Stephen J. Norton

Compton scattering tomography

Apparatus and methods for Compton scattering tomography employ a source of monoenergetic gamma rays and a detector capable of detecting the energy of scattered photons and determining the detector location both disposed on one side of an object to be imaged. Based on analysis of the measurement of the energy of the detected photons and the detector locations, a circle of possible scattering locations is determined as to each scattering event. By performance of a number of experiments as a function of detector location and energy, the density of the object can be reconstructed by filtering and back-projecting the data to yield an image responsive to variation in the density of the material of the object to be imaged.

Theory of eddy current inversion

The inverse eddy current problem can be described as the task of reconstructing an unknown distribution of electrical conductivity from eddy‐current probe impedance measurements recorded as a function of probe position, excitation frequency, or both. In eddy current nondestructive evaluation, this is widely recognized as a central theoretical problem whose solution is likely to have a significant impact on the characterization of flaws in conducting materials. Because the inverse problem is nonlinear, we propose using an iterative least‐squares algorithm for recovering the conductivity. In this algorithm, the conductivity distribution sought minimizes the mean‐square difference between the predicted and measured impedance values. The gradient of the impedance plays a fundamental role since it tells us how to update the conductivity in such a way as to guarantee a reduction in the mean‐square difference. The impedance gradient is obtained in analytic form using function‐space methods. The resulting express...

Reconstruction of a two‐dimensional reflecting medium over a circular domain: Exact solution

If a two‐dimensional acoustic reflectivity function is defined within the interior of a circle, reflectivity data may be acquired by transmitting acoustic pulses from isotropic elements distributed around the circumference of the circle and recording the resulting backscattered sound as a function of time. If the reflectivity function fulfills the conditions of an ’’idealized’’ weakly reflecting medium, the resulting pulse–echo data may be regarded as the line integrals of this function defined over circular arcs centered at points lying on the circumference of the enclosing circle. In this paper we show that on the basis of these line integrals the unknown reflectivity in the interior of the circle can be expressed explicitly in terms of its line integrals defined over the set of paths consisting of all circular arcs whose centers lie on the circumference of the enclosing circle. We propose that the resulting reconstruction equations could provide the foundation for a new approach to reflectivity tomogra...

Plasmonic nanoprobes: from chemical sensing to medical diagnostics and therapy

This article provides an overview of the development and applications of plasmonics-active nanoprobes in our laboratory for chemical sensing, medical diagnostics and therapy. Molecular Sentinel nanoprobes provide a unique tool for DNA/RNA biomarker detection both in a homogeneous solution or on a chip platform for medical diagnostics. The possibility of combining spectral selectivity and high sensitivity of the surface-enhanced Raman scattering (SERS) process with the inherent molecular specificity of nanoprobes provides an important multiplex diagnostic modality. Gold nanostars can provide an excellent multi-modality platform, combining two-photon luminescence with photothermal therapy as well as Raman imaging with photodynamic therapy. Several examples of optical detection using SERS and photonics-based treatments are presented to illustrate the usefulness and potential of the plasmonic nanoprobes for theranostics, which seamlessly combines diagnostics and therapy.

Plasmonics of 3-D Nanoshell Dimers Using Multipole Expansion and Finite Element Method

The spatial and spectral responses of the plasmonic fields induced in the gap of 3-D nanoshell dimers of gold and silver are comprehensively investigated and compared via theory and simulation using the multipole expansion (ME) and the finite element method (FEM) in COMSOL, respectively. The E-field in the dimer gap was evaluated and compared as a function of shell thickness, interparticle distance, and size. The E-field increased with decreasing shell thickness, decreasing interparticle distance, and increasing size, with the error between the two methods ranging from 1 to 10%, depending on the specific combination of these three variables. This error increases several fold with increasing dimer size, as the quasi-static approximation breaks down. A consistent overestimation of the plasmons fwhm and red shifting of the plasmon peak occurs with FEM, relative to ME, and it increases with decreasing shell thickness and interparticle distance. The size effect that arises from surface scattering of electrons is addressed and shown to be especially prominent for thin shells, for which significant damping, broadening, and shifting of the plasmon band is observed; the size effect also affects large nanoshell dimers, depending on their relative shell thickness, but to a lesser extent. This study demonstrates that COMSOL is a promising simulation environment to quantitatively investigate nanoscale electromagnetics for the modeling and designing of surface-enhanced Raman scattering (SERS) substrates.

