Atmospheric Path Characterization

Abstract

This chapter describes how atmospheric paths can be characterized by measuring certain key intensity properties of point-object (star) images formed by telescopes observing over these paths. The characterization is given in terms of the rms and the autocorrelation function of the OPD fluctuation over the paths, σ and \(\rho (\xi ,\eta )\). Once σ and \(\rho (\xi ,\eta )\) have been established for a given path, so too are the two-point two-wavelength correlation function and the atmospheric MTF for that path. The wavefront structure function, the refractive index structure function, and the turbulence spectrum are also determined by σ and \(\rho (\xi ,\eta )\). When the measures σ and \(\rho (\xi ,\eta )\) are appropriately combined with a telescope pupil function, all meaningful statistical properties of point-object images formed by that telescope are determined. When the image intensity measurements are obtained using AO-equipped telescopes, the OPD properties that arise are those of the AO-corrected image-forming waves, properties that we denote by σ AO and \(\rho_{AO} (\xi ,\eta )\). Naturally, for a properly functioning AO system, \(\sigma_{AO} < \sigma\).