Influence of axial-force errors on the deformation of the 4  m lightweight mirror and its correction

The lightweight primary mirror of the four meter Chinese telescope is supported axially by a passive hydraulic system, in parallel with an active system. The figure is sensitive to the errors in the axial forces, which can be effectively corrected using active optics. The squared RMS of this figure approximately follows the χ² distribution, as verified by Monte Carlo analysis. The probability distributions of the squared norm of the active-forces vector, of the squared norm of the leg-lengths vector in the hexapod platform, and of the squared RMS of the residual figure are discussed in terms of the bending modes obtained by singular-value decomposition of the influence matrix, the optical sensitivity matrix deduced through ray trace, and the Jacobian matrix of the hexapod platform. The results show that, within the 90% confidence interval, the RMS of the figure caused by the axial-force errors is less than 232.38 nm and is corrected to less than 3.26 nm by the active optics. The maximum values of the corresponding squared norms of the active-force vector and of the leg-lengths vector are deduced.