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