Figuring high aspheric mirrors by elastic deformation method
Date
1990
Authors
Kang, Yan
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Abstract
Aspheric surfaces play an important role in optical systems[4], but the application of such surfaces is constrained due to difficulties of fabrication. In this thesis, the feasibility of figuring aspheric surfaces is investigated using the elastic deformation techniques. Specifically, the primary mirror of the proposed Space Debris Telescope is researched. This mirror consists of a concave hyperboloid with a fast focal ratio of f /0.66 and has a conic constant of k = -1.255. The combination results in an exceptionally aspheric mirror make this mirror very difficult to produce.
In this thesis we present a general method for production of aspheric mirrors by elastic deformation. To do this a general function describing the deflection and orientation of aspheric surfaces is presented. This function can be used for most aspheres including a sphere. By means of the elastic plate theory, the load distributions can be found to produce the desired deformation.
Different finite element models are constructed to estimate the stresses in the mirror when the deflection is prescribed. The problem of determining an adequate number of discrete points for applying the forces and a best-fitting sphere for an aspheric surface are investigated. Stresses in the mirror are determined and checked to see that the chosen material has sufficient strength.