Distorted Born Approximation Research Articles

Calculation and analysis for p + 50,52,53,54,natCr reactions

All cross sections, elastic and inelastic scattering angular distributions, energy spectra and double differential cross sections of six outgoing particles (n, p, d, t, helium-3 and α) for p+50,52,53,54,natCr reactions are calculated and analyzed at incident proton energies below 150MeV. The optical model, the intra-nuclear cascade model, evaporation model, Hauser–Feshbach theory with width fluctuation correction, exciton model which includes the improved Iwamoto–Harada model and distorted Born approximation theory are involved in the calculation. The calculated results are compared with existing experimental data.

A Generalized Radar Backscattering Model Based on Wave Theory for Multilayer Multispecies Vegetation

A generalized radar scattering model based on wave theory is described. The model predicts polarimetric radar backscattering coefficients for structurally complex vegetation comprised of multiple species and layers. Compared to conventional two-layer crown-trunk models, modeling of actual forests has been improved substantially, allowing better understanding of microwave interaction with vegetation. The model generalizes an existing single-species discrete scatterer model and, by including scattering and propagation effects through judiciously defined vegetation layers, enables its application to an arbitrary number of species types. The scatterers within each layer are modeled as finite cylinders or disks having arbitrary size, density, and orientation, as in the predecessor model. The distorted Born approximation is used to represent the propagation through each layer, while scattering from each is modeled as a linear superposition of scattering from its respective random collection of scatterers. Interactions of waves within and between each layer and direct scattering from the ground are accounted for. Validation of the model is presented based on its application to 23 wooded savanna sites located in Queensland, Australia, and comparison with Advanced Land Observing Satellite (ALOS) Phased Arrayed L-band Synthetic Aperture Radar (PALSAR) and National Aeronautics and Space Administration (NASA) Jet Propulsion Laboratory (JPL) Airborne Synthetic Aperture Radar (AIRSAR) data. Results indicate good agreement between simulated and actual backscattering coefficients, particularly at HH and VV polarizations. More discrepancies are found at HV polarizations and can be explained by uncertainties in the knowledge of input parameters, such as inaccuracies in the surface model, surface roughness parameterization, and soil moisture.

Third Bose fugacity coefficient in one dimension, as a function of asymptotic quantities

In one of the very few exact quantum mechanical calculations of fugacity coefficients, [L.R. Dodd, A.M. Gibbs. J. Math. Phys. 15 (1974) 41] obtained b 2 and b 3 for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For b 2, we have shown [A. Amaya-Tapia, S.Y. Larsen, M. Lassaut. Mol. Phys. 103 (2005) 1301–1306. < arXiv:physics/0405150>] that Dodd and Gibbs’ result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in one dimension. Now, we develop an exact expression for b 3 - b 3 0 (where b 3 0 is the free particle fugacity coefficient) in terms of sums and differences of three-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a Distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the twofold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel. The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.

Fast inverse scattering solutions using the distorted Born iterative method and the multilevel fast multipole algorithm

The distorted Born iterative method (DBIM) computes iterative solutions to nonlinear inverse scattering problems through successive linear approximations. By decomposing the scattered field into a superposition of scattering by an inhomogeneous background and by a material perturbation, large or high-contrast variations in medium properties can be imaged through iterations that are each subject to the distorted Born approximation. However, the need to repeatedly compute forward solutions still imposes a very heavy computational burden. To ameliorate this problem, the multilevel fast multipole algorithm (MLFMA) has been applied as a forward solver within the DBIM. The MLFMA computes forward solutions in linear time for volumetric scatterers. The typically regular distribution and shape of scattering elements in the inverse scattering problem allow the method to take advantage of data redundancy and reduce the computational demands of the normally expensive MLFMA setup. Additional benefits are gained by employing Kaczmarz-like iterations, where partial measurements are used to accelerate convergence. Numerical results demonstrate both the efficiency of the forward solver and the successful application of the inverse method to imaging problems with dimensions in the neighborhood of ten wavelengths.

Calculation by plane wave Born approximation of the electron-impact ionization of Ne, Ar, Kr and Xe

The relativistic and non-relativistic plane wave Born approximation is used to calculate the total electron impact ionization cross-section of Ne, Ar, Kr and Xe. The wavefunctions of the atom and residual ions are calculated with allowance for relaxation effects. The one-electron wavefunction of the continuous spectrum for the ejected electron is obtained by using the Dirac–Fock method. The role of the relativistic, exchange, orthogonalization and relaxation effects are investigated. Results of calculations are compared to available experimental measurements and theoretical calculations performed by other methods. In particular, we presented the results of our nonrelativistic distorted Born approximation calculations.

