Jose Luis Alvarez-Perez

The TerraSAR-X Antenna Model Approach

TerraSAR-X is a highly flexible X-band radar satellite. Its primary objective is the acquisition of high quality SAR images in a multitude of possible acquisition modes. The great amount of antenna patterns needed for image acquistion requires an antenna model accurately describing all beams. To guarantee the required image quality, the model has to be verified on-ground and validated in-orbit. The results of the verification will be described here as well as the validation approach.

Coherence, Polarization, and Statistical Independence in Cloude–Pottier's Radar Polarimetry

The Cloude-Pottier radar polarimetry paradigm, which is understood as the spectral decomposition theorem of the target coherency matrix plus the classification technique based on the triad of parameters given by entropy, alpha angle, and anisotropy, has become a very well-established methodology for treating high-resolution polarimetric radar images, particularly those obtained with synthetic aperture radar (SAR) sensors. This methodology is revisited here from the standpoint of the coherence and polarization theory and their mutual relationship, in the light of the interest aroused once again after Wolfs article on this subject in 2003. Despite its success in terms of acceptance by the SAR community, the Cloude-Pottier paradigm relies on the arguable assumption that different scattering mechanisms can be separated by diagonalizing the aforementioned coherency matrix and then assigning each corresponding eigenvector to one of the independent scattering mechanisms. Our main statement in this paper is that the coherency matrix illustrates the behavior of the target from the point of view of polarization and not of full coherence, which would justify this assumption, even if only partially. Therefore, it is not rigorous to identify each eigenvector of this decomposition with a distinct scattering mechanism. Cloude and Pottier argue that the eigendecomposition of the coherency matrix outperforms other target decomposition theorems due to its uniqueness. It is also suggested that this very uniqueness, together with the orthogonality of the eigenvectors, supports the injective mapping between scattering mechanisms and eigenvectors that was first assumed based on statistical independence. With the aim of providing a comprehensive overview of the problem, we discuss some important concepts with regard to both field and target coherency matrices. In addition, we revise the concepts of entropy, alpha angle, and anisotropy as defined by the aforementioned authors, which are also a central part of this paradigm and which have played an important role in SAR image classification since its introduction. Again, some disagreement is found with the meaning of these parameters as they have been discussed so far.

The IEM2M rough-surface scattering model for complex-permittivity scattering media

The integral equation model (IEM) was developed in the late 1980s and arguably became the most cited and implemented rough-surface scattering model in the field of radar remote sensing for Earth observation. It was derived by applying a second-order iteration in the incident electromagnetic field to the integral equations of the surface fields as given by Poggio and Miller. It is thus an extension of the first-order, Born approximation of these equations that produce the classical Kirchhoff approximation. The IEM has been subject to numerous amendments and variations over the last 20 years due to the imperfect introduction and handling of the Weyl representation of the spherical wave in its first version. The work presented here is a further development of the contribution made by the same author in 2001 (IEM2M), which was the first version of IEM able to blend analytically both the Kirchhoff and the small-perturbation approximations for the bistatic case. The improvement reported in this article is concerned with the inclusion of evanescent waves in the formulation of the model and the extension of the range of applicability of the second-order scattering terms to interfaces with complex-permittivity scattering media.

TerraSAR-X Antenna Pattern Estimation by a Complex Treatment of Rain Forest Measurements

Abstract—In this paper an elaborated development over the usual way of estimating a SAR antenna pattern with measurements over the rain forest is presented. The current standard procedure is to fit these data to a polynomial curve or sometimes to a power-cosine law. This antenna model is not a physical one but a convenient mathematical simplification to eliminate noise. This work’s contribution is the implementation of a physically meaningful model, i.e. a superposition of far-field wave fronts from each of the array elements, together with the Singular Value Decomposition (SVD) technique. In addition to eliminate noise, this method allows us to obtain an estimate of the in-flight corrected excitation laws of the antenna array. The motivation of the study is the characterisation of the German TerraSAR-X satellite antenna, a phased array consisting of 384 subarrays, each of which contains two slotted waveguides, one for horizontal and one for vertical polarisation. The utility of the technique is tested on data acquired by the ASAR instrument onboard the ESA ENVISAT satellite, more specifically from both image (IMP) and wide swath mode (WSM) products.

