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The theoretical treatment of the Earth's atmosphere effect on coherent measurements includes the analysis of radiation, propagation, scatter, and reception of arbitrary signals in a random medium in the presence of complicating factors such as regular refraction, finite sizes of receiving and transmitting apertures, and non-linear character of received signal processing. The complexity of the problem demands seeking approximate approaches which, on the one hand, provide acceptable accuracy and, on the other hand, are sufficiently simple to enable received signal processing analysis. These requirements may be satisfied only taking account of the specific character of each practical situation. In particular situations, the spatial structure of the radiation field can be described in terms of a finite beam wave or infinite plane or spherical waves. As regards a medium, it is necessary to include in consideration not only its random inhomogenities but also the regular variation of its refractive index in height. Under these conditions, the extended Huygens-Fresnel principle, the method of geometrical optics, the Rytov method, and the hybrid method are advantageous to use for a wave propagation description. The main advantage of these techniques is a possibility to represent the random wave field in an explicit form that is very important from the standpoint of the distorted signal processing analysis. Using the above-mentioned methods, the general scheme of measurement error calculation for a variety of coherent measuring systems can be developed on the basis of the consistent analysis of measurement process. This enables us not only to get simple formulas for the measurement errors but also to determine the limiting sizes of the receiving aperture and the limiting duration of the signal which are admissible in coherent signal processing.
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