## 1 Introduction  
Among the fascinating applications of lasers, the non-invasive/non-destructive analysis of diffusive samples [1] (such as biological tissues, fruit, chemicals and wood [2; 3; 4]) has recently gained a lot of interest for the promising exploitations in biomedicine, in the food sector and in industrial fields. Photons injected in a diffusive medium undergo many scattering events due to refractive index mismatches at the micro and meso scale. Moreover, if light absorption is weak, like what happens in the so-called \"therapeutic window\" (600 to 1100 nm), where biological tissues are almost transparent to red and near infrared light, diffusing photons can easily be reemitted at the medium boundaries after having travelled deep in the tissue (e.g., >1 cm below skin in biological tissue in a reflectance configuration). The information carried by diffusing photons relates to the structural properties (linked to the scattering coefficient) and to the chemical properties (linked to the absorption coefficient) of the medium. For biomedical applications, the main chromophores of interest in the range between 600-850 nm are oxygenated and deoxygenated hemoglobin (O\({}_{2}\)Hb and HHb, respectively) [5]. For this reason, diffuse optical spectroscopy is a promising tool to assess brain and muscle oxygenation. In particular, functional near infrared spectroscopy (fNIRS) exploits the difference in absorption spectrum between HHb and O\({}_{2}\)Hb to recover their concentration over time, thus enabling the ability to see variation in haemodynamics, which can be a fingerprint of a brain activation thanks to the neurovascular coupling mechanism. While the use of steady state light sources and detectors enables the so-called continuous wave (CW) approach to fNIRS, the time-resolved (TR) approach relies on the injection in the sample of short laser pulses (few tens of ps duration) and on the recording of the arrival time of re-emittedphotons (distribution of time of flight, DTOF) at a given distance, the so-called source-detector distance (SDD). It has been demonstrated that the TR-technique provides a higher information content than CW, in particular when a single SDD is used [6]. Indeed, it is possible to recover the optical properties (absorption coefficient -u\({}_{\text{a}}\)- and reduced scattering coefficient -u\({}_{\text{s}}\)), after fitting of the DTOF with a proper theoretical model [7]. Moreover, when using the TR technique in the so-called \"reflectance geometry\" (i.e., injection and collection put on the same side of the sample), the depth reached by photons is intrinsically encoded in their arrival time--the later the photon is re-emitted, the longer is its pathlength, thus increasing significantly the probability of the photon to have probed a deeper region [8]. It has also been demonstrated that the mean penetration depth of photons is independent of the SDD. For this reason, the null-SDD approach was proposed some years ago [9]. The use of short (or even null) SDD improves the confinement of photons, thus resulting in a higher spatial resolution and number of photons recorded, as well as a larger contrast at all times. To apply this approach, however, a fast-gated detector (i.e., a detector that can be turned on/off in a few hundred ps) is needed to prevent the detector saturation (or its damage). To meet this requirement, fast-gated (FG) single-photon avalanche diodes (SPADs) have been proposed in the literature [10,11]. The use of a FG-detector permits also the ability to reconstruct the DTOF with a larger dynamic range [12] and this great potentiality can be exploited if the laser source is powerful enough to increase the signal at late times, thus allowing the ability to probe deeper regions [13].