In the context of multiconjugate adaptive optics, the optimum linear estimation 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 estimator 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 current belief. Tomographic error is characterized by a new parameter δ<sub>K</sub>, equivalent profile thickness, which depends on the NGS number <i>K</i> (typically δ<sub>5</sub> = 0.5 km). The angular radius of the NGS configuration must not exceed r<sub>0</sub>/δ<sub>K</sub>. Exact profile knowledge is not required. When the optimized filters are constructed from some model profile, the loss of the field size is within 10% with respect to exact profile knowledge. Moreover, a method to measure turbulence profile using wave-front-sensor data is outlined. Noise propagation in the restoration algorithm is significant, but not dramatic. Noise increases with increasing size of NGS constellation. Practically, guide stars for tomography should be at least as bright as those for classical adaptive optics.
© 2001 Optical Society of America
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
Andrei Tokovinin and Elise Viard, "Limiting precision of tomographic phase estimation," J. Opt. Soc. Am. A 18, 873-882 (2001)