The image quality is analyzed of an extraterrestrial object formed by astronomical optical system through the turbulent atmosphere. Relative increase the Strehl parameter is calculated under adaptive correction based on the laser guide star technique. The efficiency of adaptive correction of distortions for different type of the guide sources is compared. A special wave front sensor is applied, which operates using the broad laser beam as a reference wave. The calculations are performed for different models of the vertical variations of the structural parameter of the refractive index of the turbulent atmosphere. The wave front sensor was used, which enables to reconstruct the continuous phase of the reference wave. As the estimates show, the parameters of the formed field are quite close to that plane wave. So the higher correction and big increase of the Strehl parameter are obtained, that is indirect evidence of the good correction of the higher mode components, which are badly corrected using the traditional techniques for formation of LGS by means of a focused laser beam. As comparative calculations for different models of vertical variations of the structural parameter of the refractive index have shown, there are serious differences in the behaviors of the correlation radii for the plane and spherical waves.
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