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

Abstract

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.

A large‐aperture sodium fluorescence lidar with very high resolution for mesopause dynamics and adaptive optics studies

“…In this way, near‐diffraction‐limited resolution and high sensitivity are achieved. However, the vertical extent of the sodium layer, and its varying internal structure, creates errors that increase with telescope aperture [ Herriot et al , 2006]. The performance of the system depends on the sodium mean‐altitude power spectrum at high frequencies.…”

Review of astronomical adaptive optics systems and plans

“…This problem can also be solved by dynamic refocusing if the laser is pulsed. 13 • Variations in the intensity of the photon return from the sodium layer occur due to variations in the concentration of sodium ions in the layer. There are seasonal variations which vary in amplitude from one geographical location to another, with minimum in winter as well as rapid variations, referred to as 'sporadic events'.…”

Sky coverage and tip/tilt error analysis for TMT

“…The calculation of the error in tracking the mean altitude of the sodium layer is presented in Ref. 20. This focus error calculation is made by extrapolating a power spectrum of height variations from Lidar data, and applying the rejection transfer function for using electronic offsets, which will correct for the focus of the LGS WFSs in real-time.…”