3.4 Surface Scattering

3.4 Surface Scattering

Surface scattering is defined as the scattering which takes place only on the border surface between two different but homogeneous media, from one of which electro-magnetic energy is incident on to the other. Scattering of microwave on the ground surface increases according to the increase of complex permittivity, and the direction of scattering depends on the surface roughness, as shown in Figure 3.4.1.

In the case of a smooth surface as shown in Figure 3.4.1 (a), there will be a specular reflection with a symmetric angle to the incident angle. The intensity of specular reflection is given by Fresnel reflectivity, which increases in accordance with the increase of the ratio of complex permittivity.

When the surface roughness increases a little as shown in Figure 3.4.1 (b), there exists a component of specular reflection and a scattering component. The component of specular reflection is called the coherent component, while that of scattering is called diffuse or the incoherent component.

When the surface is completely rough, that is diffuse, only diffuse components will remain without any component of specular reflection as shown in Figure 3.4.1 (c). Such surface scattering depends on the relationship between the wavelength of electro-magnetic radiation and the surface roughness which is defined by the Rayleigh Criterion or Fraunhofer Criterion.

Rayleigh Criterion : if h < / 8 cos , the surface is smooth
Fraunhofer Criterion : if h < / 32 cos , then the surface is smooth

where h : standard deviation of surface roughness
: wavelength
: incident angle

Generally the scattering coefficient, that is scattering area per unit area, is a function of incident angle and the scattering angle. However in the case of remote sensing, the scattering angle is identical to the incident angle because the receiving antenna of radar or scatterometer is located at the same place as the transmitting antenna. Therefore, in remote sensing only back- scattering may be taken into account. The radar sectional area i Ai is given as follows.

where P t : transmitting power
G : antenna gain
: wavelength
Pr : receiving power
R : distance between radar and object
Ai : differential area of surface scattering

Scattering area per a unit area is called the backscattering coefficient.

= i / Ai

The backscattering coefficient depends on the surface roughness and incident angle as shown in Figure 3.4.2.