Sphero-cylindrical lenses based on fluidic shaping on elliptical frames

We present a theoretical framework for designing ophthalmic lenses using the Fluidic Shaping method—a process in which liquid polymer is shaped into an optical component via surface tension under neutral buoyancy conditions. In contrast to conventional methods that rely on machining, molding, or polishing, Fluidic Shaping allows lenses to be formed directly in a liquid environment without any mechanical processing. In previous works we have demonstrated the creation of spherical lenses based on circular frames. In this work, we expand the method and show that elliptical frames can be used to achieve optical powers for both focus and astigmatism corrections. We analytically solve the governing equations for the equilibrium shape of the liquid interfaces and establish closed-form expressions that relate the spherical and cylindrical powers of a desired lens to frame geometry and injected liquid volume. The model lays the groundwork for establishing Fluidic Shaping as a practical method for fabrication of single-vision ophthalmic lenses.