The problem of supporting an optical element in a l-g force field on a multi-level kinematic mount arises, when a single level 3-point kinematic mount is inadequate for keeping the stress and/or surface deflection within specified design limits. In this paper, a solution of the biharmonic differential equation for the bending of a flat thin circular plate is first derived for m-point (m > 2) supports, equi-spaced on a concentric circle, and then applied to the problem of a two-level kinematic mount, which is also known as a 9-point Hindle mount. From this, normalized design curves are developed for determining nominal locations of the nine support points, associated RMS deflections and support location sensitivity. These design curves provide the practicing engineer with a useful, efficient and accurate means for developing a preliminary Hindle mount design without resorting to FEM analysis. Several cases of the 9-point Hindle mount solution were compared with independent NASTRAN based finite element solutions. Excellent correlation between the two was obtained in all cases. The methodology used in this paper is not limited to flat optical elements. The solution of the problem of curved optical elements on a 9-point Hindle mount in a l-g force field can be similarly obtained by the same approach with E. Reissner's thin shallow spherical shell equations.

Date Published: 5 January 1984
PDF: 13 pages
Proc. SPIE 0450, Structural Mechanics of Optical Systems I, (5 January 1984); doi: 10.1117/12.939275

Published in SPIE Proceedings Vol. 0450:
Structural Mechanics of Optical Systems I
Lester M. Cohen, Editor(s)