Variance of the Strehl ratio of an adaptive optics system

Abstract

The variance σS2 of the Strehl ratio of a reasonably well-corrected adaptive optics system is derived as a power series in the log-amplitude variance σl2 and the residual phase error variance σδϕ2. It is shown that, to leading order, the variance of the Strehl ratio is dependent on the first power of the log-amplitude variance, (σl2)1, of the incident optical field but only on the second power of the residual phase variance, (σδϕ2)2, of that field after adaptive optics correction, and on the first power of the product of the log-amplitude variance times the phase variance, (σl2σδϕ2)1. As long as the adaptive optics correction is good enough to ensure that the variance of the residual phase, σδϕ2, is significantly less than unity, then even for fairly small values of the log-amplitude variance σl2, the value of the variance of the Strehl ratio, σS2, will be dominated by the value of the log-amplitude variance.