1 Introduction

The method described in this paper for remote turbulence profiling is based upon the SCIntillation Detection And Ranging (SCIDAR) technique which relies upon the analysis of crossed beam (i.e. binary star) scintillation patterns. This technique has been developed by Vernin and co-workers over a number of years (Vernin & Roddier 1973; Rocca et al. 1974; Vernin & Roddier 1975; Roddier & Vernin 1977; Azouit et al. 1978; Vernin et al. 1979; Azouit & Vernin 1980; Vernin & Azouit 1983; Vernin et al. 1991) and more recently by Tyler (1992). A number of specific site investigations have been attempted using either SCIDAR alone (e.g. Racine & Ellerbroek 1995) or in combination with temperature and pressure data obtained using balloon-borne instrumentation (Vernin et al. 1990; Vernin & Muñoz-Tuñôn 1992, 1994). A number of spatial filtering techniques applied to scintillation signal detection from single stars have also been proposed for this particular problem (e.g. Ochs et al. 1976; Churnside et al. 1988; Zavorotny 1992). However, although the performance of SCIDAR is constrained by the availability of suitable binary star objects, one is able to obtain reliable profiles of a finer altitude sampling than that possible using spatial filtering methods on single stars.

With SCIDAR the strength of scintillation is used to estimate both the value of the atmospheric optical turbulence profile, C_n²(h), and the turbulence velocity, V(h), as a function of height, h, using a triangulation technique. The methodology used here involves recording a large number of instantaneous scintillation patterns from a double star, calculating the average spatial and temporal correlation, and extracting the C_n²(h) profile using an integral inversion method and the V(h) profile using template correlation.

Until very recently it was expected that such a method would be unable to characterise low altitude (< 5 km) turbulence, thus requiring other techniques to be used in unison with SCIDAR to complete the profile information. However, as discussed later, the introduction of the concept of generalised SCIDAR by Fuchs et al. (1994), has shown that a simple modification of the basic SCIDAR method can allow this information to be recovered without this requirement, and here we show example results from our generalised SCIDAR experiments at various observing sites.

Although the profiling of optical turbulence and velocity is of great intrinsic interest in terms of atmospheric science, the main impetus for these experiments has been to obtain real C_n²(h) and V(h) data for our theoretical work in the study of adaptive optics (AO) systems for astronomy.

The main concern of optimising traditional astronomical observations at a particular observing site has been with respect to the angular extent of the seeing disc observed at ground level, $\Phi$, which can be expressed simply as,

$$\Phi \sim \lambda/r_{0}$$ (1)

where r₀ is the turbulence coherence length given by,

$$r_{0} = \left[ 0.42 k^2 \cos^{-1}(z) \int C_n^2(h) {\rm d}h \right]^{-3/5},$$ (2)

k is the wavenumber and z is the zenith angle of observation. Since $\Phi$ can be measured directly using long exposure imaging or indirectly using differential image motion (DIMM) methods (Martin 1987), explicit knowledge of the C_n²(h) profile itself is unnecessary for this purpose. However, in the design of an AO system for a particular astronomical observing site, not only does one require some knowledge of the statistics of the size of the seeing disc, but also that of the turbulence and velocity profile with height so that one may have some expectation of the detrimental effects of anisoplanatism. For example, for Angular Anisoplanatism (AA), the decorrelation with angle $\phi$ between the science object wavefront and the measured wavefront can be quantified in terms of the mean squared error between the two wavefronts, such that

$${\sigma}_{\rm AA}^2 = (\phi/\phi_{0})^{5/3}$$ (3)

where $\phi_{0}$, the isoplanatic angle, is given by,

$$\phi_{0} = \left[ 2.9 k^2 \cos^{-1}(z) \int C_n^2(h) {h}^{5/3} {\rm d}h \right]^{- 3/5}.$$ (4)

Similarly, for an AO system guided by an artificially produced laser beacon, the decorrelation between the science object wavefront and the wavefront sampled by the beacon which leads to Focal Anisoplanatism (FA), can also be quantified in terms of C_n²(h) such that the mean squared error between the two wavefronts is given by,

$${\sigma}_{\rm FA}^2 = (D/d_{0})^{5/3}$$ (5)

where D is the telescope diameter and d₀ can be interpreted as an measure of the effective diameter of the AO imaging system when a single laser beacon is being used and can be approximated as,

$$d_{0} \simeq \left[ k^2 \cos^{-1}(z) \int_{0}^{H} C_n^2(h) {(h/H)}^{5/3} {\rm d}h \right]^{- 3/5},$$ (6)

where H is the laser beacon altitude.

Knowledge of the velocity profile of the turbulent layers becomes useful when one considers the effect of Temporal Anisoplanatism (TA) in the AO corrected image due to the finite dwell time of the system between measuring the guide star wavefront and correcting the science object wavefront, $\rm \tau_d$. Once again, this can be quantified in terms of the mean squared error between the two wavefronts such that,

$${\sigma}_{\rm TA}^2 = (\tau_{\rm d}/\tau_{0})^{5/3}$$ (7)

where $\tau_{0}$ is given in terms of both V(h) and C_n²(h) as,

$$\tau_{0} = \left[ 2.9 k^2 \int C_n^2(h) {V(h)}^{5/3} {\rm d}h \right]^{-3/5}.$$ (8)

Consequently if one has knowledge of both C_n²(h) and V(h), then all of the parameters which describe the performance of an AO system can be obtained.

In the future one could also envisage a real-time SCIDAR system being available to allow anisoplanatic effects to be quantified during an AO observing run, thus enabling image quality diagnostics to be made and provide information for reliable point spread function deconvolution if deemed necessary.