an annular force mechanism and a control circuit is developed to compensate the sphere error brought by thermal deformation of a laser mirror. Under the effect of two coaxial annular forces with different radii
the circular mirror produces parabolic deformation in the inner region
which can compensate the sphere error brought by the thermal deformation of the mirror. The finite element method is used to analyze the mirror and the relation among the center displacement with energy absorbance and the force is derived. The experiments of force-deformation and energy absorbance-force-deformation are conducted for a flat mirror with the diameter of 100 mm and the thickness of 8 mm
in which a interferometer is used to monitor the surface deformation. Obtained results show that under different forces
the deformation of effective region always maintains a parabolic shape. Furthermore
the force-deformation curve is obtained
which shows that the centre displacement is over 3 m under 225 N.Under different energy absorbances
the central displacement of the mirror varies with the force in linearity and the coefficient of force-centre displacement is 0.013 m/N.
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