An extension of the IEM/IEMM surface scattering model

The integral equation model (IEM) has been developed over the last decade and, since its first presentation by Fung and Pan (1986 Proc. Int. Symp. on Multiple Scattering of Waves in Random Media and Random Surface (PA: Pennsylvania State University Press) pp 701-14), it has become one of the theoretical models most widely used for rough surface scattering in microwave remote sensing. The aim of this model was the study of the scattering by random rough surfaces under more general conditions than the Kirchhoff or the small-perturbation approximations. Furthermore, the IEM was meant to include multiple-scattering effects at second order. The IEM has been gradually corrected in two later releases by its original authors (Hsieh C-Y et al 1997 IEEE Trans. Geosci. Remote Sensing 35 901-9, Chen et al 2000 IEEE Trans. Geosci. Remote Sensing 38 249-56). However, the model still presents several theoretical hiatuses in its current formulation which call for a new revision. Most importantly, the IEM in its current form does not reduce in the general bistatic context to the small-perturbation method (SPM) when the scattering surface is slightly rough. A good description of multiple-scattering mechanisms implies that the single scattering is correctly described. This condition is not met by IEM as given hitherto. In the work presented here, a corrected version of IEM reproducing SPM for small roughness is proposed. Since it is also compliant with the physical and geometrical optics results, this new integral equation model is an appropriate candidate to bridge the gap between the Kirchhoff approximation and the SPM.