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- Polarimetric Radar Imaging: From Basics to Applications
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A fully polarimetric SAR system transmits alternatively horizontally and vertically polarized signal and receives returns in both orthogonal polarizations, allowing for complete information of the radar target [ 6 , 8 ]. While full polarimetric SAR systems provide complete information about the radar target, the coverage of these systems is half of the coverage of single or dual polarized SAR systems.

Also, the energy required by the satellite for the acquisition of full polarimetric SAR imagery and the pulse repetition frequency of the SAR sensor are twice the single or dual polarized SAR systems. A new SAR configuration named compact polarimetric SAR is currently being implemented in SAR systems, where a circular polarized signal Figure 4 is transmitted and two orthogonal polarizations horizontal and vertical are coherently received [ 9 ]. Thus, the relative phase between the two receiving channels is preserved and calibrated, but the swath coverage is not reduced.

In comparison to the full polarimetric SAR systems, compact polarimetric SAR operates with half pulse repetition frequency, reducing the average transmit power and increasing the swath width. Consequently, this SAR configuration is associated with low-cost and low-mass constraints of the spaceborne polarimetric SAR systems. The wider coverage of the compact SAR system reduces the revisit time of the satellite, making this system operationally viable [ 10 ].

These advantages come with an associated cost in the loss of full polarimetric information. Fully polarimetric SAR systems measure the complete polarimetric information of a radar target in the form of a scattering matrix [S]. The scattering matrix [S] is an array of four complex elements that describes the transformation of the polarization of a wave pulse incident upon a reflective medium to the polarization of the backscattered wave and has the form [ 6 ]:. The elements of the scattering matrix [S] are complex scattering amplitudes.

Two polarimetric scattering vectors can be extracted from the target scattering matrix, which are the lexicographical scattering vector and the Pauli scattering vector [ 12 ]. Assuming the reciprocity condition, the lexicological scattering vector has the form:. The multiplication of the cross-polarization with 2 is to preserve the total backscattered power of the returned signal.

The Pauli scattering vector can be obtained from the complex Pauli spin matrices [ 6 ] and, assuming the reciprocity condition, has the form:. Deterministic scatterers can be described completely by a single scattering matrix or vector. However, for remote sensing SAR applications, the assumption of pure deterministic scatterers is not valid.

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Thus, scatterers are non-deterministic and cannot be described with a single polarimetric scattering matrix or vector. This is because the resolution cell is bigger than the wavelength of the incident wave. Non-deterministic scatterers are spatially distributed. Therefore, each resolution cell is assumed to contain many deterministic scatterers, where each of these scatterers can be described by a single scattering matrix [S i ].

Therefore, the measured scattering matrix [S] for one resolution cell consists of the coherent superposition of the individual scattering matrices [S i ] of all the deterministic scatterers located within the resolution cell [ 6 , 12 ]. The relationship between the covariance matrix [C] and the coherency matrix [T] is linear.

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Both matrices are full rank, hermitian positive semidefinite and have the same real non-negative eigenvalues, but different eigenvectors. Moreover, both matrices contain the complete information about variance and correlation for all the complex elements of the scattering matrix [S] [ 12 ]. A compact polarimetric SAR system transmits a right- or left-circular polarized signal, providing a scattering vector of two elements:. A four-element vector called Stokes vector [g] can be calculated from the measured compact polarimetric scattering vector, as follow [ 11 ]:.

The first Stokes element g 0 is associated with the total power of the backscattered signal while the fourth Stokes vector is associated with the power in the right-hand and left-hand circularly polarized component [ 13 ]. The elements of the Stokes vector can be used to derive an average coherency matrix, which takes the form [ 14 ]:. Radar backscattering is a function of the radar target properties dielectric properties, roughness, target geometry and the radar system characteristics polarization, band, incidence angle.

Three major backscattering mechanisms can take place during the backscattering process. These are the surface, double bounce and volume scattering mechanism Figure 5. In the case of surface scattering mechanism Figure 5 , the incident radar signal features one or an odd number of bounces before returns back to the SAR antenna. In this case, a phase shift of o occurs between the transmitted and the received signal [ 6 ]. However, a very smooth surface could cause the radar incident signal to be reflected away from the radar antenna, causing the radar target to appear dark in the SAR image.

In this case, scattering is called specular scattering. An example of such surfaces is the open water in wetlands [ 12 ]. In the case of double bounce scattering mechanism Figure 5 , the incident radar signal hits two surfaces, horizontal and adjacent vertical forming a dihedral angle, and almost all of incident waves return back to the radar antenna.

Thus, the scattering from radar targets with double bounce scattering is very high. The phase difference between the transmitted and the received signal is equal to zero. Double bounce scattering mechanism is frequently observed in open wetlands, such as bog and marsh, as the results of the interaction of the radar signal between the standing water and vegetation [ 15 ]. In the case of volume scattering mechanism Figure 5 , the radar signal features multiple random scattering within the natural medium.

Thus, illuminated radar targets with volume scattering appear bright in a SAR image. Volume scattering is commonly observed in flooded vegetation wetlands due to multiple scattering in the vegetation canopy. In general, the penetration capabilities and the attenuation depth of radar signal in a medium, such as flooded vegetation, increases with the increasing of the wavelength [ 6 , 12 ].

Figure 6 presents the penetration of radar signals for different bands.