Iterative inverse scattering algorithms: Methods of computing Fréchet derivatives

Iterative approaches to the nonlinear inverse scattering problem generally attempt to find the scattering distribution that best predicts the data by minimizing a global error norm (e.g., the mean-square error) which quantifies the misfit between a set of measured data and data predicted on the basis of a forward calculation. A crucial quantity in this minimization is the Frechet derivative of the error norm which tells us how to update the current estimate of the scattering distribution to reduce the global error at each iteration. This paper demonstrates how to compute the Frechet derivative using three different, but fundamentally equivalent, methods: the conventional adjoint method, the Lagrange multiplier method, and the integral equation method. The first two begin with the wave equation, while the latter method is based on a Lippmann–Schwinger integral equation. These techniques are not only far more efficient, but also numerically less error prone, than “brute force” methods for computing derivati...

Optoacoustic diffraction tomography: analysis of algorithms

We consider the problem of using the photoacoustic effect to image the optical properties of tissue. A region of tissue is assumed to be illuminated by frequency-modulated light that creates an ultrasonic wave of the same frequency. This wave is detected on a passive array of receiving transducers distributed over a circular or a cylindrical aperture. If the frequency is swept over a broad band (or, equivalently, if we illuminate with a pulse and Fourier transform the response), then a spatial map of a parameter that depends on the optical absorption coefficient of the tissue can be recovered. Analytical inversion formulas are derived in both two and three dimensions. The effects of band-limited data on image quality are also investigated.

Annular array imaging with full‐aperture resolution

The problem of imaging with an annular array of transducers by employing all pairs of transducer elements around the circumference of the annulus as transmitters and receivers is considered. If θt and θr are, respectively, the angular locations of a pair of transmitting and receiving elements, then weighting the received signal with the positive weight 2‖sin(θt−θr)‖ before coherent summation results in an image point spread function of the form J1(R)/R. This corresponds to the point spread function of a full circular (area) aperture. Moreover, it is shown that the diameter of this synthetic aperture is twice that of the annulus. A more general weighting function is also derived that results in a point spread function of the form Jn(R)/Rn, n=1,2,..., which is shown to correspond to an apodized circular aperture of diameter twice that of the annulus.

Reconstruction of multi-energy X-ray computed tomography images of laboratory mice

A new X-ray computed tomography (CT) system is being developed at Oak Ridge National Laboratory to image laboratory mice for the purpose of rapid phenotype screening and identification. One implementation of this CT system allows simultaneous capture of several sets of sinogram data, each having a unique X-ray energy distribution. The goals of this paper are to (1) identify issues associated with the reconstruction of this energy-dependent data and (2) suggest preliminary approaches to address these issues. Due to varying numbers of photon counts within each set, both traditional (filtered backprojection, or FBP) and statistical (maximum likelihood, or ML) tomographic image reconstruction techniques have been applied to the energy-dependent sinogram data. Results of reconstructed images using both algorithms on sinogram data (high- and low-count) are presented. Also, tissue contrast within the energy-dependent images is compared to known X-ray attenuation coefficients of soft tissue (e.g. muscle, bone, and fat).

Eddy-current interaction with an ideal crack. II. The inverse problem

Eddy‐current inversion is the process whereby the geometry of a flaw in a metal is derived from electromagnetic probe measurements. An inversion scheme is described for finding the shape and size of cracks from eddy‐current probe impedance measurements. The approach is based on an optimization scheme that seeks to minimize a global error function quantifying the difference between predicted and observed probe impedances. The error minimum is sought using a standard descent algorithm that requires a knowledge of the gradient of the error with respect to a variation of the flaw geometry. Computation of the gradient is based on a provisional flaw estimate, then the flaw estimate is updated in a ‘‘direction’’ that reduces the error. The process continues iteratively until a convergence criterion has been satisfied. Then the final flaw estimate should match the shape of the real defect. An equation for the gradient has been derived using an integral formulation of the ideal crack problem. Numerical estimates of the error gradient and the probe impedances have been calculated using approximations based on the moment method. Tests of the inversion scheme using single frequency probe impedance measurements have been carried out by calculating the shapes of narrow slots in aluminum alloy plates. Good agreement is found between the optimum profiles and the measured slot shapes.