Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope

Laser guide star (LGS) adaptive optics systems for extremely large telescopes must handle an important effect that is negligible for current generation telescopes. Wavefront errors, due to improperly focusing laser wavefront sensors (WFS) on the mesospheric sodium layer, are proportional to the square of the telescope diameter. The sodium layer, whose mean altitude is approximately 90 km, can move vertically at rates of up to a few metres per second; a few seconds lag in refocusing can substantially degrade delivered image quality (15 m of defocus can cause 120 nm residual wavefront error on a 30-m telescope.) As well, the range of temporal frequencies of sodium altitude focus, overlaps the temporal frequencies of focus caused by atmospheric turbulence. Only natural star wavefront sensors can disentangle this degeneracy. However, applying corrections with representative focus mechanisms having modest control bandwidths causes appreciable tracking errors. In principle, electronic offsets measured by natural guide star detectors could be rapidly applied to laser WFS measurements, but to provide useable sky coverage, integrating sufficient photons causes an unavoidable time delay, again resulting in potentially serious focus tracking errors. However, our analysis depends on extrapolating to temporal frequencies greater than 1 Hz from power spectra of sodium profile time series taken at 1-2 minute intervals. In principle, with a pulsed laser, (e.g. 3-μs pulses) and dynamic refocusing on a polar-coordinate CCD, this focus tracking error may be eliminated. This result is an additional benefit of dynamic refocusing beyond the commonly recognized amelioration of LGS WFS spot elongation