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We present an analytic solution for the scattering of diffuse photon density waves by spherical inhomogeneities within turbid media. The analytic result is compared to experimental measurements. Close agreement between theory and experiment permits the use of the theory to determine the properties of unknown sphere-like objects embedded in turbid media. The analytic solution is extended to encompass several problems of practical interest in imaging, including the influence of multiple sources, multiple objects, and boundaries on the characterization of spherical inhomogeneities. We also extend the solution to encompass time-domain measurements.Recently, useful information about turbid media such as human tissue has been derived from photons migrating through these media (1). The diffusing photons enable us to noninvasively probe highly scattering materials and determine their average scattering and absorption properties (2, 3). Furthermore, the diffusing photons can also be utilized in imaging objects such as tumors hidden in turbid media (4-7). We present an analytic solution for the scattering of diffuse photon density waves (DPDWs) from spherical inhomogeneities embedded in an otherwise homogeneous medium and apply it to object imaging.The occurrence of DPDWs has been described in detail (8,9). In general, these waves arise when an intensity-modulated source oflight is introduced into a highly scattering or diffusive medium. Microscopically, individual photons undergo a random walk within the medium. Collectively, a wave of photon density is produced that propagates spherically outward from the source. These waves have a well-defined phase and amplitude at every point in the diffusive medium. When a localized heterogeneity is embedded in the medium, the spherical wave is distorted. The degree of distortion is determined by object characteristics (such as its position, shape, size, and scattering) and absorption properties.Since the Helmholtz equation is known to describe the transport of DPDWs in a piecewise homogeneous media (9, 10), we expect that an exact solution exists for the scattering of DPDWs by spherical objects. The solutions will be similar to, and simpler than, the theory of Mie scattering (11) often used in optics.We derive the analytic solution ofthe Helmholtz equation for a piecewise homogeneous system consisting of a spherical object composed of one highly scattering medium embedded in a second highly scattering medium of infinite spatial extent. This solution is easily extended to semiinfinite media by using the extrapolated zero boundary condition (2, 12, 13). The analytic solution is compared with experimental data to assess the theory's predictive power, and a simple inverse localization algorithm is demonstrated to determine the size and location of a spherical object. Finally, the theory is extended to include more complex problems in imaging. THEORYThe incoherent transport of photons in a highly scattering medium is generally described by a transport equation (11,13). In most m...

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Variations in the amplitude and phase of diffuse photon density waves is known to yield important information about the structural properties of turbid media, such as the scattering and absorption coefficients. Information on the dynamical properties of turbid media may be obtained from the temporal fluctuations of light fields emanating from the media. In this contribution, we demonstrate that variations in temporal correlation functions of the temporal intensity fluctuations of different speckles of light can be used to derive information about the spatially varying dynamical properties of turbid media. We first present a diffusion for the temporal correlation function for systems where the dynamics are governed by Brownian motion and shear and random flow. We demonstrate the validity of the correlation diffusion for heterogeneous systems by comparing the theoretical results with experimental results for systems governed by different dynamical processes, e.g. flow. As an illustration of the usefulness of this correlation technique to biomedical optics, we discuss the application of this technique to diagnosing the thickness of burned tissue. The correlation diffusion is an important, unique tool for analyzing the complex dynamical signals that arise from heterogeneous biological systems.

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