APPLICATIONS TO THE ADAPTIVE OPTICS

The characterization of the optical turbulence is fundamental to quantify the performances of adaptive optics systems (AO systems), i.e. those systems conceived to measure and correct the perturbations induced by the atmospheric turbulence on the wavefront coming from the space and arriving at the pupil of ground-based telescopes. The adaptive optics systems can not work under whatever seeing conditions and it is, therefore, important to know which is the typical temporal and spatial distribution of the turbulence developed above an astronomical site.

If extended site testing surveys of the integrated optical turbulence are fundamental to quantify the AO systems performances, for the most advanced systems, such as the Multi-Conjugated Adaptive Optics (MCAO) and Ground Layer Adaptive Optics (GLAO), the integrated turbulence budget is not sufficient to quantify their performances and a detailed turbulence vertical distribution measurement is mandatory.

For the Ground Layer Adaptive Optics (GLAO), a concept/system proposed in 2000 (Rigaut, 2000), that aims to correct the turbulence developed near the ground to obtain a uniform and homogeneous wavefront correction over a large field of view (of the order of, at least, a few arcminutes), it is extremely important to know the typical distribution of the optical turbulence developed in the first kilometer with high vertical resolution (up to a few tens of meters). The required vertical resolution depends on many parameters.  Among these: the field of view of the optical instrument, the pitch size of the actuators of the deformable mirror used to correct the perturbed wavefront and the wavelength. A GLAO system can correct the turbulence below a minimum threshold (Hmin) depending on the mirror pitch size ΔX and the field of view. It corrects partially the turbulence in the 'gray zone' (Hmin < h < Hmax) and it does not correct at all the turbulence above the threshold Hmax (Tokovinin 2004). Hmax depends on the selected field of view and the residual turbulence budget after the AO correction called r. Knowing how the turbulence is distributed above an astronomical site (CN2) and the turbulence budget (seeing), it is possible to retrieve the extent of the gray zone for each wavelength. The Laser Guide Star system of LBT (ARGOS) is conceived to work, in its baseline, with a GLAO configuration.

In a recent paper (Masciadri et al., 2010)  we summarized the results of the richest statistical analysis ever done so far above Mt. Graham for many among the most important parameters useful to charcaterize the AO systems: the seeing, the wavefront coherence time, the isoplanatic angle, ect....



Fig. 1:
(from Masciadri et al. 2010): Extent of the 'gray zone' i.e. Hmin< h < Hmax for different fields of view and wavelengths when one considers the median turbulence distribution (50%) (central columns of Table 6 and Table8 - Masciadri et al. 2010). Hmax (colored lines) is calculated for J=1.25 m (blue), H=1.64 m (red) and K=2.2 m (yellow) band. The pupil size D=8 m and the pitch size ΔX=0.5 m. The FWHM is equivalent to r, i.e the residual wavefromt coherence size after the adaptive optics correction.  For median turbulence conditions (see Table 1), the residual are resepctively, 0.13" in K band, 0.20" in H band and 0.30" in J band.





Table1:
(from Masciadri et al. 2010): Values of Hmax calculated for θ = 4 arcmin and different residual FWHM. The FWHM values  are obtained with the GLAO simulations (ARGOS PDR Report) using, as inputs, Table 6 and Table 8 (Masciadri et al. 2010).


It is worth noting that the Adaptive Optics systems evolved and experience showed that more and more sophisticated new methods/technics appeared in the last decades. As a consequence,  new parameters and function of merit have been introduced to characterize the performances of the new AO systems. An atmospherical model is an extremely useful tool of investigation because it can easily be adapted to quantify and characterize a new parameter without the necessity to conceive a dedicated instrument with precise technical specifications to measure it. Most of the parameters used at present in astronomy to characterize the optical turbulence and its effects on instrumentation have been implemented in the Meso-Nh Astro-Code.

GLAO performances: Dome C versus Mt. Graham (mid-latitude site)

The real challenge of Dome C for astronomical applications in the near-infrared range is the wide field because the optical turbulence is concentrated in a thin surface layer in this region. The wider the angle, the shorter is the depth of field on which the GLAO system can correct the turbulence efficiently. We can envisage two solutions to by pass the turbulence at Dome C:
(1) a telescope whose primary mirror is located above the surface layer (i.e. 50-60 m including the statistical dispersion).
(2) a telescope embedded in the strong surface turbulent layer equipped with a GLAO system conceived to correct the surface layer and for which the final performances should be better than what achievable at mid-latitudesites. But...Is there any turbulence or technical constraints in this second hypothesis ? The wavefront correction stops typically on a spatial scale roughly equivalent to the r0 for the wavelength we are considering and the correction performances strongly depends on the pitch size of the AO system. Fig.2 shows the results of simulations (Stoesz  et  al. 2008) obtained for a GLAO system conceived for a 8 m telescope equipped with 4 guide stars and different pitch size Δ X in J band (1.25 μ m). The vertical optical turbulence distrbution above Dome C is extracted from Trinquet  et  al. (2008) and above Mt. Graham is extracted from Masciadri  et  al. (2010). Mt. Graham is taken as representative of a mid-latitude site (in Masciadri et al. (2010) it has been shown that the turbulence characteristics above Mt. Graham are comparable with those of the best astronomical sites in the world). It can be observed that, with  Δ X = 0.5 m, the encircle energy (EE50) obtained above Dome C is larger that that achievable above Mt. Graham. To obtain a smaller EE50 we are forced to consider a smaller pitch size i.e. one has to consider a more sophisticated AO system that corrects higher orders of the wavefront perturbations (Fig.2 - left size).
For this set of simulations, Dome C provides better performances than Mt. Graham for  Δ X ≤ 0.38 m.

Conclusions: From a general point of view for small telescopes (2 m class telescopes) it is relatively easy to figure out a standard GLAO system with a reasonable number of actuators that fit the constraint of a small pitch size. For a larger telescope (8 m class telescopes or even more), on the contrary, we are forced to envisage a higher order AO system to be compettive with an equivalent facilities at a mid-latitude site.

Def: EE50 = angular size (arcsec) in which 50% of the PSF is included.

Fig. 2: (from Stoesz 2008): EE50 i.e. the angular size ("") in which 50% of the PSF is incldued versus the Field of View (FOV). Red lines: Mt. Graham. Blue lines: Dome C. Thick lines: median value, thin lines: first and third quartiles. Left: the pitch size Δ X = 0.1 m. Right: the pitch size Δ X = 0.5 m.

Acknowledgments:
This work is funded by the Marie Curie Excellence Grant ForOT - MEXT-CT-2005-02387
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  E.Masciadri, 11/2009