| The membrane mirror which is made of flexible polymer membrane as the substrate is figured to the desired profile by applying proper methods. It is characterized by ultra-lightweight, compact-deployable and low cost. The membrane mirror used as the primary mirror of space-born telescope is one of the most novel technologies for the manufacture of large aperture, ultra-lightweight space-borne optical systems in future.The membrane mirror figured by electrostatic field is one of the most promising methods to control the membrane mirror profile. The method is firstly researched by this dissertation at home, and it is expected to lay necessary theoretical and experimental groundwork for the further research on the electrostatically figured membrane mirrors with large apertures.Contents in this dissertation are as follows.The research meaning and research progress of the membrane mirror is introduced firstly. The theoretical model of the electrostatically figured membrane mirror is established based on the elastic mechanics and electrostatic theories. The Possion equation used to describe the profile of the membrane mirrors is obtained and is solved with the boundary condition and the symmetry of the structure. The profile of the membrane mirror figured by an electrostatic field is simulated with Matlab, and the relationship between the profile of the membrane mirrors and the voltage is analyzed.A system for the electrostatic figuration of membrane mirrors of 200mm in diameter is designed. It consists of a membrane structure, a set of electrode pad and a high direct current (DC) voltage system. The fixation structure, the arrangement and the size of the electrodes are chosen to satisfy the desire of uniform tension in the membrane and to ensure the coverage of the electrostatic force on the membrane. The high direct current (DC) voltage system consisted of the basic bias voltage control system and the adjustable bias voltage control system consisted of is designed and analyzed in detail.
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