Distribution of the paths of early-arriving photons traversing a turbid medium

We describe experiments to measure the spatial and the temporal distribution of photons traversing a turbid medium in the early-arriving regime in which the photons are multiply scattered but are not completely randomized. The photon paths are resolved temporally by a streak camera and spatially by an adjustable absorbing screen with a small aperture. The results are compared with predictions of a theory based on path integrals (PIs) and with the standard diffusion approximation. The PI theory agrees with the data for both long and short times of flight; this agreement is in contrast to the diffusion approximation, which fails for short times. An alternative PI calculation, based on the use of an effective Lagrangian, also agrees with the experiments. PI theory succeeds because it preserves causality. The implications for optical tomography are discussed.