Liquid lens technology: Principle of electrowetting based lenses and applications to imaging

液体透镜技术：基于电润湿的透镜原理和成像应用

Abstract : The principle of liquid lenses based on electrowetting will be presented, with emphasis on the key features that enables to produce a useful component for complex optical systems: equality of the densities of the two non miscible liquids, centering mean for the liquid-liquid interface which allows the optical axis to remain always stable, choice of the suitable insulating material for the supporting body etc… We will present experimental results discussed in the light of amodelization.

摘要：介绍了基于电润湿的液体透镜的原理，重点介绍了能够为复杂光学系统生成有用成分的关键特征：两种不混溶液体的密度相等，液 - 液的中心平均值允许光轴始终保持稳定的界面，为支撑体选择合适的绝缘材料等......我们将根据模型化提出实验结果。

1. I NTRODUCTION

Recently a number of new optical applications have arisen, which require a high degree of miniaturization.Photonics, optical communications, optical sensors,optical pick-up for CD/DVD reading or writing, as well as miniature cameras for the security or the
consumer electronic markets are demanding optical parts in the 1-10mm range. Whereas the realization of lens elements of this sizes is well mastered, using plastic or glass materials, the problems of actuation of such lenses for bringing autofocus, or zooming functions is still a challenging problem.

最近出现了许多新的光学应用，这些应用需要高度的小型化。光子学，光学通信，光学传感器，用于CD / DVD读取或写入的光学拾取器，以及用于安全或消费电子的微型相机。市场要求1-10mm范围内的光学部件。尽管使用塑料或玻璃材料很好地掌握了这种尺寸的透镜元件的实现，但是用于实现自动聚焦或变焦功能的这种透镜的致动问题仍然是一个具有挑战性的问题。

Optical engineers have naturally looked at adaptive optics coming from high-end scientific world to correct the wavefront curvature, in order to enable closed loop servo.

光学工程师自然而然地研究了来自高端科学界的自适应光学系统来校正波前曲率，以实现闭环伺服。

Variable focus lenses offer these optical functions while having no moving part. There have been a number of principles of variable focus lenses which have been experienced since about 60 years, starting with the work of Graham 1 who developed a principle
of deformable chamber filled with liquids. More recently the work of many companies of industries has been oriented to produce solutions at a very small scale.Liquid crystals actuators have been known since a long time to produce wave front corrections, which are easy to configure in a fully addressable 2D pattern. Several practical realizations have come though, as in the group of Commander et al 2 . Recently a simplified version has been produced by Naumov et al 3 , using a special design of electrodes which allows a gradient of electric field, thus producing a variable focal lens. The main drawback of the liquid crystal lens is that the
amplitude is rather small, achieving a few dioptries of optical power variation.

可变焦距镜头提供这些光学功能，同时没有移动部件。自从大约60年以来已经经历了变焦镜头的许多原理，从Graham 1的工作开始，他开发了充满液体的可变形腔室的原理。最近，许多工业公司的工作已经被定位为以非常小的规模生产解决方案。长时间以来已知液晶晶体致动器产生波前校正，其易于以完全可寻址的2D图案配置。已经有了几个实际的实现，如Commander等人2中所示。最近，Naumov等人3【 A.F. Naumov, M.Yu. Loktev, I.R. Guralnik, G. Vodkin,Liquid crystal adaptative lenses with modal control.】使用特殊设计的电极产生了简化版本，该电极允许电场梯度，从而产生可变焦距透镜。液晶透镜的主要缺点是振幅相当小，实现了光功率变化的一些屈光度。

In the recent past , we could introduce a new principle of liquid lenses based on electrowetting.While the principle of manipulating a liquid droplet was known since a long time , these principles were restricted to a single lens element systems, due to the lack of precise control of the optical axis.

最近，我们可以引入一种基于电润湿的液体透镜的新原理。虽然很久前就知道了操纵液滴的原理，但由于缺乏精确的原因，这些原理仅限于单个透镜元件系统。

One can show that major advantages of these liquid lenses are coming from the small electrical dissipation, the reduced size, the long lifetime under voltage cycling (which is a side advantage of the no-moving part principle).

