## 4 Applications
### Time Domain Diffuse Correlation Spectroscopy  
In recent years, the use of optical signals to assess the blood flow has gained increased interest in the scientific community. Indeed, DCS relies on the measurement of the autocorrelation in the fluctuations of light speckles generated by photons emerging from the tissue to non-invasively measure the blood flow [148; 149]. The basic characteristics (i.e., light transport, non-invasiveness and penetration depth) are the same as NIRS/DOS ones, recalled in Section 2. Many DCS systems rely on the use of CW sources and detectors. However, to recover the absolute blood flow value, it is fundamental to know the optical properties of the tissue under analysis [150; 151; 152]. For this reason, in literature the use of a DCS system coupled to TD or frequency-domain spectroscopic instruments have been proposed [153; 154]. Additionally, the CW DCS systems suffer from confounding effects introduced by extracerebral flow due to systemic physiological changes. In 2016 [PERSON] et al. [153], introduced for the first time the use of TD DCS in phantoms and on rats, while [PERSON] et al. [154] extended the method also on humans with first in-vivo studies on the adult forehead and arm. In all those cases, a post-processing time-windowing of the whole DTOF was applied to improve the autocorrelation of the speckles fluctuation, as well as the sensitivity to deeper layer of the tissue. However, the use of time windowing strongly reduces the number of suitable photon counts. Without time-gating, the decrease of \(\rho\) cannot be a solution since the number of early photons will be orders of magnitude higher than the number of late ones. In this scenario, the use of the time-gating would be beneficial. The first demonstration of the TG DCS at small \(\rho\) was given in 2018 by [PERSON] et al. [155]. In that paper, the authors demonstrated the possibility to use a fast-gated SPAD module to select the temporal window where photons will be collected and to compute the correlation. The detector output signal was directly connected to both a hardware correlator and to a TCSPC device working in time-tagging mode, with autocorrelation computed in a post-processing stage. After demonstrating that there is no difference between the  
Figure 15: On the (**left**), maps of recovered oxy- and deoxy-hemoglobin. On the (**right**), volume used for reconstruction (top) and the mouse after the flap surgery with indication of source (S) and detector (D) fibers position. Figure modified from [147].  
correlation computed using the hardware correlator or the software one, the authors compared the relative blood flow index for an arterial arm cuff occlusion obtained with a standard time-resolved system (free running SPAD, \(\rho=12\) mm) with the one obtained with the quasi null \(\rho\) distance (2.85 mm) exploiting the time-gating technique. The results achieved are reported in Figure 16. The relative blood flow index was quantitatively similar for both acquisitions even if two aspects are underlined by the authors: (i) the gated measurement displayed a noisier behavior; (ii) the hyperemic peak for the gated acquisition was about 37% higher but this is compatible with the deeper region probed, where muscles are expected to show faster dynamics.