As seen in Fig. 2 (click here), in the cat's eye system the VCM is located
between the input and ouput beams of
the delay-line and its diameter is then limited by these two beams. The overall
diameter of the system cannot exceed 30 mm, and this fact led us to realize a
small mirror with a 16 mm diameter. Starting the curvature variation with a
plane mirror to achieve a maximal curvature of (84 mm)-1, this range
corresponds to an f ratio varying from to f/2.6 and the maximal
central flexion achieved is then 380
m.
Due to the large bending of the mirror, the full domain of curvature is not
achievable with a classical optical material as vitroceramic glass (Zerodur).
Metal alloys having 100 times higher flexibility than glasses, a stainless
steel substrate (AISI 420) has been chosen for this reason and for the fact
that deviations to Hooke's law (stress-strain relation) are small with such
materials.
The required pressure for the maximal deformation has to be easily achievable
with industrial components and this technical constraint led us to choose a very
thin meniscus for the active part of the mirror. As displayed in Fig. 4, with a
fixed material (i.e. E and fixed), in order to reduce the load necessary
to achieve a given deflection W0 we have to reduce the thickness
.
But the flexion ratio
increases so that it is not possible to obtain a
quasi-linear relation all along the variation range. A compromise between a small
load q and a linear load/curvature relation lead us to chose a meniscus
with a 300
m central thickness. With these conditions (
and
m) the maximal required load q is lower than 10 daN/cm2 when
84 mm and the maximal stress
reach 55 daN/ mm2 well
below the elastical limit strength of the material
daN/mm2.
Remembering the amplitude of the deformation achieved at the maximal curvature
(W0 = 380m), the reason why we developed the large deformations
theory of elasticity is obvious: The flexion ratio
is larger than 1.25,
very far from the 1/3 limit of the small deformations approximation.
The realization of the VCM uses an holosteric solution where the
edge of the central active meniscus is linked with an outer rigid ring via a
very thin collar having a 50m thickness (Fig. 5 (click here)), and an air pressure is
applied on the back side of the meniscus. This simplifies the mounting and avoids
air leak by having the mirror and its outer ring in the same sample.
Figure 5: Holosteric concept developed for the VCM