## Materials and Methods
### System Functioning and Components  
The system control works as follows: during operation, time division measurements of all the SiPMs outputs are performed on the active input channels of a National Instruments USB-6255 multifunction data acquisition board at 1.25 MHz sampling frequency. The system starts performing a measurement of the dark current of all SiPMs when all the LEDs are in off state. Then the 700 nm LED of the first LED couple is turned on and the system reads all the channels and calculates each point as the average of 250 measurements on the SiPM output. Then when the 700 nm turns off  
Figure 4: Average arrival time of photons: theoretical (colored continuous lines) and measured in back diffusion configuration on the phantom (black connected points). and the 830 nm LED of the couple turns on, the system acquires all the SiPMs currents and repeats this operation for all the LED couples. Then, the cycle restarts from the beginning. This procedure prevents illumination interferences and ensures the correct definition of the channels. As far as the time resolution is concerned, the photocurrent signals are acquired on a 13-channel, 1.25 MHz frequency Analog to Digital Converter (ADC), that is, each photocurrent is monitored for 1/1.25 \(\times\) 10\({}^{6}\) s (=0.8 \(\upmu\)s) on every 13/1.25 \(\times\) 10\({}^{6}\) (=10.4 \(\upmu\)s). We perform 250 acquisitions, corresponding to a total measure time on all SiPM channels with only one LED on of 2.6 ms. Such operation is repeated for all LEDs, plus one dark phase. Hence, one complete measurement cycle may be performed in principle in 25 \(\times\) 2.6 ms = 65 ms. However, we need to avoid all the transients due to LED switch on and off and to SiPM thermal transients [19]. For such reason we used a much larger time window, with a minimum cycle time of 476 ms and an overall frequency of about 2.1 Hz. Considering the optodes configuration reported in Figure 1a, Figure 5 reports the x-y geometrical positions of the mid-points between the sources and the detectors involved in the measurements classified by the SDSs. As shown in a study by [PERSON], [PERSON], and [PERSON] [8], for a given source-detector pair the maximum sensitivity region is located for the x and y coordinates at the midpoint, and deeper and deeper as the SDS increases. Hence, in Figure 5 we report the resulting two-dimensional matrices classified by the SDSs by using such assumptions. Some of the source-detector paths identify the same point in the medium, to a total of 108 different observed points. In each map the observed points (black circles), sources (red circles), and detectors (blue squares) involved in the definition of the channels are represented for each SDS. Large area p-on-n MICROFJ-60035 SiPM detectors manufactured by ON Semiconductors were used for the measurements presented here [29]. The SiPM structure is formed by planar p+/n microcells with a total area of 6.07 \(\times\) 6.07 mm\({}^{2}\), 22,292 square microcells, a geometrical fill factor of 75%, packaged in a surface mount housing (Surface Mounting Device, SMD), sealed by transparent glass with a refractive index of about 1.53 at 436 nm. The SiPM devices have a breakdown voltage of about 24.5 V at room temperature, and a photon detection efficiency (PDE) of about 10% measured at 700 nm and 6 V overvoltage (voltage above the breakdown, OV). Roithner LaserTechnik SMC700 and SMC830 AlGaAs LEDs in SMD ceramic packages emitting respectively at 700 nm and 830 nm wavelengths, were used  
Figure 5: Maps of geometrical position of the tested points (black circles) for the case of the checkerboard pattern of SiPMs (blue squares) and sources (red circles) reported in Figure 1.  
as optical light sources. The LEDs have an area of \(2\times 2\) mm\({}^{2}\), viewing angle of \(\pm 55^{\circ}\), and average spectral bandwidth of 20 nm and 35 nm at 700 nm and 830 nm emission wavelengths, respectively.