The control method of Stretched Membrane with Electrostatic Curvature (SMEC) Mirror has advantages of simple structure and easy membrane mirror figure cybernation. Its principle is to make membrane mirror figure change with the sequence of electrostatic force to get the needed optical curvature figure. As for the complexion of membrane shaping mechanics and electrostatic field theory

there is no quantitative theory analysis in membrane shaping and mirror figure cybernation. In this article

the distribution characteristic of space electric potential is analyzed in theory

and the electrostatic force distribution is obtained by numerical calculation. Considering single electrode mode

after electrostatic force calculation with MATLAB

the membrane mirror figure is mainly inspected by finite element method. Then the analysis result of finite element method is compared with ideal paraboloid figure

the differences between them will perceptibly show that the surface shape control force in single electrode mode is simplex. To get flexible modulation

multi electrode mode control is an advisable option. It is also proposed that higher control precision can be acquired by using closed loop multi electrode control

which is instructive to the study of SMEC mirror.