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Biomedical subjects

John C Schotland

Publications and source records attributed to John C Schotland.

13 recordsLinked to original sources
PubMed2006

Self-consistent scattering theory for the radiative transport equation.

We study light propagation in a random medium governed by the radiative transport equation. We present a theory for the transport equation with an inhomogeneous absorption coefficient. We obtain an analytical expression for the specific intensity in a uniform absorbing and scattering medium containing a point absorber. Using that result we derive a self-consistent system of integral equations to study a collection of point absorbers. We show numerical results that demonstrate the use of this theory.

Journal Article↗
PubMed2005

Experimental demonstration of an analytic method for image reconstruction in optical diffusion tomography with large data sets.

We report the first experimental test of an analytic image reconstruction algorithm for optical tomography with large data sets. Using a continuous-wave optical tomography system with 10(8) source-detector pairs, we demonstrate the reconstruction of an absorption image of a phantom consisting of a highly scattering medium containing absorbing inhomogeneities.

Algorithms↗
PubMed2005

Eikonal method for calculation of coherence functions.

A 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.

Journal Article↗
PubMed2005

Multiple projection optical diffusion tomography with plane wave illumination.

We describe a new data collection scheme for optical diffusion tomography in which plane wave illumination is combined with multiple projections in the slab imaging geometry. Multiple projection measurements are performed by rotating the slab around the sample. The advantage of the proposed method is that the measured data are more compatible with the dynamic range of most commonly used detectors. At the same time, multiple projections improve image quality by mutually interchanging the depth and transverse directions, and the scanned (detection) and integrated (illumination) surfaces. Inversion methods are derived for image reconstructions with extremely large data sets. Numerical simulations are performed for fixed and rotated slabs.

Algorithms↗
PubMed2004

Symmetries, inversion formulas, and image reconstruction for optical tomography.

We 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.

Algorithms↗
PubMed2004

Dual-projection optical diffusion tomography.

We propose a new approach to optical diffusion tomography that incorporates two orthogonal projections. All the data obtained in a double projection measurement are treated simultaneously. The second projection improves image quality due to the fact that the depth and transverse directions are interchanged. An image reconstruction algorithm is derived and illustrated with simulations. It is shown that the spatial resolution of images improves by a factor of 4-5 due to the second projection.

Algorithms↗
PubMed2004

Computational lens for the near field.

A 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.

Journal Article↗
PubMed2003

Theory of total-internal-reflection tomography.

A method is presented to reconstruct three-dimensional tomographic images of weakly scattering objects with subwavelength resolution. The method may be applied to data available in phase-sensitive, total-internal-reflection microscopy. The results follow from an analysis of the near-field inverse scattering problem with evanescent waves.

Journal Article↗
PubMed2003

Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition.

We continue our study of the inverse scattering problem for diffuse light. In particular, we derive inversion formulas for this problem that are based on the functional singular-value decomposition of the linearized forward-scattering operator in the slab, cylindrical, and spherical geometries. Computer simulations are used to illustrate our results in model systems.

Models, Theoretical↗
PubMed2003

Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas.

We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized forward-scattering operator and leads to the linear inversion formulas that we have reported previously. The higher-order terms represent nonlinear corrections to this result. We illustrate our results with computer simulations in model systems.

Equipment Design↗
PubMed2002

Inverse problem in optical diffusion tomography. II. Role of boundary conditions.

We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. The role of boundary conditions in the derivation of Fourier-Laplace inversion formulas is considered. Boundary conditions of a general mixed type are discussed, with purely absorbing and purely reflecting boundaries obtained as limiting cases. Four different geometries are considered with boundary conditions imposed on a single plane and on two parallel planes and on a cylindrical and on a spherical surface.

Diffusion↗