Numerical simulation of astigmatic liquid lenses tuned by a stripe electrode.

We propose a new design for tuning the astigmatism of liquid micro-lenses using electric field and hydrostatic pressure as control parameters. We explore the feasibility and operating range of the lens with a self-consistent numerical calculation of the electric field distribution and the shape of the two-phase interface. Equilibrium shapes, including surface profiles parallel and perpendicular to a stripe electrode, are extracted to determine the astigmatism. The wavefronts are decomposed into Zernike polynomials under zero defocus conditions using a commercial ray-tracing software. We observe that the global curvature of the lens is primarily controlled by the hydrostatic pressure, while asphericity and astigmatism are controlled by the electric field. For optimized electrode geometries and simultaneous control of pressure and electric fields the astigmatism can be tuned from Z6 = 0…0.38 µm with minor changes in the focal length.