An inverse modelling technique for glass forming by gravity sagging

Some optical surfaces are formed by gravity sagging of molten glass. A glass sheet supported on a ceramic former is heated; the glass becomes a very viscous fluid and sags under its own weight until the lower surface is in full contact with the former. The smooth upper free surface is the required optical surface. Its shape is dependent on the initial geometry and, in optical terms, differs significantly from the former shape. The inverse problem is to determine the shape of the former that produces a prescribed upper surface. This is a difficult, nonlinear problem. A finite element algorithm has been developed to compute gravity sagging for any given initial axisymmetric geometry (the forward problem). The present work describes a successful iterative method, which uses the output from a number of forward problems to determine the required (axisymmetric) former shape.