# Polarization Synthesis

As described above, a polarimetric radar can be used to determine the target response or scattering matrix using two orthogonal polarizations, typically linear horizontal and linear vertical on both transmit and receive. If the scattering matrix is known, the response of the target to any combination of incident and received polarizations can be computed. This operation is referred to as polarization synthesis, and illustrates the power and flexibility of a polarimetric radar.

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Through polarization synthesis, an image can be created to improve the detectability of selected features. As an example, consider the detection of ships in sea clutter. To find the best polarization to use, the polarization signature of a typical ship is calculated, as is the signature of representative ocean areas (Bragg scattering). Then the ratio of these signatures can be determined. The transmit-receive polarization combination that maximizes the ratio of backscattered strength should improve the detectability of ships. This procedure is called "polarimetric contrast enhancement" , . A related procedure is called a "polarimetric matched filter" .

If a scattering matrix is measured by a polarimetric radar, then all the information is available about the backscattering properties of the target at each sample, for that frequency and angle with which the radar beam strikes the target. While the radar measures the response at four polarization combinations, the information obtained can be used to synthesize an image for any combination of transmit and receive polarizations. For example, a quadrature polarization radar may measure the responses at HH, HV, VV and VH, and with this information, an image can be constructed that would be received from a radar with right-hand circular polarization on both transmit and receive.

The polarization synthesis can be performed by converting the scattering matrix to the Stokes matrix, then pre-multiplying and post-multiplying the matrix by the unit Stokes vector representing the desired polarizations of the receive and transmit antennas respectively. One common use of polarization synthesis is to construct the polarization signatures for a selected class of targets, and use these geometric representations to help interpret the scattering mechanisms present in a scene (see Section 5).