A frozen surface technology is provided that can be used to provide a precisely defined surface. The frozen surface technology can include the use of a frozen membrane. For instance, frozen membrane mirrors and methods of producing frozen membrane mirrors are provided. The frozen membrane mirror includes a membrane material having a reflective surface. Active control is used to maintain a desired figure of the reflective surface while a solidifying material is applied to a back side of the membrane material. Active control of the figure of the reflective surface is maintained while the solidifying material cures. Once the solidifying material has been applied and cured, active control can be removed. The frozen surface technology also enables the formation of a surface with a precisely defined shape from a shell material that is brought into a flexible state, is actively controlled to achieve the desired surface shape, and that continues to be actively controlled until the shell material has been brought into a fixed or frozen state.