Fluctuations during observations of extraterrestrial sources from outer space through Earth's atmosphere

A model to describe random heterogeneities in the index of refraction in the atmosphere is proposed which makes allowance for sphericity of the atmosphere. The correlation functions of the phase fluctuations behind the equivalent phase screen are calculated. The phase fluctuation spectra are expressed in general form through the spectra of the index of refraction. The influence of atmospheric sphericity and anisotropy of the heterogeneities on phase fluctuations of the transmitted radiation are examined using a Gaussian correlation function of the index of refraction as an example. Simple formulas are derived in the form of single integrals which connect specified spatial spectra of the relative fluctuations of the refraction with the spectra of the wave phase fluctuations. It is shown that calculation of the second moments of the phase for isomeric heterogeneities of the index of refraction yields the same results for the proposed atmospheric models as for the assumption that the relative fluctuations of the index of refraction are a statistically homogeneous random field.