The IEM2M rough-surface scattering model for complex-permittivity scattering media

Abstract

The integral equation model (IEM) was developed in the late 1980s and arguably became the most cited and implemented rough-surface scattering model in the field of radar remote sensing for Earth observation. It was derived by applying a second-order iteration in the incident electromagnetic field to the integral equations of the surface fields as given by Poggio and Miller. It is thus an extension of the first-order, Born approximation of these equations that produce the classical Kirchhoff approximation. The IEM has been subject to numerous amendments and variations over the last 20 years due to the imperfect introduction and handling of the Weyl representation of the spherical wave in its first version. The work presented here is a further development of the contribution made by the same author in 2001 (IEM2M), which was the first version of IEM able to blend analytically both the Kirchhoff and the small-perturbation approximations for the bistatic case. The improvement reported in this article is concerned with the inclusion of evanescent waves in the formulation of the model and the extension of the range of applicability of the second-order scattering terms to interfaces with complex-permittivity scattering media.

Effects of Spatial Sampling Interval on Roughness Parameters and Microwave Backscatter over Agricultural Soil Surfaces

“…Finally, a theoretical electromagnetic scattering model is employed to identify the spatial scales more relevant to accurately account for the microwave response of a soil surface. This model, referred to as IEM2M [23,24], predicts co-polarized backscattering coefficients HH and VV from a random rough surface given its dielectric constant, roughness parameters and autocorrelation function, besides the observation geometry parameters frequency and beam incidence angle.…”

“…However, it is able to record only the small-scale roughness component, while the rest of the topography is not possible to characterize. The second goal is to present a simulation study to understand how the sampling-interval-dependent roughness parameters s and l impact on surface backscattering response, using the Integral Equation Model IEM2M [23,24] as scattering model. As a result, progress was made in the understanding of the different scales in soil surface roughness characterization and their impact on the microwave backscatter response of soil surfaces.…”

Extension and Validation of an Advanced Integral Equation Model for Bistatic Scattering From Rough Surfaces

“…When the medium is very lossy, contributions from the lower medium propagation is expected to be small. However, in general, all modes must be included to get a more complete scattered power, as claimed in [19]. After some algebraic manipulations and arrangements, we can reach the final expression of a relatively compact form as:…”

“…Note that in IEM model, the terms involved (R h + R v ) in (19) are all dropped off. Keeping in mind that the Kirchhoff field coefficients f qp are spatially dependent on the Fresnel reflection coefficients R p , p = h, v and the surface slope term s 1 .…”

“…Driven by the need of predicting bistatic scattering and microwave emissivity, much effort has been devoted to further improving the IEM accuracy [9][10][11][12][13][14][15][16][17][18][19] by removing some of the assumptions originally imposed for the purpose of mathematical simplicity during the course of derivation. Another leap forward step was the introduction of a transition function into the Fresnel reflection coefficients to take spatial dependence into account, removing the restrictions on the limits of surface roughness and permittivity [3,11].…”