to decrease the aperture size and the

34 focal length of the lens. In fact, the PDMS membrane can easily be deformed by the pressure exerted by the liquid. For these reasons, this material has been used in the following works in order to create different shapes and designs: plano-convex or concave lens (Figure 3.1 (a)), double convex or concave (Figure 3.1 (b)), multi-chamber (Figure 3.1 (c)), and hybrid lens (Figure 3.1 (d)).

Fig 3.1: Different types of pneumatic lenses: (a) plano-convex lens [2] (b) double convex and concave lens [3], (c) multi-chamber lens [4], (d) hybrid lens [5]

In particular, this latter design was used by Hongbin Yu et al. [6] to produce a novel liquid-filled lens, in which the quality of the images obtained with pneumatic tuning was improved. The structure of the proposed design is similar to other reported liquid-filled lenses. The main body is fabricated into a PDMS substrate and consists of a sealed chamber covered with an elastic membrane and connected laterally to a microchannel, through which the liquid is delivered via an external syringe pumping system. The key difference lies in the bottom surface of this chamber, where they introduced a fixed aspherical surface acting as one lens end (Figure 3.2).

35

Fig 3.2: Schematic of liquid-filled lens design (a) Entire design (b) Cross-section of the device [6]

Unlike the most commonly used flat surface, in the current case the aspherical surface can compensate the spherical aberration that appears during lens operation without decreasing the overall performances of the lens.

Nevertheless, the downsides of pressure tuning are the bulky and expensive pressure controllers and extra tubing, which make the systems integration impracticable. Therefore, variable actuators are designed for the integration of tunable lenses, aiming at realizing more compact and more flexible systems.

4.2.1.2 Electrowetting tuning

Electrowetting tuning is based on the wetting behavior of a liquid droplet on a surface. This principle consists in the application of an electrostatic field in order to change the surface tension and the contact angle of the liquid droplet.

36

Fig 3.3: Electrowetting principle [7]

One of the first proofs of concept for liquid lens based on direct electrowetting was reported by Gorman et al [8]. Hexadecanethiol was used as the lens liquid while the lens was positioned on a gold electrode immersed in an electrolyte. The interface formed by these two immiscible liquids allowed, under an electrostatic actuation, to tune the shape of the lens.

Commercial electrowetting lenses have been manufactured by Philips [9]. As illustrated in Figure 2.2, the commercial lens uses a transparent cylindrical chamber containing two immiscible liquids, one is electrically conductive (aqueous salt solution) while the other is insulating (nonpolar oil). The walls of the chamber are coated with electrodes covered with an insulating layer and a hydrophobic layer. After applying a voltage between the electrodes, an electric field is established across the insulator, lowering the interfacial tension between the conductive liquid and the insulator itself. As a result, the contact angle changes, forming a plane-concave lens.

37

Fig 3.4: Philips electrowetting lens. (a) Without voltage applied (the conducting fluid has a spherical shape). (b) With voltage application, the contact angle between the conducting fluid and the insulated electrode walls is reduced,

and the lens type becomes positive [9].

The advantages of electro-wetting lenses are fast tuning time and low power consumption because of the electrostatic actuation. For example, the response time of electrowetting lenses from Philips lies in the range of 50 ms to 200 ms [9]. Challenges of this approach are the high voltage that is required for actuation, as well as the limited refractive power due to a low refractive index difference between the two immiscible liquids.

4.2.1.3 Tuning with stimuli responsive hydrogels

Stimuli responsive hydrogels is another type of actuator that can be used to induce a pressure for deforming the liquid lens. Dong et al. [10] used hydrogels sensitive to temperature and pH values to control the lens shape. As shown in Figure 2.5, the liquid lens is shaped by the interface between water and oil. Water is contained in a ring made of hydrogels and works as the lens liquid. The temperature sensitive hydrogel expands at low temperatures and contracts at high temperatures. The temperature range is from 20 to 50 °C with a transition temperature of about 32 °C. The pH sensitive hydrogel expands in basic solutions and contracts in acid solutions. The pH range is from 2 to 12.

