Shape control of a flexible mirror using an electron gun.

Mirrors made of PVDF film are being considered for lightweight transportation and deployment in space. An array of electrodes can be used to distribute charges over the PVDF film for active shaping of the mirrors. This paper presents the derivation of a matrix that enables calculation of the shape of the two-dimensional mirror for any given electron distribution. Finite element simulation shows good agreement with a theoretical example. Furthermore, if a desired shape is given, the required voltage distribution can be computed using the singular value decomposition. Experiments were done in a vacuum vessel, where an electron gun was used to actuate a PVDF bimorph to a desired shape. Dynamic shape control is attainable at low frequencies. At higher frequencies, still significantly below structural resonance, actuation lag and parasitic DC offset can be significant problems that require future research to solve. NOMENCLATURE