## 1 Introduction  
Diffuse Optical Tomography (DOT) in the near infrared spectrum is a valuable tool for many applications, like breast cancer analysis [1; 2; 3; 4; 5], functional imaging [6; 7], small-animals imaging [8], and non-destructive assessment of food quality [9; 10]. In fact, the main chromophores that are present in biological tissues feature a low absorption coefficient (\(\mu_{a}<0.1\) mm\({}^{-1}\)) and a high reduced scattering coefficient (\(\mu_{s}^{\prime}\approx 1\) mm\({}^{-1}\)) to radiation within the so-called therapeutic window (600-1100 nm), thus permitting light to propagate for long pathlengths and to be detected when re-emitted outside of the tissue. DOT relies on sampling the external boundary of the medium with a distribution of sources and detectors [11; 12]. Depending on the light modulation, different approaches to DOT can be employed: continuous-wave (CW), frequency-domain (FD), and time-domain (TD). Due to the lower cost and complexity, DOT systems requiring a large number of sources and detectors have been implemented mainly using CW technologies. Important achievements were obtained, for instance, in the field of neuromonitoring [6], breast imaging [13; 14], tomography of osteoriticular diseases [15], and peripheral arterial disease [16]. CW approaches have permitted an easier exploration of biomedical applications, but convey a lower amount of information as compared to FD or TD techniques, in terms, for instance, of coupling between absorption and reduced scattering coefficients or strong dependence on superficial effects, movement artifacts, and optical coupling. This requires compensating lower information content with a larger number of optodes, exploiting for instance multiple source-detector distances to discriminate scalp-skull systemic fluctuations from true brain activation [17; 18]. The explosion of source-detector pairs can be challenging in view of the fascinating evolution toward a fiberless, whole-scalp diffuse optical tomography systems [19]. In general, the possibility to collect multiple information from the same optode is an interesting challenge to increase quantitation in DOT, reduce artefacts and confounding effects, and improve robustness in clinical settings or in natural/social situations [20]. The TD approach, consisting of the injection of picoseconds pulses and time-domain detection, can indeed expand the information content carried by the same optode. TD techniques have been demonstrated to be potentially sensitive and capable to localize deep perturbations (depth \(>\) 3 cm) when sources and detectors are placed on the same surface of the sample (reflectance configuration) [21]. The unique feature of TD approaches is the possibility to increase the depth sensitivity for increased photon traveling time. Thus, for the same source-detector pair, different measurements with different spatial sensitivity can be collected. Consequently, tomographic reconstruction can be achieved in the TD domain with a lower number of optodes as compared, for instance, to CW. Due to the complexity of the system and the cost of sources, detectors, and timing electronics, the TD approach has not been widely used in the DOT field. In fact, only a few systems in literature are capable of a full TD-DOT [22; 23; 24]. These systems are quite sophisticated and expensive, being based on parallel chains that are based on time-correlated single-photon counting (TCSPC) boards and Photomultiplier Tubes (PMTs). Moreover, they are cumbersome because every PMT needs its own cooling and power supply system. Further, light harvesting through fibers bundles adds to the complexity of the instruments. Another limitation of TD systems is the low measurement speed since the single-photon counting acquisition is dominated by Poisson statistics, thus requiring a large-area, low noise, and high-quantum efficiency time-domain detectors. All of these aspects have limited the number of in vivo and real-time applications.