38

Fig 3.5: Tuning with stimuli responsive hydrogels [11]

Since this actuation concept relies on thermal diffusion and molecular diffusion, the response time is relatively low (20–30 s) compared to other actuation concepts. When a fast tuning system is needed, it is possible to make a thinner and smaller hydrogel actuator; however, the system has the disadvantage to be too fragile to bear mechanical strength.

4.2.1.4 Thermal tuning

Thermal tuning of a liquid lens is based on the use of a thermal expansion liquid inserted in a cavity. By heating the liquid, a pressure change in the cavity is induced.

Wang et al. first described this concept for micro-lenses [12]. As shown in Figure 2.4, they used a silicon substrate in order to support a PDMS membrane and to form a fluid chamber on its backside by bulky micromachining. A Pyrex glass plate carrying a heater and a sensor is bonded with the silicon chip. A liquid with a high expansion coefficient (3M PF 5080) is used to fill the lens chamber. After applying voltage to the heater, the liquid expands and deforms the PDMS membrane, thereby tuning the lens.

39

Figure 3.6 (a) 2D schematic design of the thermal tunable micro-lens. (b) Pictures of the thermal tunable micro-lens. The chip size in the picture is 8.5 × 6.5 × 1.5mm3 [12]

In this approach, the thermal actuation can generate a large deflection of the membrane with relatively low driving voltages (maximum 14V in [12]), and can be realized in the very small package of a microsystem. As a disadvantage of the design, the heater is located in the lens cavity and directly heats the optical liquid, which induces the thermal gradient in the optical liquid, and results in an inhomogeneous refractive index, which degrades the optical performance. Moreover, the heating of the optical liquid with large expansion coefficient will largely increase the evaporation rate of the liquid, reducing the lens stability significantly, making this approach not suitable for long-term lens applications.

4.2.1.5 Piezoelectric tuning

Piezoelectric actuators rely on the principle of piezoelectric effect. Many materials exhibit piezoelectricity, such as naturally formed crystals and man-made ceramics. These materials have the ability to produce electricity when subjected to mechanical stress (piezoelectric effect). Conversely, a mechanical deformation is produced when an electric field is applied (inverse piezoelectric effect), causing the substance to shrink or expand. Schneider et al [12] exploited the inverse piezoelectric effect of a disk-like piezoelectric actuator to deform a liquid lens. Figure 2.38 depicts the structure of such device, which is made of an actuator chamber plus a lens chamber, separated by a glass plate. The exchange of liquid between the two chambers is possible thanks to the present of orifices in the glass substrate. The lens chamber consists of a silicone membrane and a supporting ring made of PDMS elastomer, while the actuator chamber is made up of a piezo-bending actuator embedded in silicone.

40 Both chambers are filled with water or oil. When a voltage is applied to the actuator, its interior edge bends upwards, so that the liquid in the actuator chamber is forced to move to the lens chamber. This causes an increasing bulge in the lens membrane: as a result, the radius of curvature decreased along with the focal length of the lens.

Fig 3.7: Schematic assembly of the liquid lens with a disk-like piezo-actuator [13]

Using piezoelectric actuators to drive adaptive liquid lenses is a competitive approach as compared to other actuation methods. Piezoelectric actuators are capable of generating a high-pressure force with a relatively low voltage. Moreover, they have the advantages of high actuating precision and fast reaction.

4.2.1.6 Artificial muscles tuning

Artificial actuators are synthetic materials that behave like biological muscles, with advantages in terms of power, stress, strain, response time, efficiency, and controllability. Similarly to piezoelectric actuators, they have found potential applications to drive elastic membrane liquid lenses. Among these, dielectric elastomer (DE) is the most common type of artificial muscle and has been used in the majority of tunable lenses devices, including this research project. In fact the DEA, besides the advantages described for the piezoelectric

41 actuator, presents very high energy-density (> 0,2 J/cm³) compared to piezoelectric principle (0,1 J/cm³) and an higher maximum strain [14].

