Diffuse photon density waves are currently used to probe turbid media for optical anomalies such as tumors in tissue. A basic theory is established for detection of a fixed scatterer embedded in a turbid medium, including the effects of the medium's boundaries. Several diffuse expressions are obtained for a scattered wave both reflected and transmitted through a turbid layer, as well as within the layer, including important cases of vertically incident light and vertical observation by optical fibers. The importance of the scatterer's effective cross section when it is embedded in a random medium is emphasized. Specific results are obtained with a simple model of a scatterer. # 1998 Optical Society of America [S0740-3232(98)00705-4] OCIS codes: 100.6950,170.3880,170.5270,170.7050,170.3660,170.4580,170.6960.
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