In this paper, we provide a review of the different approaches used for target decomposition theory in radar polarimetry. We classify three main types of theorem; those based on the Mueller matrix and Stokes vector, those using an eigenvector analysis of the covariance or coherency matrix, and those employing coherent decomposition of the scattering matrix. We unify the formulation of these different approaches using transformation theory and an eigenvector analysis. We show how special forms of these decompositions apply for the important case of backscatter from terrain with generic symmetries.

A review of target decomposition theorems in radar polarimetry

The authors outline a new scheme for parameterizing polarimetric scattering problems, which has application in the quantitative analysis of polarimetric SAR data. The method relies on an eigenvalue analysis of the coherency matrix and employs a three-level Bernoulli statistical model to generate estimates of the average target scattering matrix parameters from the data. The scattering entropy is a key parameter is determining the randomness in this model and is seen as a fundamental parameter in assessing the importance of polarimetry in remote sensing problems. The authors show application of the method to some important classical random media scattering problems and apply it to POLSAR data from the NASA/JPL AIRSAR data base.

An entropy based classification scheme for land applications of polarimetric SAR

An approach has been developed that involves the fit of a combination of three simple scattering mechanisms to polarimetric SAR observations. The mechanisms are canopy scatter from a cloud of randomly oriented dipoles, evenor double-bounce scatter from a pair of orthogonal surfaces with different dielectric constants and Bragg scatter from a moderately rough surface. This composite scattering model is used to describe the polarimetric backscatter from naturally occurring scatterers. The model is shown to describe the behavior of polarimetric backscatter from tropical rain forests quite well by applying it to data from NASA/Jet Propulsion Laboratory's (JPLs) airborne polarimetric synthetic aperture radar (AIRSAR) system. The model fit allows clear discrimination between flooded and nonflooded forest and between forested and deforested areas, for example. The model is also shown to be usable as a predictive tool to estimate the effects of forest inundation and disturbance on the fully polarimetric radar signature. An advantage of this model fit approach is that the scattering contributions from the three basic scattering mechanisms can be estimated for clusters of pixels in polarimetric SAR images. Furthermore, it is shown that the contributions of the three scattering mechanisms to the HH, HV, and VV backscatter can be calculated from the model fit. Finally, this model fit approach is justified as a simplification of more complicated scattering models, which require many inputs to solve the forward scattering problem.

A three-component scattering model for polarimetric SAR data

An algorithm based on a fit of the single-scattering integral equation method (IEM) was developed to provide estimation of soil moisture and surface roughness parameter (a combination of rms roughness height and surface power spectrum) from quad-polarized synthetic aperture radar (SAR) measurements. This algorithm was applied to a series of measurements acquired at L-band (1.25 GHz) from both AIRSAR (Airborne Synthetic Aperture Radar operated by the Jet Propulsion Laboratory) and SIR-C (Spaceborne Imaging Radar-C) over a well-managed watershed in southwest Oklahoma. Prior to its application for soil moisture inversion, a good agreement was found between the single-scattering IEM simulations and the L-band measurements of SIR-C and AIRSAR over a wide range of soil moisture and surface roughness conditions. The sensitivity of soil moisture variation to the co-polarized signals were then examined under the consideration of the calibration accuracy of various components of SAR measurements. It was found that the two co-polarized backscattering coefficients and their combinations would provide the best input to the algorithm for estimation of soil moisture and roughness parameter. Application of the inversion algorithm to the co-polarized measurements of both AIRSAR and SIR-C resulted in estimated values of soil moisture and roughness parameter for bare and short-vegetated fields that compared favorably with those sampled on the ground. The root-mean-square (rms) errors of the comparison were found to be 3.4% and 1.9 dB for soil moisture and surface roughness parameter, respectively.

