Applications of Power Series Solutions of Membrane Equilibrium Equations to the Optical Evaluation of Membrane Mirrors with Curvature
Abstract
Power series solutions of the Hencky-Campbell equilibrium equations for an initially planar circular membrane in a state of uniform pre-strain are used to analyze the performance of an in-house laboratory membrane mirror curved by a uniform vacuum pressure applied to one side. The results provide theoretical verification of the improvement in surface figure achievable by controlling the amount of pre-strain. In particular, a pre-strain of only 0.25%, corresponding to a uniform radial displacement of the edge of an 11-inch diameter membrane mirror by about 0.014 inches, is predicted to achieve nearly 95% reduction in the maximum deviation of an f/8 membrane from a reference sphere. These results are in good agreement with laboratory measurements of spherical aberration using a Hartmann wavefront sensor. The model was also used in an extensive investigation of the effects of control parameters (pressure and pre-strain) on the improvement of surface figure for lower f-number systems. The results indicate that comparable improvement in systems of f-number less than f/6 would require membrane materials capable of withstanding pre-strains on the order of 2.0% or greater.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1998
- Accession Number
- ADA359549
Entities
People
- James M. Wilkes
Organizations
- Air Force Research Laboratory