Analysis of the sea clutter structure using temporal sequences of X-band marine radar images

This work analyses the spectral structure of the sea clutter obtained from temporal sequences of radar images of the sea surface. The images were acquired by ordinary marine radars, which work in X-band and horizontal polarization. The study analyses the different contributions to the sea clutter spectrum due to those phenomena, such as ocean waves, speckle due to sea surface roughness, etc. that causes the final clutter image in the radar screen.

Renormalization of the Helmholtz equation for the problem of electromagnetic propagation in a layer of spherical scatterers

The main objective of the present study is to investigate the problem of coherent scattering from a half-space of discrete scatterers by importing a simple version of the renormalization formalism, which has been of great use in other fields such as solid state physics or particle physics. Thus, renormalization is applied to solve the Dyson equation for the scattering problem of a half-space of uncorrelated and isotropic, uniformly distributed scatterers of spherical shape. Renormalization has been used before for analysing wave propagation through inhomogeneous, continuous random media. However, it has not been applied to the problem of a random distribution of discrete scatterers. Here the quasiparticle view of wave propagation is introduced and renormalization in the wave vector domain for a medium containing spherical scatterers is performed. The presence of a single or even a number of well-defined scatterers, randomly repeated throughout the embedding medium, gives enough regularity to the problem so that it is possible to obtain a first-order description of the propagating field even if there is no correlation between scatterers.

Emissivity Calculations for two-dimensional ocean Surfaces with the improved Integral Equation Model IEM2M

The Integral Equation Model (IEM) was developed originally by Fung and Pan (1986). The assumptions inherent to the model were amended in later publications but there were several important points that remained unclear and that propagated across all subsequent versions of the model. One of the authors of this paper proposed an improved IEM, called IEM2M (Alvarez-Perez, 2001), which removed these unnecessary assumptions and unified the small perturbation model (SPM) and the Kirchhoff approximation (KA) for bistatic scattering. This model was first criticized by Fung (2002) but later adopted by him and co-workers in 2003 and renamed as AIEM (advanced IEM). In contrast to other versions of IEM, IEM2M (integral equation model for second-order multiple scattering) is fully consistent with the SPM. This limit arises naturally from the second-order scattering terms when they produce an extra first-order contribution due to the local non-flatness, and therefore non-Kirchhoff character, of the surface. A central role in the IEM2M is played by a rigorous use of the Weyl representation of the retarded Green function through a homogeneous medium as well as a more physically based selection of the Fresnel coefficients. A further assessment of the model is its implementation for the problem of emissivity calculation. The difference between emissivity from a flat surface and a rough sea-like surface is very small and therefore demands an accurate description of the scattering coefficient, which must be integrated for all angles. Whereas an accuracy of 25% or 1 dB is sufficient for active remote sensing, passive remote sensing calculations require that energy conservation has to be typically within 0.3% error, which is the order of the aforementioned difference for flat and rough, sea-like surface emissivities.

A Multidimensional Extension of the Concept of Coherence in Polarimetric SAR Interferometry

Interferometric synthetic aperture radar (InSAR) is a phase-based radar signal processing technique that has been addressed from a polarimetric point of view since the late 1990s, starting with Cloude and Papathanassious foundational work. Polarimeric InSAR (PolInSAR) has consolidated as an active field of research in parallel to non-PolInSAR. Regarding the latter, there have been a number of issues that were discussed in an earlier paper from which some other questions related to Cloudes PolInSAR come out naturally. In particular, they affect the usual understanding of coherence and statistical independence. Coherence involves the behavior of electromagnetic waves in at least a pair of points, and it is crucially related to the statistical independence of scatterers in a complex scene. Although this would seem to allow PolInSAR to overcome the difficulties involving the controversial confusion between statistical independence and polarization as present in PolSAR, Cloudes PolInSAR originally inherited the idea of separating physical contributors to the scattering phenomenon through the use of singular values and vectors. This was an assumption consistent with Cloudes PolSAR postulates that was later set aside. We propose the introduction of a multidimensional coherence tensor that includes PolInSARs polarimetric interferometry matrix Ω12 as its 2-D case. We show that some important properties of the polarimetric interferometry matrix are incidental to its bidimensionality. Notably, this exceptional behavior in 2-D seems to suggest that the singular value decomposition (SVD) of Ω12 does not provide a physical insight into the scattering problem in the sense of splitting different scattering contributors. It might be argued that Cloudes PolInSAR in its current form does not rely on the SVD of Ω12 but on other underlying optimization schemes. The drawbacks of such ulterior developments and the failure of the maximum coherence separation procedure to be a consistent scheme for surface topography estimation in a two-layer model are discussed in depth in this paper. Nevertheless, turning back to the SVD of Ω12, the use of the singular values of a prewhitened version of Ω12 is consistent with a leading method of characterizing coherence in modern Optics. For this reason, the utility of the SVD of Ω12 as a means of characterizing coherence is analyzed here and extended to higher dimensionalities. Finally, these extensions of the concept of coherence to the multidimensional case are tested and compared with the 2-D case by numerically simulating the scattered electromagnetic field from a rough surface.

