Measurements of profiles of the wavefront outer scale using observations of the limb of the Moon

Abstract

The wavefront outer scale is an important parameter to use when evaluating the experimental performance of large aperture telescopes. Knowledge of three‐dimensional atmospheric wavefront distortions is required for specifications of multiconjugate adaptive optics systems, which are essential for observations using Extremely Large Telescopes with a wider field of view. We aim to estimate the vertical distribution of the wavefront outer scale. We analyse the angular correlation of the fluctuations of the wavefront angle of arrival, deduced from image motion of the limb of the Moon. We use a simulated annealing algorithm to deduce the height dependence of the wavefront outer scale with given C2N profiles simultaneously measured with the scintillation detection and ranging (SCIDAR) instrument. We present results obtained during two campaigns of observation at the Mauna Kea Observatory (Hawaii) and the Observatoire de Haute Provence (France). Estimated profiles of the outer scale exhibit smaller values in the boundary layer than in the free atmosphere. Comparisons with measurements of the outer scale using the Generalized Seeing Monitor (GSM) are possible and give good agreement. We consider some implications for adaptive optics systems.

Online estimation of the wavefront outer scale profile from adaptive optics telemetry

“…The specific parameters (L 0 , h and ω) for each case are defined in Table 2; they have been arbitrarily chosen, similar to those reported in Ziad et al (2013) and Maire et al (2007). The table summarizes the results for the estimations of L 0 , h and ω, and case 1 (turbulence with four layers) is also plotted in Fig.…”

“…However, some studies have shown that it can vary significantly with altitude (Maire et al 2007;Dali et al 2010;Ziad et al 2013). This height-dependent outer scale, L 0 (h), has been introduced in the phase power spectrum of a von Kármán model by Borgnino, Martin & Ziad (1992):…”

“…L 0 gives an estimation of the spatial coherence of the wavefront and becomes significant for larger telescopes when the telescope diameter approaches this outer scale (Ragazzoni, Marchetti & Valente 2000). E-mail: aguesala@ing.puc.cl Determining the spatial coherence of the atmospheric turbulence is essential for the estimation of other atmospheric parameters on large telescopes such as seeing, isoplanatic angle and coherence time (Maire et al 2007). This has a great importance in astronomy for applications such as astrometry, interferometry, point spread function reconstruction (PSF-R), tomography and turbulence profiling (Ellerbroek 2013;Yelda et al 2013).…”

Multi-instrument measurement campaign at Paranal in 2007

“…The mode (a) corresponds to the case of small outer scale (∼12 m), the mode (c) to the high value (∼33 m) and multi-layer case is ambiguous. A general formula was proposed by Maire et al (2007): Borgnino (1990) found that for AA fluctuations n = −1/3 is appropriate. Here we find that the n = 11/3 exponent gives the best match between the GSM and MOSP outer scale values (Fig.…”

“…This increases the sensitivity of the monitor to the fluctuations of the moon limb. The exposure time was set to 1 or 2 ms in order to freeze the atmospheric effects on image motion (Maire et al 2007). …”