Comparison of σo Obtained from the Conventional Definition with σo Appearing in the Radar Equation for Randomly Rough Surfaces

A comparison is made of the radar cross section of rough surfaces calculated in one case from the conventional definition and obtained in the second case directly from the radar equation. The objective of the analysis is to determine how well the conventional definition represents the cross section appearing in the radar equation. The analysis is executed in the special case of perfectly conducting, randomly corrugated surfaces in the physical optics limit. The radar equation is obtained by solving for the radiation scattered from an arbitrary source back to a colocated antenna. The signal out of the receiving antenna is computed from this solution and the result put into a form recognizeable as the radar equation. The conventional definition is obtained by solving a similar problem but for backscatter from an incident plane wave. It is shown that these two forms for σ° are the same if the observer is far enough from the surface; However, the usual far-field criteria are not sufficient. For the two cross sections to be the same, the observer must be far from the surface compared to the radii of curvature of the surface at the reflection (specular) points. Numerical comparison of the two cross sections has been made for normally distributed surfaces and the difference can be significant.