User:Pfeghali/sandbox/liquid lens

A liquid lens is an optic using liquids rather than glass elements for applications with small lens requirements. Since there are no mechanical elements, these lenses operate by using applied current to change their properties. These lenses offer quieter and more stable solutions than mechanical lenses while simultaneously needing less operating power. Inherently their size is limited by the gravitational effect. Therefore their use cases are more limited in scope to smaller applications.

Lens Implementations
To be able to fully utilize liquids as lenses, focal properties must be adjustable. The utilization of different types of dielectrics is a common method for adjusting focus and focal length.

Dielectric elastomer film
A popular method of applying liquid lens optics is in conjunction with dielectric elastomer (DE) film. DE film is an electroactive polymer which can convert electrical energy into mechanical work; in this case the film thins and widens. To hold the liquid, a centimeter or smaller diameter through-hole is drilled into the film. The hole must be small to minimize the gravitational effect on the liquid. The liquid forms a biconvex lens, protruding over the sides of the through-hole. When a current is applied, the hole shrinks and the film thins. The liquid droplet's diameter decreases, and the focal length changes as a function of the lensmaker’s equation.[1]

Dielectric liquid
Rather than using a dielectric film, a dielectric liquid can also be used with a circular electrode underneath the liquid. A solid with a through-hole is placed above a substrate with a circularly symmetrical electrode on the surface. A dielectric droplet is then dropped into the hole, forming a spherical shape above the solid forming a spherical lens. After a current is applied, the gradient of the electric field modifies the alignment of the molecules in the droplet. The movement of these molecules leads to an extension in the droplets height. This shifts the focal point in the lens, without changing the focal length. Using a dielectric liquid allows for efficient focusing with no chance of focus breathing or a change in focal length. This is similar to electrowetting. [2][3]

Formulas
All of these researched implementations can be mathematically modeled. These models can be split into two categories, optical and electric formulas.

Optical formulas
For the DE Film lens implementation we can utilize the standard Lensmaker’s equation, as the liquid acts as a biconvex lens. The focal length is determined by a function of the refractive index n, R1 the radius of the outside curve, R2 the radius of the inside curve, and d the thickness of the lens:

$$\frac{1}{f} = (n-1)\left [\frac{1}{R_1} - \frac{1}{R_1}+\frac{(n-1)d}{nR_1R_2} \right ]$$

For the Dielectric liquid, the focal length is determined by the radius of the droplet, divided by the difference between the refractive indices of the liquid and surrounding media.

$$f_L=\frac{r}{n_L-n_M }$$

Electric formulas
For the DE film lens implementation, the actuation pressure is defined as a function of voltage over the thickness of the film. This is then multiplied by the dielectric constant of the material and the permittivity of free space.

$$P = \epsilon_0\epsilon(\frac{V}{T})^2$$

For the dielectric liquid, the electronic formula is the standard equation for calculating the strength of an electric field, since the gradient of this field affects the properties of the liquid.

Advantages
Since there are no moving pieces, liquid lenses are excellent options for high intensity use cases with no performance degradation for over 100 million actuations, compared to 2 million cycles for mechanical lenses. The lack of mechanical elements allows for an average focusing time of roughly 20 milliseconds. In addition, the low amperage requirement of a few milliamps allows for more flexibility in low power applications. Further, the lack of mechanical movement allows for near silent operation.

Disadvantages
Liquid lenses are easily affected by the gravitational effect since they are not a solid. This forces lens designs to be small so that the surface tension and adhesion can eliminate the gravitational distortion. Small lenses limit the amount of light that a sensor can gather, limiting low light applications. If operating temperatures exceed the manufacturer defined range, the liquid could boil or freeze.

Applications
Due to the near silent operation of these lenses, they are excellent lens options for autofocus tracking for video applications. The low power requirements and high shock resistance also support their usage in battery powered mobile devices. Their resilience also makes them optimal for industrial applications with millions of actuations. For industrial use, they are also intrinsically better suited to finding autofocus in open-loop control.