## 3 Results and Discussions
### Simulation Results of Brain Functional Sensing
It can be seen from Figure 9d that the simulation values are basically in accordance with the theoretical calculation values except that the deviation of \(Y\) at \(Y=10\%\) is a little large, which is because the calculation error of \(Y\) varies with the value of \(\mu_{t}\), as described in Equation (13). The results of Figure 9e are the differences between the theoretical calculation values and simulation values. The pre-estimated calculation errors in the case that \(Y=10\%\) and \(Y=70\%\) are shown in Figure 9e, which can be seen to be consistent with the results of the actual simulation. If we predict that the \(Y\) of tissues is relatively high, then the choice of wavelengths is reasonable now. On the contrary, the current wavelengths selection is unreasonable if we predict that the \(Y\) of tissues is relatively low, and other  
Figure 9: Simulation results in visible waveband: **(a)** CW fluence extracted at plane \(y=0\)\(\upmu\)m; **(b)** backscattered signals and fitting results; **(c)** fitting results when class II photons are removed and when class II photons are not removed; **(d)** theoretical calculation values and simulation values of \(C\), \(Y\), and S; and **(e)** differences between theoretical calculation values and simulation values. wavelengths should be selected to make the errors of \(C\), \(Y\), and \(S\) smaller. When optimized for the case that \(Y=10\%\), the wavelengths of 546 nm, 552 nm, and 570 nm were selected. When the error of the extinction coefficient is the same, \(dC/C\), \(dY/Y\), and \(dS/S\) were 0.235, 0.036, and 0.082, respectively, which were reduced by 1.25, 14.7 and 1.28 times, respectively, compared with the results of Figure 9e. Therefore, in practical application, if we have a prior rough estimate of \(Y\) and \(C\) of the brain tissue to be measured, we can then reasonably choose the wavelengths to improve the measurement accuracy. The simulation results show that the correct optical parameters of tissues with low concentrations of hemoglobin can be obtained by rational selection of three wavelengths. However, the error of the extinction coefficient obtained by the simulation is very small, and the maximum value does not exceed 0.05 mm\({}^{-1}\). The error of \(C\) reaches about 30% when the error of \(\mu_{i}\) is 0.1 mm\({}^{-1}\). Therefore, when the sample has a low hemoglobin concentration and does not require high spatial resolution, there is no doubt that more accurate results can be obtained by fitting the data of multiple wavelengths. In summary, we briefly describe the optimization strategy for functional sensing of brain tissue as follows: When imaging small-sized blood vessels, the optimization scheme shown in Figure 7 can be used to reasonably select three wavelengths to resolve \(C\), \(Y\), and \(S\). When imaging the cerebral cortex and the spatial resolution requirement is not high, the method of fitting multi-wavelength data should be used; when the spatial resolution requirement is high, it is necessary to roughly estimate the range of \(Y\) and \(C\) in advance, and reasonably select three wavelengths to resolve \(C\), \(Y\), and \(S\). At the end of this section, as a little supplement to this work, functional sensing in a near-infrared waveband was simulated. The simulated tissue was gray matter with 100-\(\upmu\)m depth in which a blood vessel with a 100-\(\upmu\)m diameter is embedded. Similarly, considering the errors of \(C\) and \(Y\) simultaneously, we chose three wavelengths at 750 nm, 800 nm, and 900 nm for calculation. The window function of the STFT has a width of 50 nm in the spectral domain. Their optical parameters are shown in Table 5. The parameters of blood were the same as those in Figure 2, and the \(S\) values of gray matter in Table 5 were still obtained by dividing the scattering coefficients in Figure 2 by 10. In the near-infrared waveband, the scattering coefficient is approximately linear with the wavelength, as described in Equation (7).