A comparison of modern data analysis methods for X-ray and neutron specular reflectivity data

Data analysis methods for specular X-ray or neutron reflectivity are compared. The methods that have been developed over the years can be classified into different types. The so-called classical methods are based on Parrat's or Abelès' formalism and rely on minimization using more or less evolved Levenberg–Marquardt or simplex routines. A second class uses the same formalism, but optimization is carried out using simulated annealing or genetic algorithms. A third class uses alternative expressions for the reflectivity, such as the Born approximation or distorted Born approximation. This makes it easier to invert the specular data directly, coupled or not with classical least-squares or iterative methods using over-relaxation or charge-flipping techniques. A fourth class uses mathematical methods founded in scattering theory to determine the phase of the scattered waves, but has to be coupled in certain cases with (magnetic) reference layers. The strengths and weaknesses of a number of these methods are evaluated using simulated and experimental data. It is shown that genetic algorithms are by far superior to traditional and advanced least-squares methods, but that they fail when the layers are less well defined. In the latter case, the methods from the third or fourth class are the better choice, because they permit at least a first estimate of the density profile to be obtained that can be refined using the classical methods of the first class. It is also shown that different analysis programs may calculate different reflectivities for a similar chemical system. One reason for this is that the representation of the layers is either described by chemical composition or by scattering length or electronic densities, between which the conversion of the absorptive part is not straightforward. A second important reason is that routines that describe the convolution with the instrumental resolution function are not identical.

A Modified Born Approximation for Scattering in Isotropic and Anisotropic Elastic Solids

A new modified Born approximation (MBA) is presented that significantly extends the range of validity of the Born approximation to include the pulse-echo responses of strongly scattering inclusions in an elastic solid. The MBA also improves on the doubly distorted Born approximation (DDBA), a similar modification of the Born approximation that has been recently developed. These improvements are demonstrated by comparing the MBA, the Born approximation and the DDBA with the exact separation of variables solution for spherical inclusions in isotropic media. Furthermore, it is shown that the form of the MBA remains valid even for the pulse-echo scattering of an anisotropic inclusion in a general anisotropic elastic medium so that it is potentially applicable to a wide class of flaws and materials.

Improving the Born approximation for the scattering of ultrasound in elastic solids

It has recently been demonstrated that the Born approximation for predicting the scattering response of flaws can be improved through the use of simple modifications called the “doubly distorted Born approximation”. In this paper the doubly distorted Born approximation itself is modified with phase and amplitude corrections that further improve the Born scattering results for isotropic elastic media. The reliability of this new modification of the Born approximation has been evaluated by comparison with the exact solution for spherical inclusions obtained with the method of separation of variables. Unlike the ordinary Born approximation which works well only for very weak scattering inclusions, our modification of the doubly distorted Born approximation gives improved scattering results for both weak and strong scattering inclusions.

An enhanced millimeter-wave foliage propagation model

In this paper, the behavior of wave propagation through coniferous forest stands at millimeter-wave frequencies is characterized both theoretically and experimentally. A coherent wave propagation model is used to simulate the propagation through foliage. The coherent model is composed of two components: a forest stand generator that makes use of a stochastic fractal model, and an electromagnetic model that makes use of Foldy's approximation and single scattering. An outdoor measurement system is designed and used for characterizing the channel behavior for a pine tree stand at Ka-band (35 GHz). In this experiment, 84 independent spatial samples of transmitted signal through the pine stand were collected to obtain the path-loss statistics. The comparison between measurement and simulation results showed that single scattering theory overestimates the wave attenuation through foliage. To improve the accuracy of the coherent model, partial multiple scattering occurred among the needles of highly dense leaf clusters must be included for the estimation of the coherent attenuation. Distorted Born approximation is used to macromodel the scattering pattern from needle clusters. This technique has comparable accuracy and requires much less computational resources than a full-wave solution, such as method of moment. By including multiple scattering effects of needle clusters in the simulation model, much better agreement is obtained for both mean and standard deviation of the path-loss.

Effect of source and receiver radiation characteristics in subsurface prospecting within the distorted Born approximation

Linear models are widely adopted in subsurface prospecting because of the advantages in terms of effectiveness and numerical efficiency. They make it possible to simplify the problem of inverse scattering and at the same time to obtain acceptable results in locating buried objects. In this paper, we deal with subsurface prospecting where a model linearization is performed via distorted Born approximation and considering a half‐space geometry in a two‐dimensional scalar problem within a multistatic/multiview configuration. In this realm, most inversion algorithms fail to take into account the radiation properties of both transmitting and receiving antennas. Our goal is thus twofold. First, we aim to provide an insight into the role played by the radiation properties of antennas on the quality of the reconstructed tomographic image of the investigated domain. This task is performed by first tackling the single‐frequency case in order to gain insight into the effect of the radiation pattern using simple arguments and then examining the multifrequency case. Numerical results confirm the theoretical expectation that the quality of the reconstruction gets worse for antennas with directive radiation patterns. Second, we numerically investigate the effects of inaccurate knowledge of the antenna pattern.

