Design of tip-tilt and adaptive optics servos using measured angle of arrival and phase power spectra

The astronomical applicability of laser beacons depends critically on the ability to track on a faint object to less than the diffraction limit of the telescope (1,2) .Detailed measurements taken at Apache Point Observatory and a search of published of the literature shows that measured power spectrum are often very different from the theoretical predictions of Greenwood (3) and Tyler (4). This has important consequences and it is possible that the formula usually used to design the tip/tilt servos are in error, often by large factors, and that much wider band-widths are required both for the tip/tilt and higher order correction.