Time domain analysis of photon scattering and Huygens-Fresnel back projection

Stand-off detection and characterization of scattering media such as fog and aerosols is an important task in environmental monitoring and related applications. We present, for the first time, a stand-off characterization of sprayed water fog in the time domain. Using a time correlated single photon counting, we measure transient signatures of photons reflected off a target within the fog volume. We can distinguish ballistic from scattered photon. By application of a forward propagation model, we reconstruct the scattered photon paths and determine the fog's mean scattering length μ_scat. in a range of 1.55 m to 1.86m. Moreover, in a second analysis, we project the recorded transients back to reconstruct the scene using virtual Huygens-Fresnel wavefronts. While in medium-density fog some contribution of ballistic remain in the signatures, we could demonstrate that in high-density fog, all recorded photons are at least scattered a single time. This work may path the way to novel characterization tools of and enhanced imaging in scattering media.