Frequency Diversity in a Linear Inversion Algorithm for GPR Prospecting

We investigate the frequency spacing in multifrequency/multistatic/multiview measurement configuration for GPR prospecting. The Distorted Born Approximation is assumed so leading to a linear inversion problem. The analysis is first performed in a simplified lossless environment to obtain guidelines and next results are confirmed by numerical inversion. The number of relevant frequency data is estimated according to extent of the observation and investigation domains and the dielectric permittivity of the host medium. It is found that both a non uniform and an uniform spacing provide reconstructions of comparable quality.

Effects of uncertainty on background permittivity in one-dimensional linear inverse scattering

We discuss the role of uncertainties in the knowledge of the background in inverse scattering for a buried object under the distorted Born approximation. In particular, we focus on the role played by inaccuracy in the knowledge of the dielectric permittivity of the host medium, with reference to both a lossless half-space and a lossless three-layered medium. This investigation allows us to show how reconstruction of an inhomogeneity in a three-layered medium is more critical than in the case of a half-space (two-layered) geometry.

Reconstruction of an Embedded Slab From Multifrequency Scattered Field Data Under the Distorted Born Approximation

This paper deals with the inverse scattering problem regarding a loss-less dielectric slab embedded in a loss-less homogeneous half-space starting out from the knowledge of multifrequency scattered field data. The distorted Born approximation of the electromagnetic scattering is assumed and the features of two linear operators, accounting for the electromagnetic scattering and differing on account of the excitation law of the impinging plane wave, are discussed in terms of model error and class of retrievable unknowns by means of singular value decomposition (SVD) analysis. In particular, it is outlined how a suitable choice of the excitation of the impinging wave makes it possible to improve the reconstruction capabilities of the solution algorithm. In addition, the SVD-based solution approach makes it possible to handle the ill-posedness and to regularize the problem. Numerical results confirm the effectiveness of the approach and the theoretical expectations.

Three-Dimensional Reconstruction of Objects Buried in Layered Media Using Born and Distorted Born Iterative Methods

We develop electromagnetic inverse scattering methods to reconstruct three-dimensional (3-D) objects buried in layered media. The nonlinear inverse problem is solved iteratively via the conjugate-gradient approach; within each iteration, the problem is linearized by Born and distorted Born approximations. The forward solution for layered media is provided by the stabilized biconjugate-gradient fast Fourier transform method. The inversion results from the Born and distorted Born iterative methods are presented, and the effects of the aperture size and noise on the inversion results are also investigated. Numerical results show that these methods are capable of reconstructing an arbitrary 3-D inhomogeneous object buried in a multilayered medium with high resolution.

Scattering from a layer of discrete random medium over a random interface: application to microwave backscattering from forests

The distorted Born approximation is used to calculate the bistatic scattering coefficients from a layer of sparsely distributed discrete dielectric scatterers over a random interface. After specializing to the backscatter case, the scattering coefficient is determined as a sum of direct, direct reflected and interface scatter contributions. The direct reflected term contains contributions from the average interface and the interface fluctuations. These direct reflected terms include both incoherent and coherent or enhancement terms. The results are applied to backscattering from a mature hemlock forest over a roughened ground. The model results show that the direct reflected surface fluctuation terms give the dominant contribution to backscatter at P band and are equal in magnitude to the volume scatter at L band. Use of these new results brings the model predictions and experimental results into agreement.

Analysis of the distorted born approximation for subsurface reconstruction: truncation and uncertainties effects

The problem of determining the dielectric permittivity profile of buried objects starting from the knowledge of the scattered field is considered in the two-dimensional geometry when incomplete near-zone data are collected at a single frequency under a multiview/multistatic measurement configuration. In particular, attention is paid to the practical issues of the truncated observation domain and the presence of uncertainties on data. The problem is tackled with reference to the scalar polarization by linearization of the mathematical relationship between the unknown dielectric permittivity profile and the scattered field. A homogeneous, possibly lossy, half-space geometry for the subsurface modeling is adopted, thus leading to the so-called distorted Born approximation (DBA). A thorough investigation of the class of unknown functions that can be reliably retrieved is performed by dealing with singular value decomposition of the relevant linear operator. It results that even if sources and receivers are located at the interface, a very restricted set of profile variations can be reconstructed by a stable inversion algorithm. In particular, reduced vertical features of the buried objects with respect to the horizontal ones can be reconstructed under DBA. Moreover, the truncation of the observation domain further restricts this set, affecting mainly the vertical resolution. Numerical results confirming the validity of the analysis are also provided.

