Biomedical subjects
Publications and source records attributed to V A Markel.
We consider the inverse scattering problem for the diffusion equation. A solution to this problem in the form of an explicit inversion formula is derived. Computer simulations are used illustrate our approach in model systems.
We investigate the near-field inverse scattering problem with evanescent waves. An analytic solution to this problem within the weak-scattering approximation is used to show that the usual Rayleigh limit may be overcome even when measurements are made without phase information. Applications to a novel form of three-dimensional microscopy with subwavelength resolution are described.
We develop a theoretical approach to calculating optical properties of carbonaceous soot in the long-wavelength limit. Our method is based on geometrical renormalization of clusters; it avoids both the inaccuracy of the dipole approximation in its pure form and the numerical complexity of rigorous direct methods of solving the EM boundary problem. The results are verified by comparison with the experimental measurements for specific extinction of diesel soot in the spectral region from 0.488 microm to 0.857 cm that were performed by Bruce et al. [Appl. Opt. 30, 1537 (1991)]. The theory leads to analytical expressions that are applicable to different soots, with various geometrical properties and optical constants. We show that the functional form of the long-wavelength asymptote of the specific extinction can depend critically on a parameter characterizing the sample geometry, and we identify the critical value of this parameter.
We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. Inversion formulas based on the Fourier-Laplace transform are used to establish the existence and uniqueness of solutions to this problem in planar, cylindrical, and spherical geometries.
We consider the problem of imaging the optical properties of a highly scattering medium probed by diffuse light. An analytic solution to this problem is derived from the singular value decomposition of the forward-scattering operator, which leads to explicit inversion formulas for the inverse scattering problem with diffusing waves. Computer simulations are used to illustrate these results in model systems.