A microwave scattering model for an electrically dense vegetation medium

It is known that radar response from a vegetation medium can be studied theoretically by modeling the medium as a discrete random medium with scatterers such as disks, needles and cylinders. However, at the low frequency end of the microwave region, the spacing between the scatterers may be comparable or smaller than the wavelength and the medium is considered as electrically dense. This means that the coherence effect of the scatterers should be considered as scattering from each scatterer is no longer independent from each other. In addition, when the dimensions of the scatterers (such as radius of deciduous leaves and length of branches) are comparable to the spacing between the scatterers and the wavelength, near field interaction needs to be considered. These effects are incorporated by introducing two types of correction to the phase matrix of the scatterers, namely amplitude and phase corrections. The amplitude correction is obtained from the near field amplitude term of the scattered field. The phase correction consists of two components: the Fresnel phase term and the array phase term. The Fresnel phase correction term comes from the higher order terms in the phase of the scattered field from a scatterer. The array phase correction term takes into account the phase contributions by various correlated scatterers. The corrected phase matrices for disks, needles and branches are then used in the radiative transfer formulation where second order iterative solutions are solved. Theoretical results show that the array phase correction is important for electrically dense medium. When the frequency increases and enters into the Fresnel region, the amplitude and Fresnel phase corrections are required