Imaging performance analysis of adaptive optical telescopes using laser guide stars.

The use of laser guide stars in conjunction with adaptive optical telescopes offers the possibility of nearly diffraction-limited imaging performance from large, ground-based telescopes. We investigate the expected imaging performance of an adaptive telescope, using laser guide stars created in the mesospheric sodium (Na) layer. A 2-3-m class telescope is analyzed for the case of a single, on-axis guide star at an altitude of 92 km (the nominal height of the mesospheric Na layer). We analyze an annular telescope pupil with approximately 15 wave-front sensor subapertures and mirror actuators spanning the pupil diameter. The imaging performance is quantified in terms of the pupil-averaged rms wave-front error, the optical transfer function, the point spread function, the Strehl ratio, and finally the angular resolution. The performance analysis takes into account the degradation caused by the limitation of the wave-front sensor as well as the deformable mirror. These limitations include the finite spacing and size of the wave-front sensor subapertures and the spacing and influence function of the mirror actuators. The effects of anisoplanatism and shot noise are also included in the analysis. The results of the investigation indicate that a 3-m adaptive telescope using a single Na guide star is capable of achieving a Strehl ratio of 0.57 and an angular resolution nearly matching that of diffraction-limited performance (0.05 arcsec). This performance is achieved assuming that r(0) = 20 cm and a 5-W laser is used to create the guide star. The effect of variations in seeing conditions and guide star brightness is also investigated.