A Note on the Fourier Transform of Scattering Diagrams and Selective Summation Techniques

摘要

At the present time the most satisfactory theory for propagation in an unbounded homogeneous and isotropic turbulent medium is based on selective summation techniques applied to the Neuman perturbation series for the field. In this theory the various terms in the series may conveniently be represented by graphs or scattering diagrams. In this paper a set of simple rules is presented which permit the required Fourier transform of a given scattering diagram to be obtained very quickly by inspection from the topological structure of the diagram. These rules are established for both the coherent field and its correlation function. In addition a comparison is given of the various theories referred to as Keller's method, renormalization techniques, and approximations commonly employed in obtaining approximate solutions to the exact Dyson equation for the coherent field. It is shown that the Dyson equation, Keller's method, and the renormalization theory all lead to identical results. (Author)