Reflection and scatter formula for anisotropically turbulent air

Existing formulations assume that the correlation lengths of refractive index irregularities, generated by turbulence, are small in comparison to the Fresnel length. However, there is experimental evidence that the contrary may be true. This paper extends the existing formulations for the case where the Fresnel zone radius is comparable to or smaller than the correlation length and develops a statistical solution that embraces several echoing mechanisms. Conditions are specified under which Fraunhofer and Fresnel reflection and scatter from turbulent air can be distinguished. An integral expression for echo power is developed which shows that echo intensity depends not only on a resolution volume weighting function, but also on a more important Fresnel term. The spectral sampling function demonstrates that for resolution volumes in the antenna's far field this function is independent of the location of the resolution volume. The conditions under which the echo power is proportional to the square of the pulse width are based upon the statistical approach herein adopted for Fresnel scattering.