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.
© 1998 Optical Society of America
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(290.5930) Scattering : Scintillation
(350.5030) Other areas of optics : Phase
Harold T. Yura and David L. Fried, "Variance of the Strehl ratio of an adaptive optics system," J. Opt. Soc. Am. A 15, 2107-2110 (1998)