Decoupling control for position error and surface error of segmented primary mirror

Large-aperture segmented primary mirror has been widely used in high-resolution space telescopes. After deployment, position error and surface error of each segmented mirror will lead inacceptable wavefront errors together. A critical problem is how to decouple position error and surface error from exit-pupil wavefront aberrations. We proposed a decoupling control strategy based on sensitivity matrix retrieval method. The sensitivity matrix of segmented mirror is calculated by simulation method and a new type of orthogonal polynomials is recommended to fit wavefront aberrations in non-circular area. First we give a simulation example to show how to decouple position errors in each degree of freedom if there are no surface errors. Then a further simulation reveals the decoupling control process for position and surface errors. The low order aberrations are corrected by position control actuators and high order aberrations are corrected by figure control actuators.