## 1 Introduction
During the last few years, Silicon Photomultipliers (SiPMs) have been proposed and successfully validated as novel compact solid-state detectors for diffuse optics [21; 25]. Both CW and TD diffuse optics techniques are beginning to take advantage of SiPMs, since they hold the best features of PMTs (e.g., large active area) and those of solid-state detectors (high photon detection efficiency, low cost and complexity, low bias voltage, small size, robustness, and insensitiveness to magnetic fields) [26; 27; 28; 29]. When considering, in particular, TD diffuse optics, recent studies demonstrated impressive improvements in single-photon timing resolution (down to \(<\)60 ps Full-Width at Half Maximum, FWHM) [30] and the possibility to fabricate small electronic circuits that are able to efficiently control the detector when used in contact with the tissue under investigation [31]. In this way, the collection capability of diffused light is maximized thanks to the exploitation of the whole numerical aperture of the detector. This technology, already allows for the easy fabrication of miniaturized time-domain single-photon detectors at a very low cost (\(<\)$100).  
Interesting technologies for TD diffuse optics are represented by counters [32] and Time-to-Digital Converters (TDCs) [33]. However, only the latter devices are becoming commercially available at a cost lower than $1000 per timing channel, with a high count rate, and in principle they can be profitably employed for TD diffuse optics in general, provided that proper solutions are devised to cope with the high non-linearity of their time scale (e.g., implementation of procedures for correction of the non-linearity using a reference measurement with well-known shape). The combination of these technologies is progressively decreasing the gap between CW and TD instruments in terms of size and cost, thus possibly leading to a widespread diffusion of the TD technique thanks to its inherent advantages. This breakthrough will occur when also pulsed laser sources will undergo similar technological improvements and scaling. To some extent, this development on sources is already started as well, with promising proof-of-concept results [21; 34; 35]. In this paper, we present the first compact TD DOT system that is capable of providing functional tomographies at 1 Hz rate exploiting eight fiber-free detection channels based on SiPMs and an 8-channel TDC. The aim of this work is to demonstrate that these technologies are nowadays eligible for the design of small multichannel diffuse optical tomography instruments, thus paving the way to a new class of systems featuring substantial improvement in terms of dimension and complexity. The use of SiPMs for TD DOT was already proposed in a previous work [36]. Yet, in that case: (i) SiPMs were still embedded into a table-top module [37]; (ii) the detection system was still based on optical fibers; (iii) measurements were performed in a scanning mode using a 2-channel system resulting in relatively long measurement time (some minutes); and, (iv) the timing electronic circuits were traditional TCSPC boards. Vice versa, here, we explore a simple approach, with eight SiPMs that are directly embedded onto the probe in a circular arrangement and a single source in the center, permitting continuous data acquisition at 1 Hz. The adoption of a single injection point is clearly a limitation, which is partially compensated by the in-depth scanning capability that is provided by TD acquisition. Indeed, this scheme was chosen to demonstrate the feasibility of a basic tomographic setup, focusing on the detection chain. In any case, the system can be easily expanded by adding an optical fiber switch to take advantage of the multiple injection points to improve tomographic reconstructions or embedding other laser sources for spectroscopic purposes. In the following, we first describe the system architecture. Then, we present simulated results of the expected performance of the system.