Statistical properties of the Strehl ratio as a function of pupil diameter and level of adaptive optics correction following atmospheric propagation.

The propagation of an optical beam through atmospheric turbulence produces wave-front aberrations that can reduce the power incident on an illuminated target or degrade the image of a distant target. The purpose of the work described here was to determine by computer simulation the statistical properties of the normalized on-axis intensity--defined as (D/r0)2 SR--as a function of D/r0 and the level of adaptive optics (AO) correction, where D is the telescope diameter, r0 is the Fried coherence diameter, and SR is the Strehl ratio. Plots were generated of (D/r0)2 (SR) and sigmaSR/(SR), where (SR) and sigma(SR) are the mean and standard deviation, respectively, of the SR versus D/r0 for a wide range of both modal and zonal AO correction. The level of modal correction was characterized by the number of Zernike radial modes that were corrected. The amount of zonal AO correction was quantified by the number of actuators on the deformable mirror and the resolution of the Hartmann wave-front sensor. These results can be used to determine the optimum telescope diameter, in units of r0, as a function of the AO design. For the zonal AO model, we found that maximum on-axis intensity was achieved when the telescope diameter was sized so that the actuator spacing was equal to approximately 2r0. For modal correction, we found that the optimum value of D/r0 (maximum mean on-axis intensity) was equal to 1.79Nr + 2.86, where Nr is the highest Zernike radial mode corrected.