 
Summary: Influence functions of a
thin shallow meniscusshaped mirror
Luc Arnold
Thin shallow spherical shell theory is used to derive the general influence function, owing to uniform
and or discrete actuators loads, for a thin shallow meniscusshaped mirror of uniform thickness with
a central hole and supported at discrete points. Small elastic deformations are considered. No sym
metry on the load distribution constrains the model. Explicit analytical expressions of the set of
equations are given for calculating the influence functions. Results agree with the finite element
analysis FEA to within 1%. When the FEA requires megabytes of RAM memory, the analytical method
needs only kilobytes and typically runs 30 times faster. This is a crucial advantage for the iterative
optimization of mirror supports such as large passive or active meniscusshaped primary mirror supports
or Cassegrain Gregorian adaptive secondary actuator configurations. References are given on estimat
ing the shear effects thick mirror , the thickness variation effect, and the influence of the size of the
support pads. © 1997 Optical Society of America
Key words: Telescope mirrors, mirror deformations, active optics, influence functions, meniscus
shaped mirrors.
1. Introduction
The finite element analysis1 FEA is the classic nu
merical method used to calculate the deformations of
telescope mirrors, i.e., the influence functions IF's ,
