| The membrane mirror technology which break constraints of the traditional telescope manufacture technology , is one of the novel technologies for the manufacture of large aperture, ultra-lightweight telescopes. The membrane mirror used as a primary mirror has characters of a low areal density, compact-deployable and low cost. The membrane mirror technology has become a hot spot of research on the space telescope system.This paper mainly do the research on the mechanism and experiment of the figuration of membrane mirror on substrate of flexible membrane film with large deformation. The main contents are as follows.Firstly, the research background of the membrane mirror technology is introduced. The development and present research situation of membrane mirror figuration and control methods in domestic and foreign are summarized.Then, based on Karman's equation for symmetrical circular membrane and Qian's theory of circular membrane under the action of uniformly distributed loads in its central portion, a theoretical study on the mechanism of the figuration of membrane mirror on a substrate of flexible membrane film with large deformation is carried out. An equation of displacement on every point on a membrane under an outer load is established. The relationship between the curvature of center cross section of the membrane mirror on polyethylene terephthalate (PET) membrane substrate and the pressure load , and the deviation between the surface shape of the membrane mirror and that of an parabolic mirror with the same diameter and F number are calculated. The changes of the membrane mirror figuration under various initial boundary conditions and various load added on it are analyzed theoretically.Finally, a figuration experiment system of membrane mirror with 100mm in diameter and 780mm in focal length has been designed in this paper The experiment adopt the pre-shaped method, atmospheric pressure, and electrostatic field to control the figuration of surface shape of the membrane mirror. The focal lengths of the membrane mirror under different initial boundary condition, atmospheric pressure and electrostatic field have been measured with a collimated narrow-beam. The relationship between the focal length and electrostatic filed in the condition of different atmospheric pressure has been got on the experiment. The focal lengths of the membrane mirror measured in experiment and that of the theory calculation are compared and analyzed. The feasibility of the experiment system and methods has been verified by the result above. This paper provides the further research on methods in the figuration on large aperture, ultra-lightweight membrane mirror with the necessary theoretical and experimental basis.
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