Integral field spectroscopy supports atmospheric optics to reveal the finite outer scale of the turbulence

Abstract

The spatial coherence wavefront outer scale (L_0) characterizes the size of the largest turbulence eddies in Earth's atmosphere, determining low spatial frequency perturbations in the wavefront of the light captured by ground-based telescopes. The motivation of this work is to introduce a novel technique for estimating L_0 from seeing-limited integral field spectroscopic (IFS) data. This approach is based on the impact of a finite L_0 on the light collected by the pupil entrance of a ground-based telescope. We take advantage of the homogeneity of IFS to generate band filter images spanning a wide wavelength range, enabling the assessment of image quality (IQ) at the telescope's focal plane. Comparing the measured wavelength-dependent IQ variation with predictions from Tokovinin (2002) analytical approach offers valuable insights into the prevailing L_0 parameter during the observations. We applied the proposed technique to observations from MUSE in the Wide Field Mode obtained at the Paranal Observatory. Our analysis successfully validates Tokovinin's analytical expression, which combines the seeing (E_0) and the L_0 parameters, to predict the IQ variations with the wavelength in ground-based astronomical data. However, we observed some discrepancies between the measured and predictions of the IQ that are analyzed in terms of uncertainties in the estimated E_0 and dome-induced turbulence contributions. This work constitutes the empirical validation of the analytical expression for estimating IQ at the focal plane of ground-based telescopes under specific E_0 and finite L_0 conditions. Additionally, we provide a simple methodology to characterize the L_0 and dome-seeing (E_d) as by-products of IFS observations routinely conducted at major ground-based astronomical observatories.