the influence of the boundary conditions care was exercised in the manufacturing of the inner and outer rings and in the membrane mounting process the outer ring where the film is initially mounted and the inner ring where the boundary of the doubly curved surface is initiated were both optically polished planar to less than 150 nanometers the outer ring defines the outer boundary of the membrane and if the edge is not well defined an aberrated optical surface will result the degradation in mirror quality is proportional to the magnitude of the boundary deviation a large deviation at the boundary of the mirror will transmit undesirable figure error into the clear aperture of the membrane the volume between the inner ring and the outer ring forms an outer annulus the inner ring has a doubly curved optically polished top surface so that the membrane can slide across it with near zero friction while maintaining a seal between the inner ring and the outer annulus even when the membrane has a concave curvature in both regions incremental stress is defined as membrane stress caused by other than the evacuation stress of the inner ring e g the initial clamping of the membrane to the outer ring out of plane translation of the outer ring with respect to the inner ring or evacuation of the outer annulus incremental stress for example can be uniformly applied to the membrane by varying the differential pressure in the outer annulus a pressure that in general is different than that in the inner ring volume the outer ring should be coplanar with the inner ring otherwise a.