Geometrical optics provides an accurate description of electromagnetic phase fluctuations under a wide range of conditions. The phase variance computed in this way is a benchmark parameter for describing propagation in random media. One can calculate this quantity for most situations of practical interest. We shall find that it is proportional to the first moment of the spectrum of irregularities and is therefore sensitive to the small-wavenumber portion of the spectrum. This is the region where energy is fed into the turbulent cascade process. We have no universal physical model for the spectrum in this wavenumber range and phase measurements provide an important way of exploring that region.

In analyzing these situations, we must recognize the anisotropic nature of irregularities in the troposphere and ionosphere. Large structures are highly elongated in both regions and exert a strong influence on phase. These measurements are also sensitive to trends in the data that are caused by nonstationary processes in the atmosphere. Sample length, filtering and other data-processing procedures thus have an important influence on the measured quantities. By contrast, aperture smoothing has a negligible effect.

Single-path phase measurements have been made primarily at microwave frequencies because phase-stable transmitters and receivers were available in these bands. Early experiments were performed on horizontal paths using signals in the frequency range 1–10 GHz. At least one experiment has measured the single-path phase variance at optical wavelengths. Phase-stable signals from navigation satellites and other spacecraft are beginning to provide information about the upper atmosphere.