Fresnel-Kirchhoff theory applied to terrain diffraction problems


  • J. H. Whitteker


Fresnel-Kirchhoff theory is adapted to the problem of finding the diffraction attenuation at VHF and UHF over terrain profiles of arbitrary shape. Approximations are based on the assumptions of small wavelength and small diffraction angles. As a preliminary step, the theory is applied to the multiple-knife-edge problem. The field is found as a function of height above each knife edge in turn. In an application of Huygens' principle, an integration over the field above one knife edge provides the field at any point above the next. This formulation is equivalent to knife-edge formulations used in the past. Then each pair of neighboring knife edges is bridged with an imperfectly reflecting plane surface, representing the terrain. Huygens' principle is used again for the reflected wave, neglecting backscatter. The field found in this way is accurate for a good reflector but not a poor one. An analytical comparison shows agreement with rigorous diffraction theory for the problem of a plane wave incident on a perfectly reflecting wedge. Numerical comparisons with rigorous diffraction theory for a spherical Earth and for a small-radius hill (approximated with linear segments) show agreement to within 1.5 dB for the parameters chosen.