Variance of the Strehl Ratio of an Adaptive Optics System
AEROSPACE CORP EL SEGUNDO CA ENGINEERING AND TECHNOLOGY GROUP
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The variance sigmas2 of the Strehl ratio of a reasonably well-corrected adaptive optics system is derived as a power series in the log-amplitude variance sigmal2 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, sigmal21 of the incident optical field but only on the second power of the residual phase variance, sigmadelta phi22, of that field after adaptive optics correction, and on the first power of the product of the log-amplitude variance times the phase variance, sigmal2sigmadelta phi21. As long as the adaptive optics correction is good enough to ensure that the variance of the residual phase, sigmadelta phi2 is significantly less than unity, then even for fairly small values of the log-amplitude variance sigmal2 the value of the variance of the Strehl ratio, sigmas2, will be dominated by the value of the log-amplitude variance.