| In this dissertation we explore the use of highly-scattered photons in an analog of conventional emission tomography: an imaging modality we term Diffusing Wave Emission Tomography (DWET). Through this technique we quantitatively reconstruct images of the spatial distributions of fluorophores in turbid media that have been previously excited by amplitude-modulated continuous-wave light sources. Propagation of light in such systems takes place in the multiple-scattering regime and can thus be described in terms of diffusing waves. These waves are highly-damped, scalar waves of light energy density somewhat akin to evanescent electromagnetic waves; capable of conveying information on subwavelength length-scales with resolution approaching the photon's transport mean free path length.; We begin with the mathematical description of diffusing wave propagation in the presence of spatially inhomogeneous absorption and scattering. We then extend these results to characterize the forward problem of DWET: the reradiation of diffusing waves from fluorescing objects. Numerical methods are next introduced by which the forward problem is inverted, enabling the quantitative spatial reconstruction of fluorophore number densities. To evaluate the robustness of our inversion algorithm when confronted with noise and experimental error, as well as aid in the parametric optimization of hardware, we derive and numerically implement exact, analytic solutions to the forward problems of scattering and fluorescent emission of diffusing waves from cylindrical inhomogeneities. Such analytic solutions may be of general interest for experimental studies of imaging with diffuse light since the use of cylindrical objects leads to a reduction in dimensionality and thereby the computational complexity of the inverse problem.; We then present the detailed experimental validation of DWET, demonstrating the quantitative reconstruction of images of cylinders containing micromolar to nanomolar concentrations of fluorophore in highly-scattering media that approximate biological tissues. These are the first images ever made of a fluorescing object in a highly-scattering system using only multiply-scattered light. Here we also assess DWET's ability to detect small changes in absolute fluorophore number density for images reconstructed from data sets of reduced size. Biomedical applications, including mammography and tomographic electroencephalography, are considered. |