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As shown in Figure 6 , X-band SAR has a short wavelength signal with limited penetration capability, while L-band SAR has long wavelength signal with higher penetration capability. As shown in Figure 6 , the scattering mechanism of a radar target could be affected by the penetration depth of the radar signal. Thus, dense flooded vegetation could present volume scattering mechanism in X- or C-band SAR return from canopy , but double bounce scattering mechanism in L-band due to scattering process from trunk-water interaction Figure 6 [ 12 ].

Different decomposition methods have been proposed to derive the target scattering mechanisms for both full polarimetric [ 6 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] and compact polarimetric [ 11 , 25 ] SAR data. One of the earliest and widely used decomposition methods is the Cloude-Pottier decomposition [ 17 ]. This method is incoherent decomposition method based on the eigenvector and eigenvalue analysis of the coherency matrix [T]. Given that [T] is hermitian positive semidefinite matrix, it can always be diagonalized using unitary similarity transformations.

That is, the coherency matrix can be given as. Based on the Cloude-Pottier decomposition, three parameters can be derived [ 17 ].

## Free Polarimetric Radar Imaging: From Basics to Applications (Opticalâ€¦

This parameter is an indicator of the number of effective scattering mechanisms which took place in the scattering process [ 6 ]. The anisotropy A provides additional information only for medium values of H because in this case secondary scattering mechanisms, in addition to the dominant scattering mechanism, play an important role in the scattering process [ 6 ].

Another widely used polarimetric decomposition method is the Freeman-Durden method [ 18 ]. Contrary to the Cloude-Pottier decomposition, which is a purely mathematical construct, the Freeman-Durden decomposition method is a physically model-based incoherent decomposition based on the polarimetric covariance matrix. It relies on the conversion of a covariance matrix to a three-component model. The results of this decomposition are three coefficients corresponding to the weights of different model components. A polarimetric covariance matrix [C] can be decomposed to a sum of three components, corresponding to volume, surface, and double bounce scattering mechanisms [ 18 ]:.

The Freeman-Durden decomposition is particularly well adapted to the study of vegetated areas [ 18 ]. Thus, it is widely used for multitemporal wetland monitoring to track changes of shallow open water to flooded vegetation [ 26 ]. Scattering mechanism information can also be obtained using compact polarimetric SAR data. Two decomposition methods are commonly used.

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The accurate, effective, and continuous identification and tracking of changes in wetlands is necessary for monitoring human, climatic and other effects on these ecosystems and better understanding of their response. Wetlands are expected to be even more dynamic in the future with rapid and frequent changes due to the human stresses on environment and the global warming [ 27 ]. Different methodologies can be adopted to detect and track changes in wetlands using SAR imagery, depending on the type of the change and the available polarization option.

For example, a change in the surface water level of a wetland area due to e. Such a change can be easily detected using SAR amplitude images before and after the event acquired with similar acquisition geometry. The specular scattering of the radar signal can highlight the open water areas dark areas due to low returned signal. Spatiotemporal changes in wetlands as dynamic ecosystems could be interpreted using SAR amplitude imagery only.

## Polarimetric Radar Imaging: From Basics to Applications

This is because changes within wetlands could change the surface type illuminated by the radar. Sometimes, the change could be more complex with alternations in surface water, flooded vegetation and upland boundaries. In this case, the additional polarimetric information from full or compact polarimetric SAR is necessary for the detection and interpretation of changes within wetlands. As shown in Figure 7 , a change within a wetland from wet soil with a high dielectric constant to open water is usually accompanied with a change in the radar backscattering from surface scattering with a strong returned signal Figure 7a to specular reflection with a weak returned signal Figure 7b.

The change in wetland could also be due to its seasonal development over time. Hence, intermediate marsh with large vegetation stems properly oriented could allow for double bounce scattering mechanism Figure 7c. As the marsh develops, the strong observed double bounce scattering mechanism gradually decreases in favor of the volume scattering Figure 7d from the dense canopy of the fully developed marsh [ 28 ]. Shallow open water wetlands Figure 2e are ponds of standing water bodies, which represent a transition stage between lakes and marshes.

Spaceborne remote sensing technology is necessary for effective monitoring and mapping of wetlands. The use of this technology provides a practical monitoring and mapping approach of wetlands, especially for those located in remote areas [ 5 ]. Wetlands are usually located in remote areas with limited accessibility. Thus, remote sensing technology is attractive for mapping and monitoring wetlands. Synthetic Aperture Radar SAR systems are active remote sensing systems independent of weather and sun illumination.

SAR systems transmit electromagnetic microwave from their radar antenna and record the backscattered signal from the radar target [ 6 ]. The sensitivity of SAR sensors is a function of the: 1 band, polarization, and incidence angle of the transmitted electromagnetic signal and 2 geometric and dielectric properties of the radar target [ 7 ].

Radar targets can be discriminated in a SAR image if their backscattering components are different and the radar spatial resolution is sufficient to distinguish between targets [ 6 ].

### Remote Sensing, GIS, and Radar

In SAR systems, polarization is referred to the orientation of the electrical field of the electromagnetic wave. A single polarized SAR system is a SAR system which transmits one horizontally or vertically polarized signal and receives the horizontal or vertical polarized component of the returned signal. A dual polarized SAR system is a SAR system which transmits one horizontally or vertically polarized signal and receives both the horizontal and vertical polarized components of the returned signal. A single or dual polarized SAR system acquires partial information with respect to the full polarimetric state of the radar target.

A fully polarimetric SAR system transmits alternatively horizontally and vertically polarized signal and receives returns in both orthogonal polarizations, allowing for complete information of the radar target [ 6 , 8 ].