We present an analytical perturbation analysis for studying the sensitivity of diffusive photon flux to the addition of a small spherical defect object in multiple-scattering media such as human tissues. As a first simple application of our perturbation method, we derive analytically the photon migration path distributions and the shapes of the so-called banana regions in which the photon migration paths are concentrated. We then derive analytically the sensitivity of detected photon flux densities to the inclusion of small spherical defects in the multiple-scattering medium for both single-source and two-source configurations, at both steady-state (dc) and frequency-modulation conditions, and compare the results with Monte Carlo simulations.
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