For this reason, the behavior of this material will be largely described in the next chapter.

4.2.2 Solid lenses

The advantages of the described liquid lenses are: fast response time, low power consumption and reversibility without any mechanical parts. However, the liquid lenses have fundamental problems such as gravity effect that causes optical distortion and shape instability with movements or vibrations. Besides, for applications that require a wide range of operating temperature, designing a liquid lens is a challenge because almost all physical properties of a liquid are temperature dependent. For micro-optofluidic lenses that require a continuous supply of liquid streams, flow control and the large amount of liquid are the main disadvantages toward practical applications of these innovative devices.

For these reason, other types of tunable solid-body lenses has been proposed in the literature, even if they are fewer compared to liquid lenses. Examples of tunable solid-body lenses that can be found in literature are made of the following actuation mechanism:

 Thermal tuning  Mechanical tuning

4.2.2.1 Thermal tuning

As with a liquid lens, solid PDMS lenses can also be tuned by temperature changes. The approach was initially reported by Fang et al. [15,16]. The principle is based on the mismatching of coefficients of thermal expansion and stiffness between PDMS and silicon. As shown in figure 2.6 the lens consists of a silicon heater, a conduction ring, and a solid PDMS lens. The heat is conducted to the micro-lens via the conduction ring, and the PDMS lens expands under the high temperature. The shape of PDMS is confined by the conducting ring in the edge, and further changes the radius of curvature as well as the focal length.

42

Figure 3.8: SEM pictures of the device (a) before PDMS dispensing; (b) after PDMS dispensing [15]

This solid polymer lens offers a more robust approach and can more readily withstand fluctuations of temperature, pressure, and motion than liquid lenses. Nevertheless, in order to achieve enough change of the lens curvature, high temperature (up to 350°C) and large power consumption are required.

4.2.2.2 Mechanical tuning

The device proposed by Santiago–Alvarado [17] et al. consists in a solid elastic lens (SEL) made of Polydimethylsiloxane (PDMS), deformed by applying continuously a radial stress on its perimeter by means of a rotating cogwheels mechanism (Figure 3.9)

43

Fig 3.9: Rotating cogwheels mechanism used to tune the lens [17]

The lens is produced using a plastic mould and its shape, when no forces are applied, has two spherical surfaces with the same curvature radii. These surfaces change shape as radial forces are applied on the perimeter of the lens by means of the rotating mechanism that applies continuous linear forces. As a result, the optical performances of the lens changes while varying its shape.

44 In a following project Santiago–Alvarado et al. [18] compared the SEL with a tunable pneumatic liquid lens and they found out that the liquid lens has better performance than the SEL in terms of tunability and optical power.

Liebetraut et al. employed a similar actuation mechanism to realize a tunable solid-body diffractive lens consisting of 790 rings of a silicone elastomer (Sylgard 184) [19]. The diffractive lens was mounted on eight anchors (figure 3.11), embedded in opposing periphery of the lens.

Figure 3.11: Elastomeric lens for tunable astigmatism [19]

The advantage of this structure consists in the fact that the eight anchors can be individually adjusted, allowing asymmetric deformation of the lens along four independent axes. Actuation along fewer than all axes reduces the overall symmetry of the lens and allows the tuning of specific wavefront errors. In particular, vectored actuation allows a controlled deformation of the elastomeric lens and consequently a controlled change of the resulting wavefront. Pseudo-radially symmetric actuation (that consists of actuating all anchors at once) may be used to influence radially symmetric wavefront aberrations such as defocus and spherical aberration and ‘asymmetric’ actuation can be used to control astigmatism. Despite this design has shown good performances in terms of correction of aberrations, the mechanical tuning mechanism makes the device bulky and more expensive compared to DEA tuning.