Estimation of bare surface soil moisture and surface roughness parameter using L-band SAR image data

The Kennaugh-Huynen scattering matrix con-diagonalization is projected into the Pauli basis to derive a new scattering vector model for the representation of coherent target scattering. This model permits a polarization basis invariant representation of coherent target scattering in terms of five independent target parameters, the magnitude and phase of the symmetric scattering type introduced in this paper, and the maximum polarization parameters (orientation, helicity, and maximum return). The new scattering vector model served for the assessment of the Cloude-Pottier incoherent target decomposition. Whereas the Cloude-Pottier scattering type alpha and entropy H are roll invariant, beta and the so-called target-phase parameters do depend on the target orientation angle for asymmetric scattering. The scattering vector model is then used as the basis for the development of new coherent and incoherent target decompositions in terms of unique and roll-invariant target parameters. It is shown that both the phase and magnitude of the symmetric scattering type should be used for an unambiguous description of symmetric target scattering. Target helicity is required for the assessment of the symmetry-asymmetry nature of target scattering. The symmetric scattering type phase is shown to be very promising for wetland classification in particular, using polarimetric Convair-580 synthetic aperture radar data collected over the Ramsar Mer Bleue wetland site to the east of Ottawa, Ontario, Canada

https://www.pcigeomatics.com/pdf/whitepapers/Touzi_target_scattering.pdf

Target Scattering Decomposition in Terms of Roll-Invariant Target Parameters

In this paper we applied Cloude's decomposition to imaging radar polarimetry. We show in detail how the decomposition results can guide the interpretation of scattering from vegetated areas. For multifrequency polarimetric radar measurements of a clear-cut area, the decomposition leads us to conclude that the vegetation is probably thin compared to even the C-band radar wavelength of 6 cm. For a frosted area, we notice an increased amount of even number of reflection scattering at P-band and L-band, probably the result of penetration through the coniferous canopy resulting in trunk-ground double reflection scattering. However, the scattering for the forested area is still dominated by scattering from randomly oriented cylinders. It is found that these cylinders are thicker than in the case of clear-cut areas, leading us to conclude that scattering from the branches probably dominates in this case.

/pdf/application-of-cloude-s-target-decomposition-theorem-to-4stwukyudj.pdf

Application of Cloude's target decomposition theorem to polarimetric imaging radar data

Tunable semiconductor lasers are disclosed requiring minimized coupling regions. Multiple laser embodiments employ ring resonators or ring resonator pairs using only a single coupling region with the gain medium are detailed. Tuning can be performed by changing the phase of the coupling coefficient between the gain medium and a ring resonator of the laser. Another embodiment provides a tunable laser including two Mach-Zehnder interferometers in series and a reflector coupled to a gain medium.

/pdf/tunable-semiconductor-lasers-45hqk8hdo6.pdf

Tunable semiconductor lasers

The invention discloses a semi-ring Fabry-Perot (SRFP) optical resonator structure comprising a medium (102) including an edge (106) forming reflective facet and a waveguide (104) within the medium, the waveguide having opposing ends (108A, 108B) formed by the reflective facet. The performance of the SRFP resonator can be further enhanced by including a Mach-Zehnder interferometer (110) in the waveguide on one side of the medium. The optical resonator can be employed in a variety of optical devices. Laser structures using at least one SRFP resonator are disclosed where the resonators are disposed on opposite sides of a gain medium. Other laser structures employing one or more resonators on one side of a gain region are also disclosed.

/pdf/optical-resonator-and-laser-applications-1nkaamzbrp.pdf

Optical resonator and laser applications

The preliminary results of algorithm development and testing for soil moisture retrieval at high incidence angles are reported. Based on first-order surface backscattering models, a physically based algorithm for retrieval of soil moisture was developed and evaluated using NASA/JPL aircraft synthetic aperture radar (SAR) data. It shows that the copolarization ratio is sensitive to soil moisture change but not to surface roughness at high incidence angles. This algorithm performed well at L-band and should be useful. This study suggests that incidence angles greater than 40 degrees are optimal for such monitoring.

Soil moisture measurements from airborne SAR

The objective is to establish an empirical relationship between measurements of radar, aeolian, and surface roughness on a variety of natural surfaces and to understand the underlying physical causes. This relationship will form the basis for developing a predictive equation to derive aeolian roughness from radar backscatter. Results are given from investigations carried out in 1989 on the principal elements of the project, with separate sections on field studies, radar data analysis, laboratory simulations, and development of theory for planetary applications.

/pdf/radar-aeolian-roughness-project-1w97daqvqg.pdf

Jakob J. Vanzyl

Papers

Application of Cloude's target decomposition theorem to polarimetric imaging radar data

Tunable semiconductor lasers

Optical resonator and laser applications

Soil moisture measurements from airborne SAR

Radar-Aeolian Roughness Project.