Measurements Of Scattered Field Research Articles

A neural network warm-start approach for the inverse acoustic obstacle scattering problem

In this paper, we consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the object. One of the standard approaches for solving this problem is to reformulate it as an optimization problem: finding the boundary of the domain that minimizes the L2 distance between computed values of the scattered field and the given measurement data. The optimization problem is computationally challenging since the local set of convexity shrinks with increasing frequency and results in an increasing number of local minima in the vicinity of the true solution. In many practical experimental settings, low frequency measurements are unavailable due to limitations of the experimental setup or the sensors used for measurement. Thus, obtaining a good initial guess for the optimization problem plays a vital role in this environment.We present a neural network warm-start approach for solving the inverse scattering problem, where an initial guess for the optimization problem is obtained using a trained neural network. We demonstrate the effectiveness of our method with several numerical examples. For high frequency problems, this approach outperforms traditional iterative methods such as Gauss-Newton initialized without any prior (i.e., initialized using a unit circle), or initialized using the solution of a direct method such as the linear sampling method. The algorithm remains robust to noise in the scattered field measurements and also converges to the true solution for limited aperture data. However, the number of training samples required to train the neural network scales exponentially in frequency and the complexity of the obstacles considered. We conclude with a discussion of this phenomenon and potential directions for future research.

Scattering properties of protoplanetary dust analogs with microwave analogy: Aggregates of fractal dimensions from 1.5 to 2.8

Context. The growth of dust grains in protoplanetary disks is not understood in detail. Several studies have proposed the presence of aggregates and irregular grains to overcome the physical barriers in grain growth models. In order to understand the scattering properties of these aggregates, laboratory measurements of light scattering and microwave scattering have been developed over the last 50 years. Aims. We aim to measure the scattering properties of different protoplanetary analog aggregates with fractal dimensions of 1.5, 1.7, 2.0, 2.5, and 2.8. Methods. We used the microwave scattering technique (microwave analogy) for the measurements. The analog particles were virtually generated and fabricated by 3D printing with a controlled size (scaling factor), geometry, and refractive index. The seven analogs were measured at wavelengths ranging from 16.7 mm to 100 mm, leading to aggregate size parameters ranging from Xagg = 1 to Xagg = 20. The results were compared to finite element method calculations of the same analogs for cross-validation. Results. The phase function and the degree of linear polarization were deduced from the scattered field measurements of the different aggregates. These scattering properties are compared and discussed as a function of the fractal dimension. Conclusions. The scattering properties of aggregates with different fractal dimensions are different. Three different realizations of aggregates with the same fractal dimension but different monomer configurations yield the same phase functions. We verified that the maximum degree of linear polarization is higher for porous aggregates than for compact aggregates. Furthermore, the maximum polarization occurs at larger scattering angles for high fractal dimensions, while the half width at half maximum of the phase functions present larger values for small fractal dimensions.

Generation of Prior Information in a Dual-Mode Microwave-Ultrasound Breast Imaging System.

A new breast imaging system capable of obtaining ultrasound and microwave scattered-field measurements with minimal or no movement of the breast between measurements has recently been reported. In this work, we describe the methodology that has been developed to generate prior information about the internal structures of the breast based on ultrasound data measured with the dual-mode system. This prior information, estimating both the geometry and complex-valued permittivity of tissues within the breast, is incorporated into the microwave inversion algorithm as a means of enhancing image quality. Several techniques to map reconstructed ultrasound speed to complex-valued relative permittivity are investigated. Quantitative images of two simplified dual-mode breast phantoms obtained using experimental data and the various forms of prior information are presented. Though preliminary, the results presented herein provide an understanding of the impacts of different forms of prior information on dual-mode reconstructions of the breast and can be used to inform future work on the subject.

On the Use of an Equivalent Currents-Based Technique to Improve Electromagnetic Imaging

Accurate imaging from scattered field measurements is one of the main research topics in the field of Non-Destructive Testing. Different methodologies for inverse scattering have been developed, ranging from backpropagation techniques to full-wave inversion methods. While far field approaches are valid for the majority of the imaging systems, there are some scenarios where these approaches do not provide accurate modeling of the field radiated by the antennas of the imaging system. This results in some kind of distortion in the resulting output microwave images. To address this issue, proper characterization and modeling of the fields radiated by the antennas is required. This contribution proposes the use of an equivalent currents-based technique to characterize the transmitting and receiving antennas of the imaging sensor. The goal is to calculate accurately the field radiated by these antennas within the imaging domain, using it in the backpropagation algorithm. The methodology described in this contribution is supported by measurements for monostatic and multistatic configurations.

