Principles of Modern Radar - Volume 2 1891121537

602 CHAPTER 13 Introduction to Radar Polarimetrysystem, the local coordinate systems at the transmitter and the target are the same as in theFSA convention, but the one at the receiver is defined as a right-handed system with thez-axis pointed away from the receiver toward the target. For a monostatic or backscatteringconfiguration, when the transmitter and the receiver antennas are collocated, both FSAand BSA systems coincide. Typically FSA convention is used to represent the scatteringmatrix for the bistatic mode, including forward scattering, whereas both BSA and FSAconventions can be employed in the monostatic case, although it is physically intuitive touse the BSA. The Sinclair matrix is used to describe the scattering matrix with a monostaticradar [27]. The Jones matrix is used to describe bistatic scattering matrix [20], [33](see also Section 6.4 in [3]).A second approach for scattering matrix theory is based on the description of transmittedand received back-scattered energy in terms of real power measurements, and leadsto Kennaugh and Mueller matrices for monostatic and bistatic cases, respectively [14, 34].The advantage of power measurements is that the elimination of the absolute phase fromthe target means that the power-related parameters become incoherently additive [11].Either the voltage-measured Sinclair matrix or the power-measured Kennaugh matrixleads to the same result for completely polarized target returns, which occur when (a) thetarget geometry as projected on the radar antenna aperture does not change with time (e.g.,stationary target) or (b) the target or the intervening medium does not depolarize the scatteredsignal. In this case, for both formulations, the scattering matrices may be expressedin terms of a common set of five physically significant parameters [14, 19, 23]. However,the Kennaugh matrix is especially useful for partially polarized return signals, which occurwhen the target geometry varies with time. In this case, the time-averaged Kennaughmatrix is described by nine parameters derived from the Stokes vectors of transmit andreceive polarization states [14]. Next, in Section 13.3.2, the five significant parameters ofthe Sinclair formulation are derived by appealing to radar polarimetry theory based oneigenvector decomposition, introduced by Kennaugh first [13] and later generalized byHuynen [14]. In Section 13.3.3, the Kennaugh matrix is extended to partially polarizedtarget returns, and the similarity between Kennaugh and Mueller matrices is discussed.The theory and notation used to describe the scattering matrix in terms of physicallysignificant parameters follow closely Huynen’s seminal exposition on phenomenologicaltheory of radar polarimetry [14].13.3.1 Sinclair FormulationThe scattering matrix characterizes a radar target’s scattered response to an incident waveand describes how the polarization, amplitude and phase of an incident wave are transformedby backscattering from a target. The scattering matrix is a ‘transfer function’ ofthe target and hence is independent of the polarization states of the transmit and receivechannels of the radar. A monostatic radar transmitting and receiving two orthogonal polarizationstates is assumed in the following discussion. The target-scattered signal receivedby a radar can be expressed as [3, 14, 23]V rt = Sê t · ê r (13.26)where S is the Sinclair scattering matrix, measured in meters, and ê t and ê r are thenormalized polarization unit vectors of the transmit and receive channels of the radar. TheRCS of the target is given byσ rt = |V rt | 2 (13.27)