Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography

Optical diffraction tomography is an imaging technique that permits retrieval of the map of permittivity of an object from its scattered far field. Most reconstruction procedures assume that single scattering is dominant so that the scattered far field is linearly linked to the permittivity. In this work, we present a nonlinear inversion method and apply it to complex three-dimensional samples. We show that multiple scattering permits one to obtain a power of resolution beyond the classical limit imposed by the use of propagative incident and diffracted waves. Moreover, we stress that our imaging method is robust with respect to correlated and uncorrelated noise.     

Superresolution in total internal reflection tomography

We simulate a total internal reflection tomography experiment in which an unknown object is illuminated by evanescent waves and the scattered field is detected along several directions. We propose a full-vectorial three-dimensional nonlinear inversion scheme to retrieve the map of the permittivity of the object from the scattered far-field data. We study the role of the solid angle of illumination, the incident polarization, and the position of the prism interface on the resolution of the images. We compare our algorithm with a linear inversion scheme based on the renormalized Born approximation and stress the importance of multiple scattering in this particular configuration. We analyze the sensitivity to noise and point out that using incident propagative waves together with evanescent waves improves the robustness of the reconstruction.     

Scattering from anisotropic plasma-coated PEMC cylinder buried beneath a slightly rough surface

A general theoretical formulation is done to calculate the field scattered by perfect electromagnetic conductor (PEMC) cylinder coated with anisotropic plasma material. It is buried below a slightly rough surface. Spectral plane wave representation of fields and small perturbation method are used to calculate multiple reflections between coated cylinder and rough surface. To validate the present formulation, scattered field from a PEMC cylinder coated with double negative (DNG) material is obtained from the present formulation. Scattering pattern of non coated PEC/PEMC cylinder or coated with isotropic material can also be obtained by the proper selection of physical parameters such as anisotropy, admittance of PEMC cylinder and permittivity of hosting medium. Analytical expressions of scattered field for a sinusoidal rough surface are given along with their physical interpretation to get a good insight. Effect of geometrical and physical parameters on scattering pattern is observed.     

Second-order iterative approach to inverse scattering: numerical results

We introduce an iterative algorithm for the reconstruction of dielectric profile functions from scattered field data, in which each step corresponds to the solution of a quadratic inversion problem. This means that, at each iteration, we perform a second-order approximation of the scattering operator connecting the unknown profile to the data about a reference profile function. This procedure is then compared with a linear iterative inversion algorithm, and it is pointed out that, within a prescribed class of profile functions, the linear iterative inversion does not converge to the actual solution, whereas the proposed approach does. This feature can be explained by reference not only to the improved approximation provided by the addition of a further term for profile functions of a larger norm but also to the different classes of functions that can be reconstructed by either the linear or the quadratic model. Numerical examples of profile reconstruction in the scalar two-dimensional geometry, with far-zone scattered field data at a fixed frequency, confirm the theoretical analysis.     

Polarized light scattering by microroughness and small defects in dielectric layers

The polarization of light scattered by the surface of a material contains information that can be used to identify the sources of that scatter. Theories for light scattering from interfacial roughness of a dielectric layer and from defects in that dielectric layer are reviewed. Methods for calculating the Mueller matrix or the Stokes vector for scatter from multiple sources and for decomposing a Stokes vector into contributions from two nondepolarizing scattering sources are derived. The theories are evaluated for a specific sample and geometry. Results show that some incident polarizations are more effective than others at discriminating among scattering sources, with s-polarized light being least effective. The polarization of light scattered from interfacial roughness depends upon the relative roughness of the two interfaces and the degree of correlation between the two interfaces. The scattering from defects in the film depends on the depth of the defect and differs from that from any one of the cases of interfacial roughness. The scattering from defects randomly distributed in the film and for small dielectric permittivity variations in the film is also calculated. Experimental results are presented for a 52-nm SiO2 film thermally grown on microrough silicon.     

