## 4 Conclusions  
The double-wavelength time-gated system proposed can perform measurements at SDD of few millimeters, showing the improvements theoretically predicted--increased contrast and CNR as highlighted by phantom and in vivo tests. Furthermore, the simultaneous acquisition of photon counts in a temporal window at two wavelengths allowed for the estimation of the changes in O\({}_{2}\)Hb and HHb concentration during brain activation. The use of time gating--necessary for short SDD--however, can be useful also for long SDD measurements. In fact, as demonstrated with phantom measurements,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Subject** & **SDD** & **Gated** & \begin{tabular}{c} **Time** \\ **Window** \\ \end{tabular} & \begin{tabular}{c} **Contrast** \\ **O\({}_{2}\)Hb** \\ \end{tabular} & \
\begin{tabular}{c} **CNR** \\ **O\({}_{2}\)Hb** \\ \end{tabular} &
\begin{tabular}{c} **Contrast** \\ **HHb** \\ \end{tabular} & **CNR HHb** \\ \hline Subject 1 & 6 mm & Yes & 2.5–3 ns & \(21.9\pm 4.4\) & \(2.1\pm 0.6\) & \(4.5\pm 2.8\) & \(1.1\pm 0.7\) \\ \hline Subject 1 & 6 mm & No & 2.5–3 ns & \(5.1\pm 4.7\) & \(0.4\pm 0.4\) & \(1.7\pm 0.5\) & \(0.3\pm 0.1\) \\ \hline Subject 2 & 6 mm & Yes & 3–3.5 ns & \(23\pm 6.3\) & \(3.7\pm 2.5\) & \(11.2\pm 6.2\) & \(3.2\pm 3.2\) \\ \hline Subject 2 & 6 mm & No & 3–3.5 ns & \(6.9\pm 6.5\) & \(0.6\pm 0.5\) & \(1.7\pm 3\) & \(0.3\pm 0.5\) \\ \hline Subject 1 & 20 mm & Yes & 2.5–3 ns & \(18.1\pm 7\) & \(1.3\pm 0.7\) & \(6.3\pm 3.9\) & \(1\pm 0.7\) \\ \hline Subject 1 & 20 mm & No & 2.5–3 ns & \(12.4\pm 3\) & \(0.7\pm 0.2\) & \(5.4\pm 1\) & \(0.7\pm 0.2\) \\ \hline Subject 2 & 30 mm & Yes & 4.5–5 ns & \(44.8\pm 14.7\) & \(2.6\pm 1.2\) & \(25.4\pm 4.9\) & \(2.5\pm 1.1\) \\ \hline Subject 2 & 30 mm & No & 4.5–5 ns & \(50.2\pm 13.6\) & \(3.6\pm 1.1\) & \(13.5\pm 16.8\) & \(2.3\pm 3.2\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the in vivo measurements—finger tapping with the controlateral hand. Error for contrast and CNR is the standard deviation over the 5 finger tapping task repetitions. SDD = source-detector distance, O\({}_{2}\)Hb = oxygenated hemoglobin, HHb = deoxygenated hemoglobin.  
Figure 4: In vivo measurements of subject 2. Changes in O\({}_{2}\)Hb (red) and HHb (blue) averaged over the five repetitions of finger tapping with the contralateral hand for the gated and non-gated approach (left and right column, respectively) at the short and long distance (upper and bottom lines, respectively). Error bars represent the standard deviation over the five repetitions.  
CNR for an absorption perturbation was always higher in time gated measurements. This was true because, in the presence of enough laser power, time gating allowed the exploitation of the entire dynamic range of the acquisition chain of the system to collect more late photons--which brought about information about the deeper structure in the medium--than without time gating. This last aspect was demonstrated with phantom measurements, but not completely with in vivo measurements. It is noteworthy that the in vivo measurements at different gates and at different distances were performed at different times; it is therefore plausible that their comparison is not completely reliable because of the intrinsic variability of the brain activation.  
Conceptualization, A.D.M., A.T., L.S., A.P. and D.C.; data curation, L.D.S., A.D.M. and D.C.; formal analysis, L.D.S., A.T., L.S., R.R. and D.C.; validation, L.D.S., A.D.M., A.T., L.S., A.P. and D.C.; writing--original draft, L.D.S., A.D.M., A.T., L.S., A.P. and D.C. writing--review and editing, L.D.S., A.D.M., A.T., L.S., R.R., A.P. and D.C.  
This research was partially supported from the EU project nEUROPt (grant agreement 201076).  
The authors declare no conflict of interest.