Abstract: Edge-supported and fully supported membranes having substantially uniform thickness, and substantially parallel surfaces, and having the capacity to transmit at least about 90% of incident light with very little diffraction, dispersion or absorption of incident light are made by forming a polymer/solvent mixture, spin-coating a film of the polymer from the mixture onto a rotatable surface, which may have a release agent thereon, and, where a release agent is present, joining a frame or other support to the membrane and removing the membrane with its attached support from the surface. Apparatus for making such membranes includes a dispenser for dispensing a polymer/solvent mixture onto a rotatable support; a device for spinning the rotatable support at gradually increasing speeds from a first to a second speed; and a device for maintaining the speed of rotation of the support at the second speed until the membrane forms.