Abstract

The optimum feedback matrix for a general segmented mirror adaptive optics system is derived assuming the use of two different wavefront sensors. The system is assumed to be used as an imaging telescope encountering wavefront degradations due to both propagation through a turbulent atmosphere and mirror figure errors such as segment misalignment. The first study is for a sensor that measures the average wavefront gradient over each segment, as a Hartmann sensor might do. The second case assumes that the instantaneous phase derivatives in the x and y directions are measured at an array of discrete locations over the mirror aperture. A shearing interferometer wavefront sensor could provide this type of data. In both cases a feedback matrix is derived that converts the measured data into linear displacements for the actuators positioned on the back of the segments. The feedback matrix derived is optimum in the sense that the mean residual wavefront variance is minimized. This optimization assumes knowledge of the statistics of the atmospherically induced aberrations, the mirror figure errors, and the wavefront sensor errors.

© 1988 Optical Society of America