Optical performance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstructors

Abstract

Adaptive optics systems have been proposed as a means of compensating for the effects of atmospheric turbulence on optical imaging systems. Many previously studied adaptive optics systems process measurements acquired from slope sensors to generate commands for the actuators in a deformable mirror. The act of generating actuator commands is referred to as reconstruction. Two types of phase reconstructor have been proposed for use in such systems: (1) the least squares reconstructor; and (2) the minimum variance reconstructor. The mean square phase error performance of these two reconstructors has been previously analyzed. However, the impact of the choice of reconstructor on the average optical transfer function and image signal-to-noise ratio in the spatial frequency domain have not been addressed. In this paper the optical performance of the two reconstructors is explored using the single frame signal-to-noise ratio as a function of spatial frequency as a comparative performance measure. The average optical transfer function and the second moment of the optical transfer function are computed. Performance is analyzed for fully and partially compensated systems. It is shown through theoretical calculations and simulation that the minimum variance reconstructor provides superior performance.