The deflection of a circular parabolic telescope mirror on an elastic foundation

In this article we describe the deflection due to gravity of a parabolic mirror, supported by an annular shaped elastic foundation. We calculate the deflection by solving the thin plate equation for plates with a non-constant thickness numerically. It will be shown that a central hole in the elastic foundation of a certain diameter will minimize the deflection of the mirror and will result in minimal RMS values. We compare the mirror deflection caused by 18 and 27 axial point support to the deflection of a mirror on an annular shaped elastic foundation. It will be shown that an annular shaped elastic foundation results is much less deflection and smaller RMS values compared to the multiple point axial support for mirrors smaller than 1 m diameter and F# ratios larger than 2. Using this foundation method, mirrors may become thinner which results in lightweight constructions.