Application of generalized least squares method in the calibration of active optics mode

In order to relieve the coupling effect of 4 m lightweight mirror support system, a generalized least square method was proposed to calibrate active optics. Firstly, the support system of 4 m lightweight mirror was introduced, and the constraints needed to meet in hydraulic Whiffletree passive support system was deduced. Then the Zernike polynomial corrected by node area weighted factor was used to fit the mirror deformation, resulting to influence matrix between Zernike coefficients of mirror deformation and active forces. After that, a generalized least squares method was adopted to obtain the optimal correction forces which simultaneously satisfied the equality and inequality constraints. Finally, the proposed method was applied to the calculation of the optimal active forces to correct the mirror deformation caused by the gravity, and the influence of different damping factors on the calculation results were analyzed. Results show that the optimal correction effect is achieved when the damping factor is 7.4e-9, and the RMS of the mirror deformation is changed from the original 271.5 nm to 8.3 nm after correction, verifying the feasibility of the generalized least squares method to the calibration of the 4 m lightweight mirror active optics.