45

REFERENCES

[1] Ahn S-H and Kim Y-K, Proposal of human eye’s crystalline lens-like variable focusing lens Sensors, Actuators A 78, 48–53 (1999)

[2] A. Werber and H. Zappe, Tunable microfluidic microlenses, Appl. Opt. 44, 3238–3245 (2005) [3] Agarwal, M, R A Gunasekaran, P Coane, and K Varahramyan: Polymer-based variable focal length microlens system. Journal of Micromechanics and Microengineering, 14(12):1665 (2004)

[4] Mader, Daniel: Tunable microfluidic multi-chamber membrane lenses. PhD thesis, Department of Microsystems Engineering (IMTEK), University of Freiburg (2011)

[5] W. Zhang, Thermo-pneumatic micro-lenses, Research in Micro-optics Volume 11, Department of Microsystems Engineering – IMTEK, University of Freiburg Georges-Köhler-Allee 102, Germany [6] H. Yu, G. Zhou, H. M. Leung, and F. S. Chau Tunable liquid-filled lens integrated with aspherical surface for spherical aberration compensation, Optics Express, Vol. 18, Issue 10, 9945-9954 (2010) [7] http://www.ece.uc.edu/devices/Research.html (Accessed September 2014)

[8] Gorman, Christopher B., Hans A. Biebuyck, and George M. Whitesides: Control of the shape of liquid lenses on a modified gold surface using an applied electrical potential across a self-assembled monolayer, Langmuir, 11(6):2242–2246, (1995)

[9] S. Kuipera and B. H. W. Hendriks: Variable-focus liquid lens for miniature cameras, Philips Research Eindhoven (2004)

[10] Dong, Liang, Abhishek K. Agarwal, David J. Beebe, and Hongrui Jiang: Adaptive liquid microlenses activated by stimuli-responsive hydrogels. Nature, 442(7102):551–554 (2006)

[11] H. Ren, S-T Wu: Introduction to AdaptiveLenses, John Wiley & Sons, Inc., Hoboken (2012) [12] Wang, Weisong and Ji Fang: Design, fabrication and testing of a micromachined integrated tunable microlens. Journal of Micromechanics and Microengineering, 16(7):1221 (2006)

[13] F. Schneider, D. Eberhard, D. Strohmeier, C. Müller, U. Wallrabe Adaptive fluidic PDMS-lens with integrated piezoelectric actuator, Conference: Micro Electro Mechanical Systems (2008)

[14] http://cdn.intechopen.com/pdfs-wm/34076.pdf (Accessed September 2014)

[15] Lee, Sz Yuan, Hsi Wen Tung, Wen Chih Chen, and Weileun Fang: Thermal actuated solid tunable lens. Photonics Technology Letters, IEEE, 18(21):2191–2193 (2006)

[16] Lee, Sz Yuan, Hsi Wen Tung, Wen Chih Chen, and Weileun Fang: Novel micro lens with tunable astigmatism. Solid-State Sensors, Actuators and Microsystems Conference, 2007, 2147–2150 (2007) [17] A. Santiago–Alvarado, S. Vázquez–Montiel, F. Iturbide–Jiménez, R. Arriaga–Martínez, and J. González–García: The Design, Construction and Characterization of a Solid Elastic Lens, Current Developments in Lens Design and Optical Engineering IX, Proc. of SPIE Vol. 7060 (2008)

[18] A. Santiago-Alvarado, S. Vazquez-Montiel, J. Munoz-López, V. M. Cruz- Martínez, G Díaz-González and M Campos-García: Comparison between liquid and solid tunable focus lenses, Journal of Physics, Conference Series 274 (2011)

[19] P. Liebetraut, S. Petsch, J. Liebeskind and H. Zappe, Elastomeric lenses with tunable astigmatism, Light: Science & Applications (2013) 2, e98 (2013)

46

Chapter 5

Electroactive polymers actuators

5.1 Introduction

As previously described, in this chapter we will show the potential of a different class of ‘smart’ materials to develop electrically tunable optical lenses with simple and compact structure, low weight, high response speed, and low power consumption. More specifically, we will describe the dielectric elastomer actuator (DE) and an optical application of this type of technology with a bio-inspired design of the lens architecture, to which the device developed in this project is inspired.

