Probability distribution of random cylinder's total scattering cross section

An arbitrary shaped scatterer is often modeled as a canonical structure while solving an electromagnetic boundary value problem. This approach approximates the boundary to provide complex analytical solutions. However, most real life structures do not have canonical or regular boundaries. Determining an analytical solution of electromagnetic scattering problem is quite a tedious task, especially for random geometries. This work proposes a method to compute the scattering statistics of a random cylinder. A formulation is developed to determine the probability density function (pdf) of scattering cross section, σT, from the statistics of random cylinder's radius. This approach eliminates the need to actually solve an electromagnetic scattering problem. The optical theorem is employed to estimate the pdf of σT from the pdf of lateral width. The proposed results are found in good agreement with the numerically simulated results.