Images of Inhomogeneous Turbid Media Using Diffuse Photon Density Waves

In this paper we present images derived from measurements of diffuse photon density waves in turbid media. After a brief introduction and description of the experimental set-up, this document is divided into two sections. In the first, we present an analytic solution for the scattering of diffuse photon density waves by spherical and cylindrical inhomogeneities within turbid media and discuss the application of this solution to systems containing multiple objects and multiple sources. This exact solution is a useful tool for simulating the distortion of a diffuse photon density wave due to simple inhomogeneities. Until recently, simulations of heterogeneous media were achieved by Monte-Carlo methods, finite element analysis, or other time consuming techniques. More recently, Feng et al. [1] presented a perturbative solution for a single, point-like heterogeneity. The exact calculation we present is not limited to small objects, and numerical calculations using this solution are fast compared to Monte Carlo simulations[2]. Finally, we experimentally demonstrate that this analytic solution enables us to fit for the optical and geometric properties of arbitrary spherical and cylindrical objects, and we discuss the detector sensitivity required to characterize such objects. In the second section we derive images of more general inhomogeneous scattering media. Our method is based on the diffusion approximation, but is not an iterative approach; it is a direct inversion that is exact to first order in variations of the sample absorption. An increase in sensitivity is achieved through the use of multiple-source/single-detector units placed around the turbid medium. In our particular case, each unit consisted of a set of two modulated diffuse light sources phased 180° out of phase with respect to one another, and a single detector located at positions equidistant from each source. In this report we will describe the general theoretical approach, provide experimental evidence of its utility, and discuss potential applications.