Schotland, John C
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Publication Inverse Scattering and Acousto-Optic Imaging(2010-01-28) Bal, Giullaume; Schotland, John CWe propose a tomographic method to reconstruct the optical properties of a highly scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes use of the principle of interior control of boundary measurements by an external wave field.Publication Classical Theory of Optical Nonlinearity in Conducting Nanoparticles(2008-02-01) Panasyuk, George Y; Schotland, John C; Markel, Vadim A.We develop a classical theory of electron confinement in conducting nanoparticles. The theory is used to compute the nonlinear optical response of the nanoparticle to a harmonic external field.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 Eikonal Method for Calculation of Coherence Functions(2005-07-22) Zysk, Adam B; Carney, P. Scott; Schotland, John CA method is presented for computing the cross-spectral density of a special class of partially coherent fields in which the coherent modes obey an eikonal equation. This method allows for statistical analysis of optical systems based on simple ray tracing.Publication Single-scattering Optical Tomography: Simultaneous Reconstruction of Scattering and Absorption(2010-01-05) Markel, Vadim A; Florescu, Lucia; Schotland, John CWe report theory and numerical simulations that demonstrate the feasibility of simultaneous reconstruction of the three-dimensional scattering and absorption coefficients of a mesoscopic system using angularly resolved measurements of scattered light. Image reconstruction is based on the inversion of a generalized (broken ray) Radon transform relating the scattering and absorption coefficients of the medium to angularly resolved intensity measurements. Although the single-scattering approximation to the radiative transport equation (RTE) is used to devise the image reconstruction method, there is no assumption that only singly scattered light is measured. That is, no physical mechanism for separating single-scattered photons from the rest of the multiplyscattered light (e.g., time gating) is employed in the proposed experiments. Numerical examples of image reconstruction are obtained using samples of optical depth of up to 3.2. The forward data are obtained from numerical solution of the RTE, accounting for all orders of scattering.Publication Phaseless Three-Dimensional Optical Nanoimaging(2009-11-16) Govyadinov, Alexander A.; Panasyuk, George Y; Schotland, John CWe propose a method for optical nanoimaging in which the structure of a three-dimensional inhomogeneous medium may be recovered from far-field power measurements. Neither phase control of the illuminating field nor phase measurements of the scattered field are necessary. The method is based on the solution to the inverse scattering problem for a system consisting of a weakly-scattering dielectric sample and a strongly-scattering nanoparticle tip. Numerical simulations are used to illustrate the results.Publication Quantum Imaging and Inverse Scattering(2010-10-07) Schotland, John CWe consider the inverse scattering problem that arises in two-photon quantum imaging with interferometric measurements. We show that the two-point correlation function of the field contains information about the scattering medium at a spatial frequency of twice the Rayleigh bandwidth. The linearized inverse problem, however, yields reconstructions with a resolution of λ=2, where λ is the wavelength of light.Publication Computational Lens for the Near Field(2004-04-23) Carney, P. Scott; Frazin, Richard A; Bozhevolnyi, Sergey I; Volkov, Valentyn S; Boltasseva, Alexandra; Schotland, John CA method is presented to reconstruct the structure of a scattering object from data acquired with a photon scanning tunneling microscope. The data may be understood to form a Gabor type near-field hologram and are obtained at a distance from the sample where the field is defocused and normally uninterpretable. Object structure is obtained by the solution of the inverse scattering problem within the accuracy of a perturbative, two-dimensional model of the object.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 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.