Performance of Keck Adaptive Optics with Sodium Laser Guide Stars

The Keck telescope adaptive optics system is designed to optimize performance in the 1 to 3 micron region of observation wavelengths (J, H, and K astronomical bands). The system uses a 349 degree of freedom deformable mirror, so that the interactuator spacing is 56 cm as mapped onto the 10 meter aperture. 56 cm is roughly equal to r0 at 1.4 microns, which implies the wavefront fitting error is 0.52 (λ/2π)(d/r0)5/6 = 118 nm rms. This is sufficient to produce a system Strehl of 0.74 at 1.4 microns if all other sources of error are negligible, which would be the case with a bright natural guidestar and very high control bandwidth. Other errors associated with the adaptive optics system will however contribute to Strehl degradation, namely, servo bandwidth error due to inability to reject all temporal frequencies of the aberrated wavefront, wavefront measurement error due to finite signal-to-noise ratio in the wavefront sensor, and, in the case of a laser guidestar, the so-called cone effect where rays from the guidestar beacon fail to sample some of the upper atmosphere turbulence. Cone effect is mitigated considerably by the use of the very high altitude sodium layer guidestar (90 km altitude), as opposed to Rayleigh beacons at 20 km. However, considering the Keck telescope’s large aperture, this is still the dominating wavefront error contributor in the current adaptive optics system design.