Atmospheric Path Characterization

Abstract

AbstractThis 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 integrated OPD fluctuation over the paths, \(\sigma\) and \(\rho \left( {\xi ,\eta } \right)\). Once \(\sigma\) and \(\rho \left( {\xi ,\eta } \right)\) 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 \(\sigma\) and \(\rho \left( {\xi ,\eta } \right)\). When the measures \(\sigma\) and \(\rho \left( {\xi ,\eta } \right)\) are appropriately combined with the telescope pupil function, all meaningful statistical properties are determined for point-object images formed by that telescope. When the image intensity measurements are obtained using AO-equipped telescopes, the measured OPD properties are those of the AO-corrected image-forming waves, which we denote by \(\sigma_{AO}\) and \(\rho_{AO} \left( {\xi ,\eta } \right)\). Naturally, for a properly functioning AO system, \(\sigma_{AO} < \sigma\).