The other important point related to the achievement of a coherent field at
the combined focus, is the adjustement of a precise curvature during the
operation of the VCMs. To evaluate this accuracy, we made multiple
scans on the whole curvature range from which we calculated the mean
curvatures achieved and deviations to them. This calibration is crucial
for the monitoring of the VCM curvature under an open-loop control.
The resulting error on the curvatures is less than 5 10
which is the limit value accepted by ESO in the control curvature accuracy
requirement. This result proves that the Pressure/Curvature relation
is a tight one and permits to achieve a precise curvature with a high
accuracy. The set of mean curvatures is used to modelize a
Pressure/Curvature relation, using a Lagrange interpolation, which is included in
the pressure monitoring software. As the relation depends of the active
meniscus and the collar thicknesses, this calibration has to be done for
each mirror because of small variation among the samples.
In the same time, we included the "semi-clamped edge'' effect in the relation
Load/Curvature displayed in Fig. 4 (click here). Where, in the free-edge case,
a pressure P0 is needed to achieve a given curvature, then a pressure
is necessary for a meniscus having a central thickness
t and a collar thickness c in the semi-clamped case. The Fig. 7 (click here)
presents
this new relation for various collar thicknesses from a 0 (free-edge) to 60
m,
compared with the experiment, for one of the samples (#5) having a central
thickness of 237
m and a 50
m collar thickness. The good agreement
with the theoritical predictions (Fig. 8 (click here)),
also verified with other samples,
proves that the effect added by the collar rigidity has been properly analysed
and included in the numerical simulation which is now accurate.
Figure 7: Semi-clamped edge pressure law calculated for the mirror
#5
Figure 8: Experimental pressure law compared with different collar
thickness theoretical cases