11.2 Polarimetric Measurements

Here we deal only with the most common form of polarimetric SAR, in which a linearly polarized signal is transmitted and two orthogonal polarizations of the backscattered signal are measured. When a horizontally polarized wave is transmitted, the signals received in the horizontal (H) and vertical (V) channels undergo separate SAR processing to produce measurements S _hh and S _vh of the local copolarized and crosspolarized complex scattering amplitudes. By interleaving H and V polarized transmitted pulses, the corresponding terms S _vv and S _hv can also be measured to give the full polarimetric response of a scatterer. These four measurements allow the response to an arbitrary transmitted polarization to be calculated (for a fixed frequency, incidence angle, resolution, and time), as follows. Any polarization state of the transmitted wave can be uniquely described by an electric field vector of the form

(11.1)

where the subscript i denotes incident and and are unit vectors defined by and . Here is a unit normal to the Earth's surface and is a unit vector parallel to the wave vector k. The backscattered wave observed at a distance R in the far field of the scatterer is then given by

(11.2)

where the subscript s denotes scattered. Note that in this expression the coordinate system is throughout defined relative to the direction of the transmitted wave (the backscatter alignment convention); the transformations needed if the scattered wave...