## Materials and Methods
### Phantom Optical Characterization  
The optical characteristics of the EPE layers are relatively close to those of human brain tissues. To investigate such an aspect, we performed reflectivity measurements of the phantom by varying the SDS. Such measurements provide a quantitative evaluation of the parameter \(\sqrt{\mu_{a}\mu_{s}^{\prime}}\), where \(\mu_{a}\) is the absorption coefficient and \(\mu_{s}^{\prime}\) is the reduced scattering coefficient. In the brain cortex tissues \(\mu_{a}\) and \(\mu_{s}^{\prime}\) are of the order of 0.1 cm\({}^{-1}\) and 10 cm\({}^{-1}\), respectively [25], so that \(\sqrt{\mu_{a}\mu_{s}^{\prime}}\) is approximatively 1 cm\({}^{-1}\)  
Figure 1: (**a**) Arrangement scheme of light source and detectors (top view). (**b**) Silicon photomultiplier (SiPM) and light emitting diode (LED) holders (bottom view). Figure 2: Scheme of the three-layer phantom with a mobile metal bar. In back-scattering measurements, on which the CW-fNIRS principle of operation is based, the light diffusion transport is modeled by using the modified Lambert-Beer law:  
\[I(\lambda)=I_{0}(\lambda)\exp[-\mu_{\alpha}(\lambda)\cdot SDS\cdot DPF(\lambda)+G( \lambda)] \tag{1}\]  
where \(I(\lambda)\) is the measured wavelength-dependent diffused reflected light intensity, \(I_{0}(\lambda)\) is the incident light intensity, \(\mu_{\alpha}(\lambda)\) is the absorption coefficient, \(DPF(\lambda)\) is the differential path length factor, and \(G(\lambda)\) is a wavelength-, medium-, and geometry-dependent constant. \(DPF(\lambda)\) is a scaling factor shown to be approximately equal to \(\frac{1}{2}\)\(\sqrt{3\mu_{s}^{\prime}/\mu_{a}}\)[26]. Hence, \(I(\lambda)\) can be rewritten as  
\[I(\lambda)=k\cdot\exp\left[-\sqrt{3\cdot\mu_{a}(\lambda)\cdot\mu_{s}^{\prime}( \lambda)}\cdot\frac{SDS}{2}\right] \tag{2}\]  
a decreasing exponential function of SDS. Figure 3 reports the photocurrents measured on the phantom at different SDSs under 700 nm and 830 nm illumination. From the data reported in Figure 3, we directly measure the effective attenuation coefficient using the photocurrent slope [27]. Therefore, we estimate that the EPE layer \(\sqrt{\mu_{a}\cdot\mu_{s}^{\prime}}\) is approximately 0.53 cm\({}^{-1}\), relatively close to the human brain cortex tissues for which the \(\sqrt{\mu_{a}\cdot\mu_{s}^{\prime}}\) values are about 1 cm\({}^{-1}\) in the near-infrared (NIR) range. Hence, though the effective attenuation coefficient of the EPE medium is close to the human tissues one, the phantom is relatively more \"transparent\" in the NIR range. Our phantom is characterized by an air gap, so we evaluate the weight of such an air gap on the light back diffusion. Figure 3 reports the comparison of near-infrared light back diffusion for two types of phantom: phantom 1 is a 50 cm \(\times\) 40 cm \(\times\) 6 cm EPE slab with no air gap while phantom 2 is the multilayer phantom used in this work, made of an EPE slab of 50 cm \(\times\) 40 cm \(\times\) 3 cm, on a 3 cm air gap, and on a second EPE slab of 50 cm \(\times\) 40 cm \(\times\) 3 cm. The measurements were taken by a voltage drop across a 50 \(\Omega\) resistor in series to a single SiPM detector illuminated alternatively by two LEDs (700 nm and 830 nm wavelengths) both biased at a fixed current of 1.40 \(\mu\)A and mounted on a board with an inter-LED distance of 2 mm. The comparison of the measurements taken at different SDSs on phantom 1 and phantom 2 shown in Figure 3 confirms that the air gap gives a small contribution: the CW photocurrents in phantom 2 are only slightly lower  
Figure 3: SiPM photocurrents measured on the phantoms at multiple source detector separations (SDSs) under 700 nm and 830 nm illumination. Moreover, the measured \(\sqrt{\mu_{a}\mu_{s}^{\prime}}\) values are quite similar at the two used wavelengths, 700 nm and 830 nm. The coupling of the data in Figure 3 to measurements of time-of-flight (TOF) in phantom 1 allows for evaluating both \(\mu_{a}\) and \(\mu_{s}\)' for the used EPE material.