Microwave imaging: Reconstructions from experimental data using conjugate gradient and enhancement by edge-preserving regularization

A method for reconstructing the complex permittivity profile of lossy dielectric objects from measured scattered far-field data is presented. An iterative reconstruction algorithm based on a conjugate gradient method is derived from an integral representation of the electric field and applying a moment method solution. Results obtained from experimental data are shown for both known and unknown targets. Then, a new regularization procedure is developed to enhance the quality of the reconstruction. This method, based on a Markov random fields approach, models the object to be reconstructed by homogeneous areas separated by borderlike discontinuities. Finally, the enhancement is shown by the reconstruction of a polystyrene square cylinder. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 337–342, 1997     

Multistatic-multiview resolution from Born fields for strips in Fresnel zone

We address the inverse scattering problem of estimating the resolution limits achievable in the reconstruction of a dielectric strip object within a two-dimensional and scalar geometry. The scattered field is observed over a bounded rectilinear domain located in the Fresnel zone, and a single-frequency multistatic-multiview configuration is considered. The analysis is performed by casting the problem as the inversion of the linearized scattering operator arising from the Born approximation and by means of its singular-value decomposition. Finally, the role of the geometrical parameters of the measurement configuration is highlighted.     

Time Domain Inverse Scattering of Buried Inhomogeneous Dielectric Cylinders

This paper presents the studies of time domain inverse scattering for a two-dimensional inhomogeneous dielectric cylinder buried in a half-space by the finite difference time domain (FDTD) method and evolutionary algorithms (EAs). For forward scattering, the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering the evolutionary algorithms are utilized to determine the permittivity of the buried cylindrical scatterer with arbitrary cross section. The results obtained for different examples show that the dynamic differential evolution (DDE) algorithms outperform the non-uniform steady state genetic algorithm (NU-SSGA) variants in terms of finding best optima. The suitability and efficiency of applying these two methods for microwave imaging of 2-D inhomogeneous dielectric cylinders are examined. Moreover, when the measured scattered fields are contaminated with Gaussian noise, DDE is able to yield good reconstructed quality.     

同轴传输反射法测量高损耗材料微波介电常数

同轴传输反射方法可以用来测量高损耗材料的微波介电常数。该方法将环形样品嵌入同轴线内,通过测量样品两端的散射系数来确定材料的微波介电常数。文中介绍了测量原理及测量系统,测量了一种石蜡基混合样品的微波介电常数,并通过改进的Bruggeman数学模型,推算出其中陶瓷材料的介电常数。     

Image reconstruction of buried multiple conductors by genetic algorithms

This paper presents an inverse scattering problem for recovering the shapes of multiple conducting cylinders with the immersed targets in a half‐space by genetic algorithm. Two separate perfectly conducting cylinders of unknown shapes are buried in one half‐space and illuminated by transverse magnetic (TM) plane wave from the other half‐space. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations are derived, and the electromagnetic imaging problem is reformulated into an optimization problem. The improved steady state genetic algorithm is used to find out the global extreme solution. Numerical results are given to demonstrate the performance of the inverse algorithm. Good reconstruction can be obtained even when the initial guesses are far different from the exact shapes, and then the multiple scattered fields between two conductors are serious. In addition, the effect of Gaussian noise on the reconstruction is investigated. We can find that the effect of noise is negligible for the normalized standard deviations below 0.01. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 18, 276–281, 2008; Published online in Wiley InterScience (www.interscience.wiley.com).     

Scattering of electromagnetic plane wave from a perfect electric conducting strip located in topological insulator medium

In this article, scattering from a perfectly electric conducting strip located in an infinitely extended topological insulator (IT) medium is investigated using the Kobayashi potential method. For solving mixed boundary value problem, KP method is a fast and semi-analytical technique. In this method, edge conditions and boundary conditions are incorporated simultaneously. The scattered field is calculated from the strip geometry embedded in IT medium. The far zone scattered field is investigated with respect to different parameters of the geometry, i.e. topological parameter of the IT medium, size of the strip etc. It has been observed that the scattered field can be enhanced by increasing topological parameter of the IT medium. On the other hand, size of strip, permittivity of IT medium may also be used to enhance the main lobe of the scattering width/scattered field.     

Comparison of Dynamic Differential Evolution and Self-Adaptive Dynamic Differential Evolution for Buried Metallic Cylinder

The application of two techniques for the reconstruction of shape reconstruction of a metallic cylinder from scattered field measurements is studied in this paper. These techniques are applied to two-dimensional configurations, for which the method of moment (MoM) is applied to solve the integral equations. Considering that the microwave imaging is recast as a nonlinear optimization problem, an objective function is defined by the norm of the difference between the measured scattered electric fields and those calculated for each estimated metallic cylinder. Thus, the shape of a metallic cylinder can be obtained by minimizing the objective function. In order to solve this inverse scattering problem, two techniques are employed. The first one is based on dynamic differential evolution (DDE) algorithm, while the second one is an improved version of the DDE algorithm with self-adaptive control parameters, called SADDE. Both techniques are tested for the simulated data contaminated by additive white Gaussian noise. Numerical results indicate that SADDE algorithm outperforms DDE algorithm in terms of reconstruction accuracy and convergence speed.     