Flow monitoring by microwave imaging inside a cuboid cavity: Theory and numerical feasibility analysis

In this paper, we investigate multiphase flow monitoring inside metallic pipes by qualitative microwave imaging, where foreign objects inside the liquid flow are monitored to eliminate contamination. The motivation stems from the fact that conventional tomographic approaches of microwave imaging are inherently not suitable for real-time flow monitoring due to their computational requirements as these techniques aim to retrieve the dielectric permittivity profile inside the pipeline. In this context, we envision that the factorization method of qualitative inverse scattering theory, which is a shape retrieval algorithm from scattered field measurements, provides a better alternative for flow monitoring. To demonstrate the feasibility of such an approach, we first reformulate the factorization method by considering dyadic Green’s functions inside a cuboid cavity with perfectly conducting walls. Later, the formulation is simplified for a specific microwave measurement configuration to accelerate the reconstructions for real-time flow monitoring. Finally, flow monitoring is realized as a differential imaging procedure where foreign objects are detected by using differences of multi-static scattering parameters that are measured consecutively. The simulation studies performed for food and petroleum flows reveal the capabilities of the technique as a viable solution for different industrial flows.

On the Optimal Field Sensing in Near-Field Characterization.

We deal with the problem of characterizing a source or scatterer from electromagnetic radiated or scattered field measurements. The problem refers to the amplitude and phase measurements which has applications also to interferometric approaches at optical frequencies. From low frequencies (microwaves) to high frequencies or optics, application examples are near-field/far-field transformations, object restoration from measurements within a pupil, near-field THz imaging, optical coherence tomography and ptychography. When analyzing the transmitting-sensing system, we can define “optimal virtual” sensors by using the Singular Value Decomposition (SVD) approach which has been, since long time, recognized as the “optimal” tool to manage linear algebraic problems. The problem however emerges of discretizing the relevant singular functions, thus defining the field sampling. To this end, we have recently developed an approach based on the Singular Value Optimization (SVO) technique. To make the “virtual” sensors physically realizable, in this paper, two approaches are considered: casting the “virtual” field sensors into arrays reaching the same performance of the “virtual” ones; operating a segmentation of the receiver. Concerning the array case, two ways are followed: synthesize the array by a generalized Gaussian quadrature discretizing the linear reception functionals and use elementary sensors according to SVO. We show that SVO is “optimal” in the sense that it leads to the use of elementary, non-uniformly located field sensors having the same performance of the “virtual” sensors and that generalized Gaussian quadrature has essentially the same performance.

A Bernoulli–Gaussian Binary Inversion Method for High-Frequency Electromagnetic Imaging of Metallic Reflectors

High-frequency electromagnetic inverse scattering of conductors has many practical applications. Its goal is to reconstruct the shape of conductors from their scattered fields at some distances. When viewed from the pixelated imaging viewpoint, any pixel in the imaging domain is either a conductor or background (air); thus such an inverse scattering problem has binary solutions for all pixels. Under the high-frequency physical optics (PO) approximation, the scattered field is formulated as a linear problem in terms of a local binary shape function. A binary inversion method is proposed for the detection and shape reconstruction of a flat PEC reflector from high-frequency scattered field measurements. To exploit the underlying binary structure, a Bernoulli–Gaussian (BG) prior model is employed to perform a binary enforcement mechanism. This binary enforcement mechanism can push each pixel of the inversion domain to have a value equal to either zero or one. Then, the damped generalized approximate message passing (GAMP) is integrated with the proposed prior model to address the binary linear inverse problem from the Bayesian inference perspective. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed BG Binary Inversion method. The performance improvement of the proposed method is attributed to the exploitation of the binary prior information of the solution and GAMP technique.

90 GHz, 3-D Scattered Field Measurements for Investigation of Foreign Object Debris

Scattering properties of millimeter waves (mmW) remain relatively unknown compared to lower frequency bands, although their study is of interest considering the increasing number of civil applications, especially in the $W$ -band. In this communication, we present an efficient measurement setup that provides scattering measurements with spatial and polarization diversities. The targeted application is foreign object debris (FOD) detection and identification for surveillance of airport runways. Most existing systems are monostatic but rapid advances in mmW technology pushes toward the deployment of multistatic radars on either side of airport runways. In the following, we investigate the contribution of multistatic measurements with a special focus on the reconstruction of glass and brake pad debris, courtesy of DGAC (French civil aviation). We also present an efficient approach for making images of FODs. For this, we process scattered field measurements with an additive (with respect to polarization) backpropagation algorithm. First images include all measured points taken from the upper hemisphere. In order to get closer to the final application, we restrict the field of view to receivers facing the transmitter. Both approaches provide very good shape reconstruction of the glass debris and the central zone of the brake pad. To the best of our knowledge, this is the first time that full-3-D measurements have been conducted on FODs in the $W$ -band. It is also the first example of a 3-D qualitative image of FOD obtained from measured data in the $W$ -band.