SCATTERING FROM WET SNOW BY APPLYING STRONG FLUCTUATION THEORY

In this study, the strong fluctuation theory is applied to calculate the scattering from a half space of wet snow. The first and second moments of the fields are calculated using the bilocal and the distorted Born approximations, and the low frequency limit is taken. The singularity of the dyadic Green's function is taken into account. The effective permittivity of wet snow is calculated using the two-phase model with non-symmetrical inclusions. In the two-phase model, wet snow is assumed to consist of dry snow (host) and liquid water (inclusions). Numerical results for the backscattering coefficients of wet snow are illustrated for random media with isotropic and anisotropic correlation functions. The three-phase strong fluctuation theory model with symmetrical inclusions is also presented for theoretical comparison. In the three-phase model, wet snow is assumed to consist of air (host), ice (inclusions) and water (inclusions) and the shape of the inclusions are spherical. The results are in good agreement with the experimental data.

Influence of surface and vegetation characteristics on C-band radar measurements for soil moisture content

Soil moisture estimation using microwave remote sensing faces challenges of the segregation of influences mainly from roughness and vegetation. Under static surface conditions, it was found that Radarsat C-band SAR shows reasonably good correlation and sensitivity with changing soil moisture. Dynamic surface and vegetation conditions are supposed to result in a substantial reduction in radar sensitivity to soil moisture. A C-band scatterometer system (5.2 GHz) with a multi-polarization and multi-angular configuration was used 12 times to sense the soil moisture over a tall vegetated grass field. A score of vegetation and soil parameters were recorded on every occasion of the experiment. Three radar backscattering models Viz., Integral Equation Model (IEM), an empirical model and a volume scattering model, have been used to predict the backscattering phenomena. The volume scattering model, using the Distorted Born Approximation, is found to predict the backscattering phenomena reasonably well. But the surface scattering models are expectedly found to be inadequate for the purpose. The temporal variation of soil moisture does show good empirical relationship with the observed radar backscattering. But as the vegetation biomass increases, the radar shows higher sensitivity to the vegetation parameters compared to surface characteristics. A sensitivity analysis of the volume scattering model for all the parameters also reveals that the radar is more sensitive to plant parameters under high biomass conditions, particularly vegetation water content, but the sensitivity to surface characteristics, particularly to soil moisture, is also appreciable.

Effect of canopy-air interface roughness on HF-VHF wave propagation in forest

The problem of electromagnetic wave propagation in a realistic forest environment in the high-frequency and very high-frequency bands is considered. In particular, the effect of the nonplanar interface between the air and the canopy, which has been ignored in previous models, is examined. An analytical formulation is obtained for the mean field when both the transmitter and the receiver are within the foliage. This formulation is based on distorted Born approximation and accounts for the surface roughness that exists between the canopy and air interface. It is shown that the surface roughness attenuates the so-called lateral wave slightly, which is the dominant source of the field at receiver locations far from the transmitter. It is also shown that this attenuation rate increases when the RMS height of the surface roughness is increased.

Soil moisture inversion at L-band using a dual-polarization technique: A model-based sensitivity analysis

The inverse problem of estimating soil moisture from vegetated and non-vegetated terrain is investigated using a passive microwave technique. The radiometer response at L-band is modelled by the Peake's approach that involves the integration of bistatic scattering coefficients to calculate surface emissivity. For vegetated terrain, a discrete scatter model employing the distorted Born approximation is used to obtain bistatic scattering coefficients. For non-vegetated rough surface, the Kirchhoff 's rough surface approximation is used to calculate bistatic scattering coefficients. A series of vegetated and non-vegetated surfaces are simulated for this study by changing vegetation densities and ground roughness conditions. The forward model is simplified so that it can be inverted with a minimum of auxiliary information about the vegetation and the ground. An inversion procedure is set up such that the ratio of horizontal to vertical Fresnel reflectivity is expressed in terms of dual-polarized microwave brightness temperatures (available from the forward model or a radiometer). The reflectivity ratio expression is then solved to obtain soil moisture. In the case of weak vegetation such as soybean canopy, no information regarding vegetation is necessary in the inversion procedure because the difference between horizontal and vertical optical depth is assumed to be negligibly small at low to medium viewing angles. The consequence of this assumption on the soil moisture estimation from canopies of higher Leaf Area Index (LAI) is analysed. Similarly, in the case of non-vegetated rough terrain, inversion is carried out without information about rough surface because the rms surface roughness height cancels out in ratioing of the Fresnel reflectivity. To account for instrument and other errors in experimental data, a random noise is added to model data and the rms error in soil moisture inversion is calculated for vegetated and non-vegetated terrain. A comparison of the dual polarization with single (horizontal) polarization technique reveals that the dual polarization is a better technique for soil moisture estimation. The sensitivities and implications of a priori information are discussed in the context of developing a soil moisture estimation algorithm from satellites to be launched in the forthcoming space missions.