A MEMS device having a deformable mirror. In a representative embodiment, the MEMS device includes a deformable membrane supporting a plurality of light-reflecting segments that form the deformable mirror. One or more actuators, at least one of which is configured to apply torque to a side of the membrane, are used to deform the membrane. Membrane deformation causes the segments to change orientation and thereby change the shape of the minor. A representative MEMS device of the invention enables segment displacements in two directions and thereby realizes effective mirror curvature values in the range from about -2 mm^-1 to about +2 mm^-1.