A physical model of how optical heterogeneities affect time-dependent measurements of photon migration in tissue-like scattering media is presented. Using this model, changes in frequency-domain measurements of phase-shift, 0, and amplitude modulation, M, are predicted in the presence of transparent and perfectly absorbing objects. Two-dimensional Monte Carlo simulations of photon migration and single-pixel measurements of 0 and M confirm the physical model. Recent experimental "images" from multi-pixel measurements of 0 and M are also consistent with the physical model. These results suggest that two dimensional frequency-domain measurements provide direct information for detection and three dimensional localization of optical heterogeneities without the use of computer intensive reconstruction algorithms.
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