Performance analysis of adaptive-optics systems using laser guide stars and slope sensors

Many current wave-front-reconstruction systems use localized phase-slope measurements to estimate wave fronts distorted by atmospheric turbulence. Analytical expressions giving the performance of this class of adaptive-optics system are derived. Performance measures include the mean-square residual phase error across the aperture, the optical transfer function, the point-spread function, and the Strehl ratio. Numerical examples show that the mean-square residual error and the Strehl ratio are sensitive to variations of the photon noise in the wave-front sensor and to variations in the sensor spacing and the actuator spacing. The Strehl ratio degrades rapidly as the diameters of the individual slope sensors are made larger than the Fried seeing-cell diameter ro and when the sensor signal levels fall below 100 counts per slope measurement. On the other hand, the resolution of the optical system is relatively unaffected by moderate changes in the photon noise or the densities of sensors and actuators. The diameter of the individual slope sensors can be as much as 1.5 times r₀ without significant degradation in angular resolution. These performance measures are particularly important in the design of adaptive telescopes used for imaging in astronomy. For adaptive telescopes using laser guide stars, these measures can be used to determine the key design parameters for the laser.