Characteristic polarization state theory is restudied for the symmetric coherent Sinclair scattering matrix case. First, the geometric relations of the characteristic polarization states on the Poincare sphere are derived. Based on these relations, simple formulas are given for all of the characteristic polarization states of this Sinclair matrix in Stokes vector form. From the formulation, it is clear that the CO-POL Nulls are fundamental characteristic polarization states for the symmetric coherent Sinclair scattering matrix case, in that the others can straightforwardly be obtained from the Stokes vectors of the CO-POL Nulls. For further study of the characteristic polarization state and the distribution of the received powers on the Poincare sphere, the authors introduce the concept of the equi-power curve. It is defined as the curve on the Poincare sphere on which the received powers in some defined channel have the same value. They deal with the characteristics of the equi-power curves for various special cases. In addition, they show how the characteristic polarization states are generated by the equi-power curves. It is demonstrated that the characteristic polarization states can usually be regarded as the points of contact of the Poincare sphere and a conicoid representing a power-related quadratic form. This leads to a new method to introduce the characteristic polarization states.

In a co- or cross-polarized channel, the polarization states of the transmitting and receiving antennas are the same or orthogonal, and the corresponding target nulls (i.e., the co-pol nulls or x-pol nulls) are defined as the polarization states of the transmitting antenna such that the received power equals zero. However, no systematic studies have been carried out to solve the problem of the corresponding target nulls if the polarization states of the transmitting and receiving antennas are independent. In this paper, the target null theory is extended to the case of two independent polarization states. For two arbitrary independent symmetric scattering matrices, it is proved that there exists only one pair of polarization states such that both of the received powers equal zero. This polarization states' pair is called the co-null of the two targets, which can easily be obtained by solving an eigenvalue problem. Based on this concept and algebraic theory, the concept of the co-null space is introduced for the symmetric scattering matrix case, and many important results are presented, e.g., the relations between the co-null and the co-pol/x-pol nulls, the properties of the co-null space, and the relation between the co-null and target decomposition. Finally, the co-null for the asymmetric scattering matrix case is studied. The concepts of the mono-co-null space and the bi-co-null space are introduced, and the relations between both spaces are presented.

In microwave remote sensing, it is desirable to select radar antenna polarizations that maximize the contrast between two classes of scatterers or scatterer ensembles. A polarimetric radar measures complete polarization properties of a target and then provides a vector description of the resulting scattered wave through various target matrices. Several optimization procedures for the completely and partially polarized cases have been proposed based on the theory of radar polarimetry. It is the purpose of this paper to present optimization procedures for the enhancement of polarimetric contrast between two time-varying targets and to extend the procedure to two spatially incoherent image pixel targets. The targets are now characterized by the time-averaged or spatially-averaged Kronecker matrices, from which one can obtain the associated Graves and Kennaugh matrices.The Graves matrices of the targets are used to find a transmitter polarization to maximize the ratio of scattered power densities at the receiver. Using the Lagrange multiplier method, the maximization problem is cast into the form of a generalized Balois eigenvalue equation. The largest eigenvalue of the equation equals the maximal power ratio, and the optimal effective length of the transmitting antenna is proportional to the corresponding eigenvector. The Kennaugh matrices of the targets are employed to obtain the Kennaugh vectors of partially polarized scattered waves from the two targets. Each of the scattered Kennaugh vectors is decomposed into a completely polarized and an unpolarized part. It is well known that the power received from the unpolarized part is independent of the polarization characteristics of the receiving antenna. Then a receiver polarization is selected to maximize or minimize the completely polarized part scattered from the desired or the undesired target.As a numerical example, the optimal Stokes vectors of transmitting and receiving antennas are given to show the validity of the optimization procedures and how it can be applied to perfecting high resolution POL-SAR/SAL Image Feature Extraction.

One of the great challenges for modern radar is to classify, sort and identify targets of all kinds for military battlespace surveillance as well as for civilian geo-environmental stress change monitoring purposes. Whereas, in military radar utilization of complete polarization scattering matrix radars is not yet fully accepted, in remote sensing on the other hand, radar polarimetry seems to have been accepted as an indispensable tool, and convincing results have been obtained for geo-environmental applications in agriculture, forestry, hydrology, flood plain and rural infrastructure maintenance, volcanology and seismology, archeology, etc. However, there still exists a large void in standardization and proper handling of basic and applied polarimetric theory and concepts. In this paper a succinct assessment of the current state-of-the-art is presented summarizing the basic polarimetry concepts spelled out in Boerner et al. (1997). It is the purpose of this paper to draw attention of the IEEE Geoscience and Remote Sensing community to this recent compendium on 'Polarimetry in Remote Sensing'.

Exact and approximate methods are developed to determine radar antenna polarizations that maximize power contrast between two scatterers. Antenna polarizations to maximize received power are also obtained. These polarizations will maximize target-noise ratio and the ratio of target power to power from unpolarized clutter. Matrices that represent unpolarized clutter are given. It is shown that a backscattering covariance matrix to represent unpolarized clutter for any incident wave does not exist. Target matrices used are the bistatic and backscattering covariance matrices, the Kennaugh matrix, and the Graves power scattering matrix.

It is often desirable to select radar antenna polarizations that maximize the contrast in received powers from two classes of scatterers. A terrain-mapping radar may use polarization to maximize the contrast between forested areas and farmland. For another radar, polarizations may be chosen to optimize an aircraft target return relative to clutter. Polarizations chosen for either purpose may give a target return that is small compared to external noise or internal receiver noise, and it may therefore be more appropriate to choose polarizations that maximize signal-to-noise ratio. An outline of methods for choosing polarizations in all of these cases is presented

A systematic approach to the measurements of the four basic scattering matrices used in radar and also recently more frequently in lidar metrology of isolated scatterers and distributed scatter ensembles is considered. The pertinent scattering matrices in use are the 2×2 complex JONES propagation matrix [T] or the 2×2 complex Sinclair scattering matrix [S] for the coherent point scatter case; the 2×2 complex radar power GRAVES matrix [G]=[S] [S] for the coherent case; the 4×4 real power density Mueller propagation matrix [M] or the 4×4 real power density Kennaugh scattering matrix [K] and the 3×3 symmetric (4×4 asymmetric) case covariance matrix [Z] for the partially polarized cases, which all are distinct but can be related to one another. The authors provide a comparison of polarimetric methods. Measurement made with respective radar and lidar systems are compared with specific applications for assessing EMC noise and clutter signatures. This study shows that the covariance matrix provides the greatest utility

Arrays, Broadband Antennas, and Noise Representations of Wave Polarization Polarization Matching of Antennas Polarization Characteristics of Some Antennas Polarization Changes by Reflection and Transmission Partial Polarization Polarization Measurements Target Detection Appendices Index.