8. A First-Principle Investigation of the Optical Properties for a Single Sessile Liquid Lens Formed by the Surface Tension and Gravitational Effects Between Water and Air

Many research teams have already investigated the feasibility of different kinds of liquid optical systems. Their research could be classified into four main categories by driving methods including mechanical, electromagnetic, dielectric and electrowetting. In this project, the design of the liquid optical system would be based on the mechanical method which alters the surface curvature of the liquid lens by changing the liquid volume above the horizontal diaphragm. The optical performance of this liquid lens system will be investigated theoretically, numerically and experimentally. For the mechanics method, no previous literatures in optical science & engineering investigate the surface shape of the liquid droplet from the first principle calculation, which means to deduce and solve the expression of the liquid surface from the Bashforth-Adams equation (a special expression of the Young-Laplace equation considering the gravitational effect) with specific boundary conditions. For the condition that the diameter of the diaphragm is sufficiently less than the capillary length of the interface system, the surface tension affects sufficiently larger than the gravity. In this case, many works ignore the gravitational effect on the water droplet and approximate the surface shape of the liquid droplet to a perfectly spherical form only under the surface tension effect. For the condition that the diameter of the diaphragm is large enough that it’s hard to ignore the gravitational effect, previous works used 3D scanning methods to determine the surface shape of the water droplet. Currently, there is no analytical method to solve the three-dimensional Bashforth-Adams equation for general conditions, so the iterative numerical method would be applied to solve it. The deviation of the aspherical surface from the spherical surface has been well studied in optical design. The numerical solution could be well described by the polynomial curve fitting which is the widely used method for optical designing software such as ZEMAX OpicalStudio. It enables us to reproduce the surface curvature in OpicalStudio and investigate its optical performance by modulation transfer function (MTF chart), etc. The experimental part of this project is mainly an application to the mechanical static liquid optical system. We would design a liquid lens telescope with a water-air interface eyepiece (focal length f1) and a water-dimethicone interface objective (focal length f2), thus the magnification is the ratio of the objective and eyepiece f1/f2. We would do real-world tests of its performance and verify the validity of our previous theoretical and numerical analysis.