Anisoplanatism in Adaptive Optics Compensation of a Focused Beam Using Distributed Beacons

In systems that achieve laser beam propagation through atmospheric turbulence by phase compensation with adaptive optics, the performance depends on the beacon’s spatial distribution. A formulation is obtained to calculate the anisoplanatic Strehl ratio of a phase compensated, focused beam for any beacon distribution and turbulence profile. Analytic results are obtained for several beacon geometries corresponding to practical systems, in the large aperture limit. The effects of finite aperture are evaluated for two representative beacon geometries, using both uniform and highly localized turbulence profiles. The spread of the beacon distribution is found to be much less deleterious than the offset of the beacon centroid from the aimpoint. The anisoplanatic effect is qualitatively different in systems characterized by a focused beam geometry and systems where the collimated beam geometry applies.