Effect of hysteresis on the performance of deformable mirrors and methods of its compensation

The bandwidth of a servo controlling a deformable mirror should be determined by the time delays introduced by integration, read out, and analysis of the signals recorded by the wavefront detector. However, many types of piezoelectric actuators used in the construction of deformable mirrors exhibit considerable hysteresis which destabilizes the servo and requires a reduction in the stable system bandwidth. The effect of various degrees of hysteresis on the overall servo performance will be discussed together with methods of its compensation. These methods include `passive correction,' in which the effect of hysteresis is modeled by the servo system and `active correction,' in which the shape of the mirror is continuously measured with a wide bandwidth servo and is used as the error signal. We discuss both types of correction and present experimental results.