We analyze the statistics of the copolarized and cross-polarized scattered intensity from a flat substrate contaminated by spherical or spheroidal interacting particles. In particular, we focus on both the cross-polarized component and the probability of detecting zeros in the cross-polarized intensity, P( I cross=0). As it is shown, the latter parameter gives information about particle interaction and can be measured with higher accuracy than other statistical parameters. A theoretical model for P( I cross=0) is presented for spherical Rayleigh scatterers. Computer simulations of P( I cross=0) by varying the shape, size and surface density of the particles are also shown.