Time-resolved detection of early-arriving ballistic waves in a quasi-diffusive regime

Ballistic waves directly carry image information in imaging through a scattering medium, but they are often obscured by much intense multiple-scattered waves. Detecting early arriving photons has been an effective method to extract ballistic waves in the transmission-mode imaging. However, it has been difficult to identify the temporal distribution of ballistic waves relative to the multiple scattering waves in the quasi-diffusive regime. Here, we present a method to separately quantify ballistic and multiple-scattered waves at their corresponding flight times even when multiple scattering is much stronger than the ballistic waves. This is realized by measuring the transmission matrix of an object embedded within scattering medium and comparing the coherent accumulation of ballistic waves with their incoherent addition. To further elucidate the temporal behavior of ballistic waves in quasi-diffusive regime, we analyze the flight time difference between ballistic and multiple-scattered waves and the effect of coherence gating on their relative intensities for the scattering medium of different thicknesses. The presented method to distinctively detect the temporal behavior of ballistic and multiple-scattered waves will lay a foundation to exploit multiple-scattered waves for deep-tissue imaging.