可以证明，这些液体透镜的主要优点来自于小的电耗散，尺寸减小，电压循环下的长寿命（这是无移动部件原理的侧面优势）。

In this paper, we will review first the operation of the liquid lens, on a given design example. The second paragraph will then examine quantitatively the most important feature of the liquid lens design: the centre-alignment of the liquid drop. Then we will present experimental results of our current lens, comparing with the theoretical model.

在本文中，我们将首先回顾液体透镜的操作，在给定的设计实例中。然后，第二段将定量检查液体镜片设计的最重要特征：液滴的中心对齐。然后我们将展示我们当前镜头的实验结果，并与理论模型进行比较。

2. PRINCIPLE OF THE LIQUID LENS DESIGN

Figure 1 shows examples of a liquid lens structure:between two glass windows, two non miscible liquids are trapped in a closed cell. One of the liquid is based on a water solution and thus it is conducting electricity. The other liquid is apolar, and should be non conducting (the oil phase). The natural interface between the liquids thus forms a natural diopter, due to the index difference of the
two liquids.

图1显示了液体透镜结构的实例：在两个玻璃窗之间，两个不混溶的液体被捕获在闭孔中。其中一种液体基于水溶液，因此导电。另一种液体是非极性的，应该是非导电的（油相）。由于两种液体的折射率差异，液体之间的自然界面因此形成自然屈光度。

图1：液体透镜实际实现的两个例子。在施加电压时，液 - 液界面被放置。实线表示零电压情况。（a）梯度配置。（b）几何定心。

The actuation of the liquid-liquid interface is using electrowetting, which enables to change the relative wettability of the two liquids by a simple voltage application. In these conditions, the liquid-liquid interface has a spherical shape, with a variable radius of curvature.

液 - 液界面的致动使用电润湿，这使得能够通过简单的电压施加来改变两种液体的相对润湿性。在这些条件下，液 - 液界面具有球形形状，具有可变的曲率半径。

In order to work properly, the liquid lens needs several key features:

为了正常工作，液体镜头需要几个关键功能：

Density requirement: the two liquids should have exactly the same density. This allows the lens to work in every possible orientation: optical axis,horizontal, vertical or in any orientation to gravity.This density equality is tuned by allowing a small adjustment of the liquid composition(mixture of dense and less-dense fluids).

密度要求：两种液体应具有完全相同的密度。这使得镜头可以在任何可能的方向上工作：光轴，水平，垂直或任何重力方向。通过允许对液体成分（稠密和低密度流体的混合物）进行小的调整来调节密度相等性。

A centering mean for controlling the stability of the optical axis when the voltage is applied.The two configurations above are representing two different ways of achieving this stability(see the next paragraph).

用于在施加电压时控制光轴稳定性的居中装置。上述两种配置代表实现这种稳定性的两种不同方式（参见下一段）。

An integral liquid-liquid interface: it is important that the design allows to have conducting phases to be connected to the
outside world without having to touch physically the liquid-liquid interface.

一体化的液 - 液界面：重要的是，该设计允许将导电相连接到外部世界，而不必物理接触液 - 液界面。

In the following chapter, we will consider in details the centering of the liquid drop, discussing the relative advantages of the configurations shown above.

在下一章中，我们将详细考虑液滴的中心，讨论上述配置的相对优势。

3. CENTRE ALIGNING THE LIQUID DROP

We will discuss the two different configurations of the liquid drop shown in the figure 1.