5.2 Electroactive polymers actuators

The perceived need for improving the traditional transducers performances, which has progressively emerged in the last few decades, has drawn considerable efforts for the development of devices based on materials with intrinsic transduction properties.

These materials, often referred to as “smart materials”, are structures that sense external stimuli and respond accordingly in real or near time. These soft, muscle-like alternatives to conventional engineering mechanisms can greatly expand the engineering design.

Among these, we can find improved piezoelectric, magnetostrictive, shape-memory materials. Beside them, newer emerging electromechanical transduction technologies based on so-called electroactive polymers (EAP) have also gained a considerable attention [1].

47

Figure 5.1: Classification of smart materials for actuation

EAP offer the potential for performance exceeding other smart materials, while retaining the cost and versatility inherent of polymer materials. EAP are currently being developed and studied as possible “artificial muscles”, i.e., functional surrogates of natural muscles, aimed at mimicking performances of biological actuation machines.

48 EAP materials have functional similarities to biological muscles including quiet operation, damage tolerance, resilience, and large actuation strains (stretching, contracting, or bending). They possess properties that can provide more life-like aesthetics, vibration and shock dampening, and flexible actuator configurations. EAP materials can be used to fabricate devices that require no traditional components, such as gears and bearings.

Among the electroactive polymers, two big classes can be find, which in turn comprise other subcategories:

1. wet EAP actuators (ionic); 2. dry EAP actuators (electric).

The first type of actuators (also called “electroactive gels”) are based on the expulsion and absorption of a solvent inside the polymeric matrix. These expulsions and absorptions are caused, for example, by the application of an electrical stimulus (such as an electric field). The volume change in the polymeric gels is the consequence of the variation of osmotic pressure, which compresses or expands the gel, thus generates a mechanical work. As this phenomenon occurs by means of a mass transport, the response time is quite low.

By contrast, the dry EAP actuators directly respond to the application of an external electric field, thus they react faster to the external stimulus as compared to the wet actuators. The dry EAP actuators can be divided in two categories: “electrostrictive polymers” and “dielectric elastomers”. A common aspect between these categories is that the stress and the strain both have a quadratic dependence as a function of the applied electric field. Nevertheless, the phenomena underlying the behavior of electrostrictive polymers and dielectric elastomers are very different: in the former, there is a re-orientation of the electric dipoles induced by an external external field while in the latter there are electrostatic interactions between electrical charges, commonly referred as “Maxwell stress”.

The dry actuators are driven by high voltages (similarly to piezoelectric materials), while the wet actuators require low voltages (of the order of few Volts) but have a lower response speed. Another difference relies on the control strategy. In fact, while the dry EAP actuators do not require complex control strategies, the polymeric gels generally present discontinuous phase transitions that make difficult to control the position of equilibrium [3].

49

5.3 Dielectric elastomers actuators (DEAs)

Within the dry EAP actuators, the dielectric elastomers actuators (DEAs) are drawing particular interest at present because of their well-established overall performance, as well as simple structure and robustness due to the use of stable and commercially available polymer materials. DEAs are rapidly emerging as high-performance “pseudo-muscular” actuators and they have been successfully applied in a wide range of applications, including the device developed in this research project.

DEAs consist of a thin elastomer membrane placed between two compliant electrodes. When a voltage is applied to the electrodes, the opposite charges on each electrode generate an electrostatic attractive force (also known as Maxwell stress).

(18)

In equation (18), represents the Maxwell pressure, are the absolute and relative dielectric permittivities, respectively, V is the voltage and d is the thickness of the membrane.

The Maxwell force squeezes the elastomer, thereby decreasing its thickness. As elastomers are generally considered to be incompressible, the decrease in thickness leads to an area expansion of the same magnitude.