This paper analyzes the efficiency of the mode shapes used to describe the displacements of the reflective surface of controllable mirrors in active optical systems. A new method is proposed for determining the orthogonal eigenshapes of the quasi-steady-state deformation of an active mirror with local-force control. This method is used to carry out modal analysis of a mirror simulator that has the same geometrical shape and the same elastic properties as the controllable mirror but possesses zero density, except for concentrated unit masses attached at the sites where the actuators act and taken into account only in the direction of application of the forces or displacements that deform the mirror. It is shown that the use of the eigenshapes obtained by means of a mirror simulator requires less energy and consequently smaller forces by the actuators than when the shapes obtained by singular decomposition are used. (c) 2018 Optical Society of America.
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