Limiting precision of tomographic phase estimation

In the context of multiconjugate adaptive optics, the optimum linear estima tion of a wave-front phase for a target object using the phases of several surrounding natural guide stars (NGS's) is studied. A Wiener-filter-type es timator is constructed. The minimum residual wave-front-phase (tomographic) error depends on the turbulence vertical profile, and for typical profiles it is almost insensitive to the presence of strong layers, contrary to cur rent belief Tomographic error is characterized by a new parameter SK, equiv alent profile thickness, which depends on the NGS number K (typically delta (5) = 0.5 km). The angular radius of the NGS configuration must not exceed r(0)/delta (K). Exact profile knowledge is not required. When the optimize d filters are constructed from some model profile, the loss of the field si ze is within 10% with respect to exact profile knowledge. Moreover, a metho d to measure turbulence profile using wave-front-sensor data is outlined. N oise propagation in the restoration algorithm is significant, but not drama tic. Noise increases with increasing size of NGS constellation. Practically , guide stars for tomography should be at least as bright as those for clas sical adaptive optics. (C) 2001 Optical Society of America.