## Schotland, John C

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Publication Photoacoustic effect for multiply scattered light(2007-09-25) Fisher, Andrew R; Schissler, Andrew J; Schotland, John CWe consider the photoacoustic effect for multiply scattered light in a random medium. Within the accuracy of the diffusion approximation to the radiative transport equation, we present a general analysis of the sensitivity of a photoacoustic wave to the presence of one or more small absorbing objects. Applications to tumor detection by photoacoustic imaging are suggested.Publication Generalized optical theorem for reflection, transmission, and extinction of power for scalar fields(2004-09-22) Carney, P. Scott; Schotland, John C; Wolf, EmilWe present a derivation of the optical theorem that makes it possible to obtain expressions for the extinguished power in a very general class of problems not previously treated. The results are applied to the analysis of the extinction of power by a scatterer in the presence of a lossless half space. Applications to microscopy and tomography are discussed.Publication Generalized optical theorem for reflection, transmission, and extinction of power for electromagnetic fields(2005-05-01) Lytle II, D. R; Carney, P. Scott; Schotland, John C; Wolf, EmilWe present a generalization of the optical theorem for electromagnetic fields. This result is used to obtain the power extinguished from a field by a scatterer contained in a dielectric half space. Applications to microscopy and tomography are described.Publication Geometrical optics limit of stochastic electromagnetic fields(2008-04-01) Schoonover, Robert W; Zysk, Adam M; Carney, P. Scott; Schotland, John C; Wolfe, EmilA method is described which elucidates propagation of an electromagnetic field generated by a stochastic, electromagnetic source within the short wavelength limit. The results can be used to determine statistical properties of fields using ray tracing methods.Publication Strong Tip Effects in Near-field Scanning Optical Tomography(2007-11-15) Sun, Jin; Carney, P. Scott; Schotland, John CA model for the interaction of the scanning probe in near-field scanning optical microscopy is presented. Multiple scattering of the illuminating field with the probe is taken into account. The implications of this so-called strong tip model for the solution of the associated inverse scattering problem are studied through simulations.Publication Near-Field Scanning Optical Tomography: A Nondestructive Method for Three-Dimensional Nanoscale Imaging(2006-12-01) Sun, Jin; Carney, P. Scott; Schotland, John CWe present the theoretical foundation for near-field scanning optical tomography, a method for three-dimensional optical imaging with subwavelength resolution. An analysis of the forward problem for both scalar and vector optical fields is described. This is followed by the construction of the pseudoinverse solution to the linearized inverse scattering problem. The results are illustrated by numerical simulations.Publication Nonlinear Inverse Scattering and Three-Dimensional Near-Field Optical Imaging(2006-11-29) Panasyuk, George Y; Markel, Vadim A; Schotland, John C; Carney, P. ScottThe nonlinear inverse scattering problem for electromagnetic fields with evanescent components is considered. A solution to this problem is obtained in the form of a functional series expansion. The first term in the expansion corresponds to the pseudoinverse solution to the linearized inverse problem. The higher order terms represent nonlinear corrections to this result. Applications to the problem of three-dimensional optical imaging with subwavelength resolution are described and illustrated with numerical simulations.Publication The Bad Truth about Laplace's Transform(2008-08-05) Epstein, Charles L; Schotland, John CInverting the Laplace transform is a paradigm for exponentially ill-posed problems. For a class of operators, including the Laplace transform, we give forward and inverse formulae that have fast implementations using the fast Fourier transform. These formulae lead easily to regularized inverses whose effects on noise and filtered data can be precisely described. Our results give cogent reasons for the general sense of dread most mathematicians feel about inverting the Laplace transform.Publication Single-scattering optical tomography(2009-03-25) Florescu, Lucia; Schotland, John C; Markel, Vadim AWe consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean-free path is on the order of the system size. It is shown that a tomographic imaging technique can be devised which is based on the assumption of single scattering and utilizes a generalization of the Radon transform which we refer to as the broken-ray transform. The technique can be used to recover the extinction coefficient of an inhomogeneous medium from angularly resolved measurements and is illustrated with numerical simulations. The forward data for these simulations were obtained by numerically solving the radiative transport equation without any approximations. Tomographic imaging in slabs of different widths was considered and it was shown that the technique can tolerate a maximum width that corresponds to approximately six scattering events. It is also shown that the use of broken rays does not result in additional ill posedness of the inverse problem in comparison to the classical problem of inverting the Radon transform. Applications to biomedical imaging are described.Publication Symmetries, inversion formulas, and image reconstruction for optical tomography(2004-11-30) Markel, Vadim A; Schotland, John CWe consider the image reconstruction problem for optical tomography with diffuse light. The associated inverse scattering problem is analyzed by making use of particular symmetries of the scattering data. The effects of sampling and limited data are analyzed for several different experimental modalities, and computationally efficient reconstruction algorithms are obtained. These algorithms are suitable for the reconstruction of images from very large data sets.