A Combined Total Reflection-Transmission Method in Application to Dielectric Spectroscopy

A combined total reflection-transmission method for permittivity measurements at radio and microwave frequencies is described. Analytical expressions for the dielectric constant and the loss factor of a sample, viewed as a two-port in the transmission system, in terms of the measured scattering parameters are given. ne uncertainty of measurements of the dielectric constant and the loss factor is discussed and a method ofselecting an optimum sample length is suggested.     

Near zone scattering and extinction properties of a left handed material cylinder buried in a semi infinite medium with rough interface

A solution utilizing the spectral plane wave representation of fields (SPRF) combined with the extended boundary condition method (EBCM) is presented to study the scattering and extinction properties of a left handed material cylinder buried in a semi infinite medium with a rough interface. The EBCM is used to evaluate the field transmitted through the interface, which excites the cylinder. The SPRF is used to study the interaction of scattered field from the cylinder with the rough interface. The effect of the negative permittivity and permeability of the cylinder on the far zone scattered field is observed. Further, the near zone scattered field is investigated, which is very helpful to characterize the scenario in which object detection is a challenging task. It is also observed that the electrical size is an important factor affecting the near zone scattered field since the extinction cross section depends upon size.     

High-resolution optical diffraction microscopy

In an optical diffraction microscopy experiment, one measures the phase and amplitude of the field diffracted by the sample and uses an inversion algorithm to reconstruct its map of permittivity. We show that with an iterative procedure accounting for multiple scattering, it is possible to visualize details smaller than lambda/4 with relatively few illumination and observation angles. The roles of incident evanescent waves and noise are also investigated.     

Electromagnetic scattering by an aggregate of spheres: far field

In electromagnetic multisphere-scattering calculations the reexpansion method for seeking a single-field representation of the total scattered field is found impracticable because of severe numerical problems. We present a simple single-field expansion of the total scattered far field based on an asymptotic form of vector translational addition theorems. With this asymptotic expansion of the far field, we derive analytical expressions for the scattering properties of an arbitrary aggregate of spheres. Resulting formulas are free from numerical problems in practical applications. Theoretical predictions from this far-field solution for various aggregates of spheres that we tested agree favorably with laboratory microwave scattering measurements. Some numerical results are presented and compared with experimental data.     

Full wave optical profilometry

We show that tomographic diffractive microscopy can be used for profilometry applications with high transverse resolution. We present an iterative reconstruction procedure, based on a rigorous wave scattering model, that permits us to retrieve the profile of rough metallic interfaces from the complex scattered field. The transversal resolution is subwavelength, and can even fall below the classical resolution limit if the profile is rough enough for multiple interactions to occur. Large profiles, with tens of wavelength size, can be investigated.     

Correction for multiple scattering in Compton profile experiments: Application for synchrotron source photons

New improvements in the Monte Carlo multiple scattering correction for Compton profiles are described. They consider the linear and well-defined polarization of a synchrotron beam and the actual geometry of the Compton spectrometer at LURE-DCI: the monochromatization by two Bragg reflections as well as the transmission of the scattered photons through the crystal analyzer enhance the main component of the electric field vector. These two properties tend to lower the multiple scattering cross-section. Measurements on beryllium performed with samples of various thicknesses prove the quality of the present simulation. A graphite Compton profile, obtained in different conditions of incident energy and sample geometry, is also corrected for multiple scattering contribution. It is finally shown that the correction is quite small, for low energy and polarized photons.     

Inverse scattering problems of near-field subsurface pulse diagnostics

Methods of near-field subsurface electromagnetic diagnostics that provides a subpulse-length resolution are developed and studied in experiments with the pulse microwave source-receiver scanning system. Proposed tomography and holography of subsurface dielectric targets are based on the solution of 3D near-field inverse scattering problems by 2D measurements of the scattered pulse signal above the surface of media with dielectric inhomogeneities. Pulse data are transformed to frequency domain, where, using the Green function formalism, the non-linear 3D integral equation has been obtained to solve this inverse scattering problem. The solution of this equation is used to derive tomograms of distributed inhomogeneities or to determine the shape of solid targets for further visualization as holography images. To retrieve depth profiles of one-dimensional subsurface inhomogeneities of sand density, the dual regularization method has been worked out and tested by experimental data.