Fig. 1.

(a) Illustration of the single scattering event and the parameters used in Eq. (1). (b) The geometry of the Monte Carlo simulation used in this manuscript and the illustration of the gating strategy for TD-DCS. The size of the detector is 2 mm, the thickness of the first layer or first tissue type is 15 mm, the reduced scattering coefficient is ${\mu }_{s^{\prime }}=1{\mathrm{mm}}^{-1}$ and absorption coefficient ${\mu }_a=0.01{\mathrm{mm}}^{-1}$. The optical properties ${\mu }_{s^{\prime }}$ and ${\mu }_a$ are set to be the same for the two layers. The dynamics in the second layer is increased when brain activation is introduced. The source detector separation is set to be $\rho =20\mathrm{mm}$ unless otherwise stated. Measurements at a later gate will be able to select photons with longer pathlengths, thus it is more sensitive to dynamics at deeper depths. (c) Illustration of the calculation of the photon arrival time for the $n$th photon as the sum of the IRF time and the transit time within the sample $t_{na}=t_{n\mathrm{RIF}}+t_{nL}$. (d) The IRF profile we have used in this manuscript obtained experimentally. The full width half maximum of the IRF is 0.31 ns. The dashed lines indicate the levels of the intensity of the IRF that corresponds to 0.1, 0.01, and 0.001 of the peak intensity, and the widths that correspond to these levels are 0.56, 0.82, and 1.18 ns, respectively.