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Statistical moments of the Strehl ratio

: Yaitskova, Natalia; Esselborn, Michael; Gladysz, Szymon


Ellerbroek, Brent L. ; American Astronomical Society -AAS-; Society of Photo-Optical Instrumentation Engineers -SPIE-, Bellingham/Wash.:
Adaptive optics systems III. Pt.4 : 1 - 6 July 2012, Amsterdam, Netherlands; part of SPIE astronomical instrumentation
Bellingham, WA: SPIE, 2012 (Proceedings of SPIE 8447)
ISBN: 978-0-8194-9148-0
Paper 84475Y
Conference "Adaptive Optics Systems" <3, 2012, Amsterdam>
Conference Paper
Fraunhofer IOSB ()
Strehl ratio; adaptive optics; speckle

Knowledge of the statistical characteristics of the Strehl ratio is essential for the performance assessment of the existing and future adaptive optics systems. For full assessment not only the mean value of the Strehl ratio but also higher statistical moments are important. Variance is related to the stability of an image and skewness reflects the chance to have in a set of short exposure images more or less images with the quality exceeding the mean. Skewness is a central parameter in the domain of lucky imaging. We present a rigorous theory for the calculation of the mean value, the variance and the skewness of the Strehl ratio. In our approach we represent the residual wavefront as being formed by independent cells. The level of the adaptive optics correction defines the number of the cells and the variance of the cells, which are the two main parameters of our theory. The deliverables are the values of the three moments as the functions of the correction level. We make no further assumptions except for the statistical independence of the cells.