Qualitative microwave imaging of breast cancer with contrast agents

A microwave imaging (MWI) methodology for early diagnosis of breast cancer is presented. Instead of generating a tomographic image of the breast, the proposed technique aims to reconstruct a map of malignant tumours inside the breast by adopting an extended form of factorization method. The implementation of factorization method requires (i) two multi-static scattered field measurements around the breast, which correspond to two different states of the breast, and (ii) the inhomogeneous Green’s function associated to the breast. For this purpose, the paper proposes the use of contrast agents, which selectively increase the dielectric properties of the malign tissues. Two multi-static field measurements are collected before and after the administration of contrast agents. Later, the inhomogeneous Green’s function of the breast is estimated by back-propagating the scattered field measurements, which are taken before the contrast agent usage. The feasibility and efficiency of the proposed technique are demonstrated with numerical examples that are performed on a slice of the realistic breast phantoms, which are derived from real three dimensional magnetic resonance imaging (3D-MRI) measurements.

Inverse Scattering Related to Cylindrical Bodies Buried in a Lossy Circular Cylinder with Resistive Boundary

Abstract An inverse scattering problem of cylindrical bodies of arbitrary cross section buried in a circular cylinder with resistive boundary is presented. The reconstruction is obtained from the scattered field measurements for a plane wave illumination under the Born approximation. Illustrative examples are presented in order to see the applicability of the method as well as to see the effects of some parameters on the solution.

Influence of the description of the scattering matrix on permittivity reconstruction with a quantitative imaging procedure: polarization effects.

This paper focuses on the role of polarization-and more specifically, the effect of its selection-in 3D quantitative imaging obtained from scattered field measurements. Although polarization is now commonly used in linear imaging procedures (when unknowns are linked by a linear relationship to the measured signal), the influence of polarization choice is generally ignored in nonlinear imaging problems. In this paper, we propose a formulation to obtain the 3D permittivity map, by a nonlinear imaging procedure, from the scattering matrix. This allows one to select, from the same data set, the desired polarization case as input data for the imaging algorithm. We present a study of the influence of the input data polarization choice on the reconstructed permittivity map. This work shows that a suitable basis choice for the description of the scattering matrix and an appropriate selection of the element of this scattering matrix can greatly improve imaging results.

Brain Stroke Microwave Imaging by Means of a Newton-Conjugate-Gradient Method in <inline-formula> <tex-math notation="LaTeX">$L^{p}$ </tex-math> </inline-formula> Banach Spaces

A conjugate-gradient-based regularization technique in $L^{p}$ Banach spaces, in conjunction with an inexact-Newton solving scheme, is presented in this paper. The proposed method is applied to obtain the reconstruction of the dielectric properties of human tissues in hemorrhagic brain stroke microwave imaging. The dielectric reconstruction is obtained by solving a nonlinear inverse problem, starting from a set of scattered-field measurements. The presented numerical simulations with 2-D and 3-D anatomically realistic phantoms, as well as the preliminary experimental results, show that this method can be useful for retrieving the dielectric properties of the human head with a reduced over-smoothing effect in the final images.

Wideband compact dipole antenna for microwave imaging applications

In this study, the authors present a novel dipole antenna for microwave imaging (MWI) applications. Different from the previous works, the designed dipole is compact while having a wide-impedance bandwidth of 1–4.2 GHz along with a moderate gain. In particular, the largest dimension of the antenna is 6 cm, which is 0.2 wavelength at the very lower end of the operating frequency bandwidth. Furthermore, the resultant design has a cross-polarisation level <20 dB. Important characteristics of the proposed design are given with the simulations through analysis system high-frequency structure simulator. Obtained simulation results are also shown to be consistent with the measurements. In addition to measuring fundamental parameters of the designed dipole, they also test the proposed antenna in a circular MWI system. In this context, several dielectric scatterers are measured in a circular scanner and obtained scattered field measurements are supplied to the well-known contrast source inversion method. Imaging results show that the proposed antenna is quite suitable for MWI applications.

