Pasquale Imperatore

Electromagnetic Wave Scattering From Layered Structures With an Arbitrary Number of Rough Interfaces

A closed-form first-order perturbative solution to the problem of electromagnetic scattering from a layered structure with an arbitrary number of rough interfaces is presented in this paper. Following the classical scheme employed to deal with a rough surface, a perturbative expansion of the fields in the rough-interface layered structure is performed, assuming that roughness heights and slopes are small enough. In this manner, in the first-order approximation, the geometric randomness of the corrugated interfaces is translated into random current sheets imposed on the unperturbed (flat) interfaces and radiating in the unperturbed (flat boundaries) layered media. The scattered field is then represented as the sum of up- and down-going waves, and a systematic approach that involves the use of matrix formalism and generalized reflection/transmission coefficients is employed. This approach permits us to avoid the necessity of the cumbersome Green function formalism. The demonstration of the consistency of the presented solution is analytically provided, showing that the proposed solution reduces to the corresponding existing ones when the stratification geometry reduces to the simplified ones considered by the other authors.

SBAS-DInSAR Parallel Processing for Deformation Time-Series Computation

The aim of this paper is to design a novel parallel computing solution for the processing chain implementing the Small BAseline Subset (SBAS) Differential SAR Interferometry (DInSAR) technique. The proposed parallel solution (P-SBAS) is based on a dual-level parallelization approach and encompasses combined parallelization strategies, which are fully discussed in this paper. Moreover, the main methodological aspects of the proposed approach and their implications are also addressed. Finally, an experimental analysis, aimed at quantitatively evaluating the computational efficiency of the implemented parallel prototype, with respect to appropriate metrics, has been carried out on real data; this analysis confirms the effectiveness of the proposed parallel computing solution. In the current scenario, characterized by huge SAR archives relevant to the present and future SAR missions, the P-SBAS processing chain can play a key role to effectively exploit these big data volumes for the comprehension of the surface deformation dynamics of large areas of Earth.

Scattering From Layered Structures With One Rough Interface: A Unified Formulation of Perturbative Solutions

In this paper, we investigate analytically the connection between the existing first-order small perturbation method solutions for the scattering from a layered structure with one rough interface. First of all, by using effectively the concept of generalized reflection coefficients, we cast the existing models in a unified more compact formulation and point out the connection between the different analytical solutions. The obtained reformulations of the available analytical solutions allow us to subsequently prove the consistency of the considered models. Finally, a suitable expansion is performed that leads us to understand the physical meaning of the analytical expressions. The obtained unified formulation also opens the way toward a general closed-form solution for the problem of scattering by a layered structure with an arbitrary number of corrugated interfaces.

Transmission Through Layered Media With Rough Boundaries: First-Order Perturbative Solution

We investigate analytically the fully polarimetric electromagnetic wave propagation through a 3-D layered structure. In the framework of the first-order limit of the perturbation theory, a transmission model for a layered structure with an arbitrary number of rough interfaces is developed and an elegant closed-form solution is obtained. The final expressions, in terms of generalized reflection/transmission coefficients, provide parametrically a direct characterization of the scattering properties of the layered structure in terms of the structures (geometric and electromagnetic) parameters. In addition, we point out the complementary character of the obtained scattering solution with respect to the existing one. Finally, we demonstrate that our solution satisfies the reciprocity principle.

Volumetric-Perturbative Reciprocal Formulation for Scattering From Rough Multilayers

We present an innovative formulation for the evaluation of the electromagnetic wave interaction with non trivial random stratifications that can include the cases of random roughnesses and volumetric inhomogeneity; the formulation is based on a volumetric perturbative approach and it is intrinsically reciprocal. The description employed to model the multilayered structure relies on a characterization of the space-variant dielectric permittivity perturbation; this approach allows us to consistently treat both interface roughness and volumetric fluctuations. Accordingly, the developed comprehensive scattering approach methodologically permits to, simultaneously and rigorously, take into account both rough-interface scattering and volume scattering. The presented first-order general formulation is then applied to the case of a layered structure with rough interfaces, but no inhomogeneities within each layer. For this case, a closed-form solution is obtained. We also demonstrate that the polarimetric solution, derived for a 3-D layered geometry and a bistatic radar configuration can be directly expressed in terms of unperturbed solutions. Our solution turns out to be formally fully consistent with the one obtained in the theoretical framework of the boundary perturbation approach. A remarkable interpretation of the analytical solution in terms of the Rumseys reaction concept is finally provided.

