Ann W. Morgenthaler

Subsurface Sensing of Buried Objects Under a Randomly Rough Surface Using Scattered Electromagnetic Field Data

This paper proposes a new inverse method for microwave-based subsurface sensing of lossy dielectric objects embedded in a dispersive lossy ground with an unknown rough surface. An iterative inversion algorithm is employed to reconstruct the geometry and dielectric properties of the half-space ground as well as that of the buried object. B-splines are used to model the shape of the object as well as the height of the rough surface. In both cases, the control points for the spline function represent the unknowns to be recovered. A single-pole rational transfer function is used to capture the dispersive nature of the background. Here, the coefficients in the numerator and denominator are the unknowns. The approach presented in this paper is based on the state-of-the-art semianalytic mode matching forward model, which is a fast and efficient algorithm to determine the scattered electromagnetic fields. Numerical experiments involving two-dimensional geometries and TM incident plane waves demonstrate the accuracy and reliability of this inverse method

Scattering from lossy dielectric objects buried beneath randomly rough ground: validating the semi-analytic mode matching algorithm with 2-D FDFD

A new semi-analytic mode matching (SAMM) algorithm is verified by two-dimensional (2-D) finite difference frequency domain (FDFD) simulations of scattering resulting from uniform plane waves incident on randomly rough dielectric half-spaces containing buried dielectric targets. The SAMM algorithm uses moderately low-order modal superpositions of cylindrical waves, each of which satisfies the 2-D-Helmholtz equation in its appropriate region (air, ground, or mine) and then matches all nonzero electric and magnetic field components at each interface by inverting a highly overconstrained dense linear matrix equation by singular value decomposition. That is, the set of cylindrical mode coefficients is found which best fits the boundary conditions in a least squares sense. For smooth ground, coordinate scattering centers (CSCs) are chosen at the mine center and at its image above the plane to model scattering. For randomly rough ground, additional CSCs are located within the rough boundary layer. Excellent agreement between 2-D-FDFD and the 2-D version of SAMM is observed, with 2-D-SAMM being at least an order of magnitude faster. 3-D-SAMM is estimated to be four orders of magnitude faster than 3-D-FDFD, with drastically reduced memory requirements.

GPR Wave Scattering From Complex Objects Using the Semi-Analytic Mode Matching Algorithm: Coordinate Scattering Center Selection

The semi-analytic mode matching (SAMM) algorithm is a quick and efficient computational method that models wave scattering from objects in half spaces. This algorithm relies on appropriately choosing coordinate scattering centers (CSCs) for modal expansions, and successful automation of the CSC selection process is the goal of this paper. CSCs are found for several complex shaped scattering test objects by considering the radius of curvature (ROC) function for each object. The CSCs are found to be largely independent of frequency and located at cusps in the ROC function for scattering objects of modest aspect ratios. Additional CSCs may be required in numbers that are directly proportional to the aspect ratios of more complicated objects, but again, the extra CSC locations are largely independent of frequency. Excellent results are found comparing SAMM and finite-difference frequency domain for 2-D scattering objects that are 0.1-15 wavelengths in size.

Semianalytic mode matching techniques for detecting nonmetallic mines buried in realistic soils

The Ultra-Wideband detection of plastic land mines buried in lossy, dielectric soils is simulated design a new semi- analytic mode matching (SAMM) algorithm. Here, we apply SAMM to the 3D canonical problem of finding the nonspecular reflection of an obliquely-incident plane wave ona lossy dielectric half-space containing a small, shallowly-varying convex-shaped mines buried under modestly rough ground. In the SAMM algorithm, the frequency-dependent scattered fields are constructed form moderately rough ground. In the SAMM algorithm, the frequency-dependent scattered fields are constructed form moderately low-order modal superpositions of spherical waves, each satisfying the Helmholtz equation in its respective material. By least squares fitting, mode coefficients are found which optimally match all boundary conditions at designated points along the boundary surfaces. Spherical wave expansions are chosen at multiple coordinate centers so that small numbers of modes are needed to given convergent results.

FDFD microwave modeling of realistic, inhomogeneous breast tissue based on digital breast tomosynthesis priors for cancer detection

A multi-modal, non-invasive technique for breast cancer detection is described. Digital Breast Tomosynthesis- Microwave imaging is presented as a method to improve tumor detection in breast tissue. Dielectric contrast between cancerous tissue and healthy high water content breast tissue is an order of magnitude greater than radiological contrast, but microwave imaging resolution is poorer than X-ray. Combining the two, DBT provides a high resolution, 3D image of the internal tissue structure, which can be used as a prior background model for finite difference frequency domain (FDFD) simulation for microwave imaging. By subtracting the modeled, assumed healthy background field from the measured field, inconsistencies generated by the lesion are highlighted and the tumor can be detected and located.

