Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars

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 θ_ipas 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 D_IPand is related to the height of the guided star z_gand the isoplanatic angle dip by D_IP= 2z_gθ_IP. 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 C_n2 model, an isoplanatic angle of D_IP= 1.64 arcsec (calculated for a value of r_o= 20 cm), and z_g= 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.