Centering by a dielectric thickness gradient

我们将讨论图1中所示的液滴的两种不同配置。

以电介质厚度梯度为中心

We will analyse the configuration of fig. 1(a) first:here the centering of the drop is obtained through a gradient of the electric field. The Figure 2(a) shows the principle of electrowetting: the contact angle of the oil drop on a planar surface which is made of an electrode covered with an insulator film of thickness “e” and of dielectric constant “ε” is well described with the following equation:

It can be shown from eq (1) that for a 60V actuation, using a low-k dielectric (e.g. polyethylene ε=2,4) using liquids with a liquid-liquid interfacial tension of about 30mN/m,leads to a thickness of the dielectric film of about e=1,3µm.The electric field in the dielectric is then of the order of E=0,4 MV/cm. This E-field is quite high, significantly below the dielectric breakdown of good polymer insulators.
Nevertheless, one can consider that the nature of the dielectric material should be carefully chosen, for sustaining the E field. This situation corresponds to figure 2a.

我们将分析图的配置。首先，在图1（a）中：通过电场的梯度获得液滴的中心。图2（a）显示了电润湿的原理：油滴在平面上的接触角很好地描述了由覆盖有厚度“e”和介电常数“ε”的绝缘膜的电极制成的平面。以下等式：

从方程（1）可以看出，对于60V驱动，使用具有约30mN / m的液 - 液界面张力的液体的低k电介质（例如聚乙烯ε= 2,4），导致厚度为电介质膜约为e =1，3μm。电介质中的电场则为E = 0，4MV / cm。该电场非常高，明显低于良好聚合物绝缘体的介电击穿。然而，人们可以认为应该仔细选择介电材料的性质，以维持E场。这种情况对应于图2a。

图2：电润湿情况（a）“正常”平面几何形状。（b）介电厚度的径向梯度，允许液滴的中心。

On figure 2b one uses the same principle for the drop actuation, but one builds a radial gradient of the dielectric thickness: e(r) , where “e” the thickness now depends on radius “r”. In this situation there are two main differences compared to the “normal planar geometry.

在图2b中，对于液滴致动使用相同的原理，但是建立电介质厚度的径向梯度：e（r），其中“e”厚度现在取决于半径“r”。在这种情况下，与“普通平面几何形状”相比，存在两个主要差异。

The dependency of the contact angle versus voltage is modified. The figure 3 for instance shows the expected evolution of the contact angle versus voltage, with and without the thickness gradient.

改变接触角与电压的相关性。例如，图3显示了接触角与电压的预期演变，有无厚度梯度。

图3：具有梯度（正方形）或无梯度（圆形）的电润湿曲线。电润湿响应随着梯度而降低，因为润湿接触线处的相关电介质厚度随电压而增加。

In the case of a conical recess, the situation for the drop is to be always stable at the centre whatever the contact angle θ. The energy of an off-centred drop is then given by

where ξ is the cone angle (see fig. 4 for definition), and the equivalent spring constant can also been estimated as K ~0,2N/m for a 45° cone angle.

在锥形凹槽的情况下，无论接触角θ如何，下降的情况总是在中心处稳定。然后给出偏心下降的能量

其中ξ是锥角（定义见图4），对于45°锥角，等效弹簧常数也可估计为K~0,2N / m。

图4：（a）给定表面上的液滴中心的一般稳定性分析。假设表面围绕垂直轴（光轴）具有完全旋转对称。切线球面曲率c 0在图上被正数计数，而实际支撑表面“c”的曲率被计数为负。（b）根据方程式，使液滴自动定心的表面的例子。（5）：锥形凹槽，圆柱孔，环形腔等。（c）液滴不稳定的表面的例子（非自定心）。

In the case of a conical recess, the situation for the drop is to be always stable at the centre whatever the contact angle θ. The energy of an off-centred drop is then given by

在锥形凹槽的情况下，无论接触角θ如何，下降的情况总是在中心处稳定。然后给出偏心下降的能量

where ξ is the cone angle (see fig. 4 for definition), and the equivalent spring constant can also been estimated as K ~0,2N/m for a 45° cone angle.

其中ξ是锥角（定义见图4），对于45°锥角，等效弹簧常数也可估计为K~0,2N / m。

Other centering means

The calculations above show that dielectric gradient and geometry centering can have roughly the same strength,bringing similar lens quality.

上面的计算表明，介电梯度和几何中心可以具有大致相同的强度，带来相似的镜头质量。

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