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5. Curvature control

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 10tex2html_wrap_inline1167 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 tex2html_wrap_inline1171 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 60tex2html_wrap_inline1029m, compared with the experiment, for one of the samples (#5) having a central thickness of 237tex2html_wrap_inline1029m and a 50tex2html_wrap_inline1029m 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.

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Figure 7: Semi-clamped edge pressure law calculated for the mirror #5

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Figure 8: Experimental pressure law compared with different collar thickness theoretical cases


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