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Assessing atmospheric turbulence at observatory sites

A simple method is proposed to measure the coherence time, τ0, an important parameter in assessing atmospheric turbulence at potential sites for the next generation of telescopes.
19 March 2007, SPIE Newsroom. DOI: 10.1117/2.1200702.0606
Site evaluation for astronomical observations

The quality of ground-based astronomical observations is limited by atmospheric turbulence. Adaptive optics can correct the wavefront phase fluctuations sufficiently to let the resolution of the largest existing telescopes, with mirrors of 8-10m diameter, attain the limit set by diffraction. Adaptive optics can likewise compensate for the fluctuation of the phase differences between individual beams of interferometers. However, with current technologies, the task is difficult because the correction is not fast enough. Even at prime observation sites, such as Paranal, Chile, exposure times must be short enough to ‘freeze’ the atmospheric turbulence. The result is a significant loss of sensitivity for interferometric observations. If sites were to be found with substantially slower turbulence, available phasing devices might be fast enough to follow the phase fluctuations, and exposure times could then be substantially increased.

Atmospheric turbulence is characterized by several parameters. Among those, we single out two: the Fried paramater, r0, and the coherence time, t0. The Fried parameter, r0, is the coherence radius of a turbulence-distorted wavefront. The root mean square (rms) phase difference equals ~1.03radian for an aperture of diameter r0. The resolution loss due to atmospheric turbulence is then just equal to that from diffraction. A large Fried parameter, i.e., a large effective cell size of the atmospheric turbulence, is a major advantage for single-dish telescopes. The coherence time, t0, is the time interval during which the rms phase variance at a given point is ~1radian. The sensitivity of interferometers increases with the coherence time.

Both parameters are site dependent. However, there is currently no suitable, simple technique to measure the coherence time, and site testing and monitoring campaigns therefore rely predominantly on the assessment of r0. Note that in the following and in line with common notation, we will refer to the seeing, e0=0.976λ/r0 at spectral wavelength λ=500nm, rather than to r0. The seeing equals the angular resolution of a telescope with a mirror of diameter r0.

The parameter t0 is roughly inferred from measurements of the wind speed and the refractive-index structure constant, Cn2, by optical or microthermal in situ soundings, but all current methods have limitations: either the instrument is not well suited for site monitoring, or the method is burdened by intrinsic uncertainties and biases.

A new site-monitoring instrument, FADE

To close the current gap, a method has recently been proposed for measuring the coherence time with a small telescope (Kellerer, Tokovinin).1 This method suggests shifting the image of a star somewhat out of focus. Due to a suitably enlarged central blind area of the telescope, this converts the image to a ring. Insertion of a lens with proper spherical aberration sharpens the ring into a narrow circle, and atmospheric turbulence then causes distortions that can be conveniently assessed because, to a first approximation, they appear as changes in the radius of the ring.

The strength of the approach lies in the fact that it is insensitive to tip and tilt, which are jointly caused by telescope vibrations and atmospheric turbulence, and are thus not a meaningful indicator of turbulence alone. Instead, the technique measures the higher-order aberration, defocus, that causes the changes in radius. A relationship between the temporal properties of the radius variations and the coherence time has been developed in the framework of the Kolmogorov theory of turbulence.

Instrumental setup

The first measurements with this fast defocus (FADE) monitor were obtained at Cerro Tololo, Chile, from 29 October–2 November 2006. The instrumental setup is based on a Celestron C14 telescope and a fast CCD detector (GE 680 from Prosilica); Table 1 gives details on the hardware. To create annular images, a conic aberration is introduced into the beam. A practical way to achieve this is to combine defocus with a spherical aberration, which provides a fairly well approximated conic wavefront.

Table 1. Hardware 

As indicated in Figure 1, the two-lens ‘aberrator’ is placed in front of the focal plane of the telescope. It consists of two plano-spherical lenses of diameter dL=25mm and focal lengths fL=±50mm, the curved sides being separated by a gap g=0.7mm. The positive lens is closer to the telescope, so that the spherical aberration is increased, the gap's curvature being opposite to that of the wavefront. This optical element creates a ring image of radius ρ=53µm, when placed at a distance l=93.5mm in front of the focal plane. Figure 1 represents the corresponding spot diagram in the focal plane at three wavelengths: 450, 500, and 600nm. It shows that the two-lens aberrator introduces negligible chromatism.

Figure 1. Layout of the two-lens ‘aberrator,’ consisting of two planar-convex lenses with F=±50mm} (left). Spot diagram (right) of the image at the focus of the Celestron C14 telescope with central obstruction plus aberrator. The inner circle indicates the diffraction-limited image in the absence of the central obstruction and the aberrator.

The spherical aberration, a11, can be regulated by varying the width of the gap g, or the distance to the focus l. The dependence on l is very strong, a11 being proportional to l6. The aberration is almost perfectly conical near the border of the aperture. To block the inner part of the wavefront, a central obstruction of 150mm diameter (i.e., a relative diameter e=0.42) was placed in the pupil plane at the telescope entrance.

Data analysis

Ring images were recorded during five nights using a broad range of instrument settings. The measurements and their uncertainties are currently being analyzed. Figure 2 shows five images of Fomalhaut out of a sequence recorded at 700Hz. Given the short exposure times of 1.3ms, the rings contain bright spots due to scintillation. Methods that are insensitive to scintillation are currently being investigated to assess the ring radii. Figure 3 represents the provisional structure function estimated from the total sequence of 4000 images, and indicates the seeing and coherence time that best account for this function.

Figure 2. Ring images of Fomalhaut recorded at 700Hz on 29 October 2006.
Figure 3. Structure function of defocus measured on 4000 images of Fomalhaut recorded at 700Hz on 29 October 2006. The function that best accounts for the measurements and the resulting seeing, e0, and coherence time, t0, are indicated.

The seeing and coherence time values obtained in terms of our instrument are to be compared with simultaneous measurements from the MASS2 and DIMM3 site-monitoring instruments. Subsequently, an operational FADE instrument needs to be elaborated. We expect to submit, within a few months, a fuller account of our experiments to the journal Astronomy & Astrophysics.

Aglaé Kellerer
European Southern Observatory
Munich, Germany
Andrei Tokovinin
Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory
La Serena, Chile