Comparison of tip-tilt controllers using the STRAP wavefront sensor in the W.M. Keck Observatory laser guide star adaptive optics system

The W. M. Keck Observatory adaptive optics (AO) system uses the STRAP wavefront sensor to sense tip-tilt using a natural guidestar. The higher-order wavefront sensing can be done using light from either a laser guidestar (LGS) or a natural guidestar (NGS). The tip-tilt guidestar can be as bright as 10th or as faint as 19th magnitude. In both cases, as high a control bandwidth as possible is desired. Thus, it is of interest to determine the potential of various control algorithms over a wide range of signal-to-noise ratios (SNRs). This paper compares two control algorithms using a set of tip-tilt data taken with the STRAP wavefront sensor (a set of four avalanche diodes arranged as a quad cell). The two algorithms are the standard integral control and a minimum variance (LQG) control designed using the power spectral density (PSD) of the data. The bandwidths of the integral control and the minimum variance control are adjusted to produce the least RMS residual wavefront error. The controllers are compared for SNRs representative of the expected range of guidestars.