The laser power requirement for an adaptive-astronomical telescope using laser guide stars is determined largely by the effects of turbulence-induced anisoplanatism. Owing to the relatively low altitude of laser guide stars and the small size of the isoplanatic angle at visible wavelengths, multiple guide stars are required for correcting large telescope apertures. The laser power requirements are proportional to the required number of guide stars. Using an analysis technique that takes into account the realistic characteristics of the wave-front sensor and deformable mirror, as well as the spherical nature of the wave front from the laser guide star, we present computational results that show how the imaging performance of a laser-guided adaptive telescope varies as a function of the number and height of the guide stars. The results are presented as a function of the isoplanatic angle θIP as defined by Fried [ J. Opt. Soc. Am. 72, 52 ( 1982)]. A new parameter, the characteristic diameter of the largest telescope requiring a single guide star, is also introduced. This parameter is designated DIP and is related to the height of the guided star zg and the isoplanatic angle θIP by DIP = 2zgθIP. The effects of anisoplanatism on the design of a 2-m-diameter adaptive telescope using laser guide stars created in the mesospheric Na layer is considered. Using a Hufnagel Cn2 model, an isoplanatic angle of θIP = 1.64 arcsec (calculated for a value of ro = 20 cm), and zg = 92 km (the nominal height of the mesospheric Na layer), we find that three Na guide stars are required in order to achieve a rms wave-front error of approximately λ/10 across the telescope aperture.
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