Microwave Imaging of Subsurface Flaws in Coated Metallic Structures Using Complementary Split-Ring Resonators

Microwave testing can detect surface and sub-surface flaws and anomalies under coatings, paint, or dirt in metallic structures. A major application of microwave sensors with an increasing interest is microwave imaging of coated metallic surfaces. Microwave imaging has the capabilities to determine the shape, size, and location of buried flaws using scattered field measurements, because microwave signals can penetrate dielectric coatings. Electrically small complementary split-ring resonators etched on printed circuit boards are strong candidates for microwave imaging as they can provide the benefit of one-sided small footprint sensors while resonating at wavelengths much lower than their dimension to provide high lateral resolution. This paper introduces and investigates the use of complementary split-ring resonators in the microwave regime for imaging subsurface flaws in coated metallic structures. Both transmission and reflection coefficients were studied to build images using magnitude and phase information. Aluminum plates with different corrosion-coated regions were studied numerically and experimentally. The results of a raster scan mechanism demonstrate the viability of the proposed imaging system.

Multi-parameter identification and shape reconstruction for unbounded fractal rough surfaces with tapered wave incidence

In this paper, we study the inverse scattering of tapered waves from sound soft surfaces or horizontally polarized electromagnetic waves from perfectly conducting surfaces. By the related Fréchet derivative with respect to a given surface of the solution of direct scattering problems, an efficient algorithm is proposed to reconstruct the parameters of unbounded rough surfaces from a set of scattered field measurements. Tapered wave is introduced to realize the asymptotic truncation for unbounded fractal rough surface. In order to improve the results of reconstruction, multi-angle and multi-frequency incidence strategy has been used. The numerical results show that the method yields satisfactory reconstructions for some rough surface profiles.

Software Calibration of a Frequency-Diverse, Multistatic, Computational Imaging System

We demonstrate a technique for calibrating a frequency-diverse, multistatic, computational imaging system. A frequency-diverse aperture enables an image to be reconstructed primarily from a set of scattered field measurements taken over a band of frequencies, avoiding mechanical scanning and active components. Since computational imaging systems crucially rely on the accuracy of a forward model that relates the measured and transmitted fields, deviations of the actual system from that model will rapidly degrade imaging performance. Here, we study the performance of a computational imaging system at microwave frequencies based on a set of frequency-diverse aperture antennas, or panels. We propose a calibration scheme that compares the measured versus simulated scattered field from a cylinder and calculates a compensating phase difference to be applied at each of the panels comprising the system. The calibration of the entire system needs be performed only once, avoiding a more laborious manual calibration step for each transmitting and receiving path. Imaging measurements performed using the system confirm the efficacy and importance of the calibration step.

Efficient combination of a 3D Quasi-Newton inversion algorithm and a vector dual-primal finite element tearing and interconnecting method

A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.

3-D Imaging of a Microwave Absorber Sample From Microwave Scattered Field Measurements

The internal structure of a sample of an absorber is retrieved from its measured scattered field. By its very nature, this target is a very weak-scatterer as it is used to cover the walls in anechoic chambers. The real part of its permittivity is rather small but its dielectric losses are non negligible. Quantitative maps of the complex permittivity of the sample were obtained from monochromatic scattered fields measured inside an anechoic chamber in a multistatic configuration. An imaging procedure taking into account the noise characteristics disturbing the measurements was used for this purpose.

Quantitative Imaging With Incident Field Modeling From Multistatic Measurements on Line Segments

In this letter, we focus on an imaging procedure that retrieves the complex permittivity map of an investigation domain from electromagnetic scattered field measurements. The transmitter and the receiver are independently moved along two parallel lines of finite extent. In such a configuration, the antenna effects are of drastic importance. We propose thus a quantitative modeling of the antennas that does not require additional calibration process. The antennas model is completely incorporated in the inversion procedure and allows to recover tubes whose diameters are of the order of [(λ)/5].

Microwave Imaging of a Slightly Varying 2-D Conducting Object Through Generalized Impedance Boundary Conditions

We consider reconstructing the shape of a perfect electric conducting object and developed a novel imaging method based on generalized impedance boundary conditions (GIBCs). The method relies on selecting a fictitious surface encircling the unknown object in which the surface impedance is reconstructed from the scattered field measurements. Later, the shape reconstruction problem is cast into an equivalent problem where the distance variation between the fictitious impedance surface and the unknown target is determined from the reconstructed surface impedance. Since the performance of the method depends on the selection of the impedance surface, we present a selection criterion according to the validity conditions of GIBCs. The method is capable of reconstructing both convex and concave structures whose shape deviates, at most, a tenth of the wavelength from the impedance surface, as demonstrated with numerical results.