Physical Meaning of Perturbative Solutions for Scattering From and Through Multilayered Structures With Rough Interfaces

Theoretical formulas without a clear comprehension of their intrinsic meaning are of difficult use in the context of practical applications. In this paper, we investigate on the physical meaning of existing first-order solutions for the field scattered by layered structures with rough interfaces, which were derived by Imperatore in the framework of perturbation theory. To capture the intrinsic significance of the closed-form scattering solutions, suitable expansions are rigorously performed by leveraging on local scattering descriptors. The obtained series expansions, which can be seen as ray series, can be then accurately analyzed showing that each term has a direct physical explanation. The analysis is carried out for both from- and through-layered-structure scattering configurations. As a result, analytical perturbative solutions turn out to be completely interpretable by simple physical concepts, so that the global scattering response can be interpreted as the superposition of single-scattering interaction mechanisms taking place locally, which are filtered by the layered structure. The meaning of the first-order approximation is also discussed in the layered structure context. Finally, we give a complete explanation for the scattering enhancement phenomenon contemplated in the first-order limit.

Integration of Optical and SAR Data for Burned Area Mapping in Mediterranean Regions

The aim of this paper is to investigate how optical and Synthetic Aperture Radar (SAR) data can be combined in an integrated multi-source framework to identify burned areas at the regional scale. The proposed approach is based on the use of fuzzy sets theory and a region-growing algorithm. Landsat TM and (C-band) ENVISAT Advanced Synthetic Aperture Radar (ASAR) images acquired for the year 2003 have been processed to extract burned area maps over Portugal. Pre-post fire SAR backscatter temporal difference has been integrated with optical spectral indices to the aim of reducing confusion between burned areas and low-albedo surfaces. The output fuzzy score maps have been compared with reference fire perimeters provided by the Fire Atlas of Portugal. Results show that commission and omission errors in the output burned area maps are a function of the threshold applied to the fuzzy score maps; between the two extremes of the greatest producer’s accuracy (omission error < 10%) and user’s accuracy (commission error < 5%), an intermediate threshold value provides errors of about 20% over the study area. The integration of SAR backscatter allowed reducing local commission errors from 65.4% (using optical data, only) to 11.4%, showing to significantly mitigate local errors due to the presence of cloud shadows and wetland areas. Overall, the proposed method is flexible and open to further developments; also in the perspective of the European Space Agency (ESA) Sentinel missions operationally providing SAR and optical datasets.

Scattering from a layered medium with one rough interface: comparison and physical interpretation of different methods

In this paper we show that existing small perturbation-based methods for computation of scattering from a layered structure with a single rough interface are substantially equivalent. In addition, a further reformulation of the scattered field expression allows us to express the final solution in series form: we then show that each term of the series has a direct physical interpretation.

Second-Order Volumetric-Perturbative Reciprocal Scattering Theory

The aim of this paper is to show how effective analytical treatment of electromagnetic scattering in random 3-D structures becomes viable passing through a complete reconsideration of the perturbative methodology. We propose a general formulation of the volumetric-perturbative reciprocal theory (VPRT), including up to second-order effects. This approach for scattering in random structures along with its derivation holds some remarkable properties: it is methodologically based on volumetric perturbations of the scattering medium structural dielectric properties, so encompassing both interfacial and volume inhomogeneities; its derivation is systematic, by using the reciprocity theorem, so providing meaningful reaction-based general expression for the scattering field; its results are rigorously and easily derived under the purview of distribution theory for discontinuous test functions; its physical counterpart is clear also showing the concepts and role of local and non local scattering. To elucidate the practical power of the VPRT construct, we apply it to the canonical gently rough surface case: the specific solution, which is here derived in a conceptually neat way, is fully consistent with classical second-order SPM one. Finally, the proposed VPRT construct provides a direct attitude to analytically approach a wide class of complex scattering problems that can be arranged in a perturbation framework.

Perturbation Theory for Scattering from Multilayers with Randomly Rough Fractal Interfaces: Remote Sensing Applications

A general, approximate perturbation method, able to provide closed-form expressions of scattering from a layered structure with an arbitrary number of rough interfaces, has been recently developed. Such a method provides a unique tool for the characterization of radar response patterns of natural rough multilayers. In order to show that, here, for the first time in a journal paper, we describe the application of the developed perturbation theory to fractal interfaces; we then employ the perturbative method solution to analyze the scattering from real-world layered structures of practical interest in remote sensing applications. We focus on the dependence of normalized radar cross section on geometrical and physical properties of the considered scenarios, and we choose two classes of natural stratifications: wet paleosoil covered by a low-loss dry sand layer and a sea-ice layer above water with dry snow cover. Results are in accordance with the experimental evidence available in the literature for the low-loss dry sand layer, and they may provide useful indications about the actual ability of remote sensing instruments to perform sub-surface sensing for different sensor and scene parameters.