Scattering from dielectric objects buried beneath random rough ground: Validating the semi-analytic mode matching algorithm with two-dimensional FDFD

A 2D finite difference frequency domain (FDFD) algorithm is used to verify new semi-analytic mode matching (SAMM) simulations of scattered fields resulting from plane waves incident on a random rough dielectric half-space containing a buried dielectric target. The SAMM algorithm uses moderately low-order modal superpositions of cylindrical waves, each of which satisfies the 2D-Helmholtz equation in its appropriate region (air, ground, or mine) and then matches all nonzero electric and magnetic field components at each interface by least squares fitting. For smooth ground, coordinate scattering centers (CSCs) are chosen at the mine center and at its image above the plane to model scattering. For random rough ground, additional CSCs are located within the rough layer. Excellent agreement between SD-FDFD and the two dimensional version of SAMM is observed, with 2D-SAMM being at least an order of magnitude faster; 3D-SAMM is estimated to be four orders of magnitude faster than SD-FDFD, with drastically reduced memory requirements.

Detecting Nonmetallic Mines Under Rough Ground Using Semi-Analytic Mode Matching

Ground penetrating radar detection of plastic land mines buried in lossy, dielectric soils under rough ground surfaces is only possible with wide bandwidth probing signals. Using the new semi-analytic mode matching (SAMM) algorithm, we model the ultra-wide bandwidth scattering of these low-contrast buried targets, using computed time domain signatures to facilitate detection. It is shown that differences between the characteristic time peaks of the non-specular signature are primarily dependent on the size, shape and material characteristics of the target, and less so on its burial depth, background soil, or ground surface roughness. Differences between time peaks are attributed to multiple roundtrip transit times through the target which are largely independent of the ground characteristics.In the SAMM algorithm, the frequency-dependent scattered fields are constructed from moderately low-order modal superpositions of spherical waves, each satisfying the Helmholtz equation in its respective material (air, ground, or mine). By least squares fitting, mode coefficients are found which optimally match all boundary conditions at designated points along the boundary surfaces, where the boundaries may be irregularly shaped. Spherical wave expansions are chosen at multiple coordinate centers so that fewer modes are needed to give convergent results. The speed advantage of SAMM over other computational methods allows for the detailed study of ultra-wideband GPR sensing of challenging, realistic subsurface detection problems.

3D fan-beam model implimentation in a Hybrid Digital-Breast-Tomosynthesis Microwave Radar Imaging breast cancer detection algorithm

A 3D Fan-Beam model is presented to reduce computation time for Hybrid Digital-Breast-Tomosynthesis Microwave Radar Imaging breast cancer detection and imaging algorithms. The physical justifications for this model are described as well as the class of problems for which it is appropriate. A numerical experiment is presented using the new model in a breast cancer imaging algorithm to successfully reconstruct the location of a cancerous lesion in three dimensions.

The Semianalytic Mode Matching Algorithm for GPR Wave Scattering From Multiple Complex Objects Buried in a Rough Lossy Dielectric Half-Space

The semianalytic mode matching (SAMM) algorithm is a quick and efficient computational method that models wave scattering from multiple objects in half-spaces. This algorithm re lies heavily on appropriate choices of coordinate scattering centers (CSCs) for various modal expansions. Here, SAMM is used to simulate scattering from irregularly shaped 2-D lossy objects embedded in realistic half-space media with rough ground surfaces. Because the CSC locations for complex scatterers are much more dependent on object or interface geometry than frequency and are independent of the dielectric contrast between scatterer and back ground, it is worthwhile to carefully analyze particular scattering object shapes and store the optimal CSC locations for future use. In addition, scattering from multiple targets buried beneath rough ground surfaces can be constructed from simpler simulations of the individual targets taken separately, where combining these simpler simulations correctly can increase robustness in large SAMM simulations. Excellent results are found by comparing 2-D SAMM with 2-D finite-difference frequency domain for multiple scattering objects on the order of a fraction to several wavelengths in size located within rough half-space dielectric backgrounds.

Time domain processing of frequency domain GPR signatures for buried land mine detection

This paper investigates the feasibility of detecting plastic antipersonnel land mines buried in lossy, dispersive, rough soils using a stepped-frequency ultra wideband (WB) ground-penetrating radar (GPR). Realistic land mine scenarios were modeled using a two-dimensional (2D) finite difference frequency domain (FDFD) technique. Assuming normal incidence plane wave excitation, the scattered fields were generated over a large frequency bandwidth (.5 to 5 GHz) for a variety of mine-like shapes, different soil types, and multiple receiver locations. The simulation results showed that for a ground penetration sensor located just above the soil surface, the strong reflection signals received from the rough ground surface obscured the buried targets frequency response signal. The simulated GPR WB frequency response data at each receiver location was transformed to the time domain using the fast Fourier transform. Time domain processing permits high resolution measurement of target features that are invariant to the ground roughness and also that are dependent on the soil characteristics as well as the burial depth and size of the mine. Specifically, two or more characteristic timing peaks are observed in the simulation results suggesting that the ultra-wideband spectral radar response may yield particular advantages not exploited by currently employed detection systems. It is also shown that by using time-gating to remove the strong ground reflection signals, the target signals are selectively enhanced (as expected), but more surprisingly, the target frequency response signature is almost completely recovered.