2 Atmospheric sodium properties relevant to LGS-AO

2.1 Introduction

Since the discovery of the presence of alkaline metals in atomic form at the altitude of the mesopause ([Slipher 1929]; [Bricard et al. 1949]), the origin and behaviour of this layer of atoms has been the subject of numerous experimental and theoretical researches; studies of the alkali metals, atmospheric sounding, studies of a meteoritic metallic layer at 100 km, radar and lidar studies of gravity waves, and, since the late 70's, studies of the sporadic sodium layers and measurements to explain the seasonal and meridional variations in the sodium layer height, thickness and density. Because of its relatively high concentration in meteors and its large resonant backscatter cross section, Na is the easiest metallic species and the easiest of the meteoric layer atoms to observe by resonance fluorescence lidar techniques ([Bowman et al. 1969]).

   
2.2 Long-term variations

All previous atmospheric studies have found that the mesospheric sodium column density has diurnal (e.g. [McNutt & Mack 1963]), nocturnal and seasonal variations (see e.g. Fig. 2 of [Papen et al. 1996]). Moreover, lidar measurements of the sodium column densities, performed since 1969 (see e.g. [Gibson & Sandford 1971]; [Simonich et al. 1979] for some of the first ones at different latitude) have confirmed the previous photometric measurements (e.g. [Donahue & Blamont 1961]; [Hunten et al. 1964]; [Rees et al. 1975]), which have shown that the sodium total abundance also presents seasonal variations dependent on the latitude (e.g. [Jegou 1985]). Once the necessary laser power has been determined from the Na column density seasonal minimum, these variations have little impact on LGS AO systems since in average over a year the sodium column density is, within a factor $\le$ 3 the same at all latitudes ($\approx$ 3 10⁹ cm^-2). The minimum in Na abundance around July in the northern hemisphere corresponds to a maximum in the southern hemisphere and inversely around January. This means that each observatory will have few months where LGS AO observations will be more performant than other months. Indeed the strongest the sodium abundance, the brightest the artificial star for a given laser power ([Milonni et al. 1998]), assuming there is no saturation at the sodium layer.

2.3 Short-term variations

2.3.1 Introduction

It has also been found, from the observations mentioned in 2.2, that both the averaged altitude of the mesospheric sodium varies as well as the column density ([Papen et al. 1996]). Some of these variations can be extremely quick due to the presence of sporadic layers, Na$_{\rm s}$ (see e.g [O'Sullivan et al. 2000]), which are very thin Na layers superposed on the mean mesospheric Na layers. They have been observed at several lidar sites, but there appears to be no significant seasonal difference in occurrence frequency or maximum sodium concentration. The formation mechanisms of these layers are not yet well-understood, but Na$_{\rm s}$ layers have always appeared to be strongly latitude-dependent phenomena, having been regularly observed at both low and high latitudes but not, until recently ([Nagasawa & Abo, 1995]), at mid-latitude sites (cf. [Clemesha et al.] 1980; [von Zahn et al. 1987]; [von Zahn & Hansen 1988]; [Gardner et al. 1988]; Kwon et al. 1988). Sporadics are characterised by a full-widths at half-maximum of typically 1 to 2 km. The ratio of maximum peak density of the sporadic layer to the density of the normal layer at the altitude of the peak sporadic layer density is typically from 3 to 5 and their values can be rarely as much as the order of 10. The events can last from a few tens of minutes to several hours. Figure 4 of [Gu et al. (1995)] is a very good illustration of observation of a sporadic event. In the late 70's, [Clemesha et al. (1978)] and [Clemesha et al.] (1980) were the first to report such observations at Sao Paulo, Brazil (23$^{\circ}$S, 46$^{\circ}$W). Later [Kwon et al.] (1988) found that most of the sporadics appearing above Mauna Kea (Hawaii) are located in the same two hours slot of Local Sideral Time (LST). The occurrence of sporadic layers of neutral sodium and other metals at heights around 100 km, with thickness much less than the atmospheric scale height, is an interesting and puzzling phenomenon, which has been nicely reviewed by [Clemesha (1995)].

2.3.2 Influence of sporadic layers on LGS operation

The recognition of Na$_{\rm s}$ layers is crucial for LGS-AO operation, because they cause rapid local increase in the column density and an associated displacement of the altitude's centroid of the whole layer (see e.g. Fig. 4 of [Beatty et al.] 1989). The effective Na layer altitude (the centroid height) moves first upwards as the sporadic layer appears and then downwards (see e.g. Fig. 2 of [Senft et al. 1989]). This produces a rapid focus shift for the LGS on a time scale of a few seconds to several minutes. The largest centroid variation observed in Fig. 4 of [Beatty et al.] (1989) produces a change of the order of 250 m in 30 s. For the VLT this would mean a wavefront error of $\sigma \sim$ 39 nm rms, exceeding the NAOS (Natural guide star Adaptive Optics System - the AO system for the VLT telescopes) mean error budget, of 15 nm rms. This also corresponds to an equivalent phase variance of 0.06 rad² at 1 $\mu$m due to defocus, which is e.g. perfectly acceptable for the VLT AO system, i.e. largely within the error bars. Although not critical to most AO LGS operation, this effect has to be taken into account in the overall error budget.

A change in the Na-layer centroid height during the astronomical exposure is seen by the AO wavefront sensor, observing the LGS, as a defocus component in the atmospheric wavefront analysis and is automatically corrected by the AO deformable mirror, partially defocussing the object at infinity. A proposed way to solve this problem is to remember that atmospheric perturbations measured in Adaptive Optics average over a time period of about 1 min to zero ([Hubin & Noethe 1991]). Using this characteristic, we propose to store the overall defocus (atmospheric + sodium layer centroid height) obtained on the LGS wavefront sensor for the deformable mirror control and to average it out over a period of 1 min. After averaging, the sole defocus produced by the sodium profile variation remains and can be corrected by defocusing the LGS wavefront sensor. This method works only if variations of the sodium profile can be neglected under 1 min, which has not been proven yet.