An extension of the integral equation model IEM2M for rough surfaces of complex permittivity

The integral equation model (IEM) developed by A.K. Fung and co-workers has arguably been the most cited and implemented rough surface scattering model in the field of radar remote sensing. It was obtained as a second-order iteration of the incident electromagnetic field to the integral equations of the surface fields. Therefore, it is an extension of the first-order Born approximation of the corresponding Neumann series that produce the classical Kirchhoff approximation. The IEM was tuned many times over the last twenty years due to the imperfect introduction and handling of the Weyl representation of the spherical wave in its first version. The work presented here is a development of the contribution made by the same author in 2001 (IEM2M) and reported extensively in [1] (IEM2Mc). It has been the first version of IEM able to blend analytically both the Kirchhoff and the small-perturbation approximations for the bistatic case and dielectric surfaces. IEM2M was celebrated by those who found the original IEM not enough rigorous but also criticized by Fung and his co-workers. In this paper an extension of IEM2M is presented that extends it in two aspects: the inclusion of evanescent waves in the formulation of the model and the extension of the range of applicability of the second-order scattering terms to interfaces with complex permittivity scattering media. These two issues had only been addressed in the IEM version developed by Du. However, Du needed to make a mathematical assumption on the correlation function which was not explained from a physical point of view. In the work proposed here this assumption is not necessary. Although all these issues are dealt with extensively in [1], this paper focuses on the comparison of IEM2M, IEM2Mc, the Kirchhoff approximation (KA) and the Small Perturbation Method (SPM). account of them. Regarding IEM, Fungs last update on his version of IEM is available in [2].

The Extended Integral Equation Model IEM2M for Topographically Modulated Rough Surfaces

Remote sensing of terrain and ocean surfaces is circumscribed in the physical domain of electromagnetic scattering by rough surfaces. The development of accurate models has gathered a great deal of efforts since the 80’s. Until that moment there were two classical approaches to be applied to two different asymptotic cases: the surfaces with small roughness and those having long correlation length. The first situation was dealt successfully via the small perturbation method (SPM)) whereas the second one was the target of the Kirchhoff approximation (KA). In effect, the abundance of models in the last two decades has made it very difficult for the Earth Observation practitioner to properly classify them and choose between them. The most important effort to that purpose was made by Tanos Elfouhaily in Elfouhaily & Guerin (2004), and we refer to his work for those interested in having a comprehensive account of the available methods for the problem. We focus here on the model that has arguably awakened the largest share of interest within the remote sensing community, that is, the Integral Equation Model (IEM) presented by Fung and Pan in Fung & Pan (1986) and later corrected in a long series of amendments by the same authors Fung (1994); Hsieh et al. (1997); Chen et al. (2000); Fung et al. (2002); Chen et al. (2003); Fung & Chen (2004); Wu & Chen (2004); Wu et al. (2008). In effect, there has been a number of issues that made the model theoretically inconsistent, even if each amendment was accompanied by properly suiting numerically simulated results. In 2001 the author of this chapter carried out a complete revision of Fung’s work and proposed a corrected IEM that successfully achieved one of the objectives of the rough surface scattering models developed so far: to unify in a single equation both the SPM and the KA in the most general case of bistatic scattering. This corrected IEM was named IEM with proper inclusion of multiple scattering at second order or IEM2M. This chapter aim is twofold: on the one had a quick summary of the IEM2M is given and on the other an extension of it is proposed to include those surfaces comprising both a zero-mean height, random component and a deterministic component that we call here “topographical”.