Optimum Distribution and Tolerance of Axial Point Supports for Structured Telescope Mirrors

Gravity will produce non-negligible deformation in large mirrors when it is acting in the direction of optical axis. An optimum support pattern can be found to minimize the self weight deformation. The approach of this problem provided the support pattern has adequate symmetry can be obtained from the solution of Nelson and Lubliner1 in which the mirror is assumed as a thin circular flat disk. For mirrors with internal honeycomb structure the support points are constrained by the symmetry of structure and cannot be placed in rings, as is usual for large mirrors. Given a particular structure alternative symmetrical placements of the supports were explored, and solutions obtained for the fraction of weight supported by each point to get the minimum deformation. Figure 1 shows the deformation of an optimum supported honeycomb mirror with the rib pattern shown by Angel and Woolf2. The support efficiency is 2.07 × 10−7 which is close to an ideal triangular grid with the same number of support points. Scaled to an 8-m diameter and 60 cm thickness disk it corresponds to surface rms deviation of .006μm. To study the force tolerance we choose errors of the force at each support point according to a Gaussian distribution function. Figure 2 shows the deformation of this kind of support in which the standard deviation is 0.055% of the nominal force. The support efficiency degrades to 5.08 × 10−7 in this case. For comparison, Figure 1 and Figure 2 have the same gray level.