## 3 Results and Discussions
### Simulation Results of Brain Functional Sensing
Within the spectral bandwidth of the source, the optimal and worst combinations are 560 nm, 575 nm, 590 nm and 553 nm, 568 nm, 583 nm, respectively. Figure 7a-c shows the calculation errors of \(C\), \(Y\), and \(S\), respectively. Since the error of the extinction coefficient is random, we compare the maximum of the 200 calculation errors of the two combinations. The maximum values of the \(dC/C\), \(dY/Y\), and \(dS/S\) of the optimal combination are reduced by 17.6, 5.8, and 14.5 times, respectively, compared to those of the worst combination. The optical parameters of the two combinations are shown in Table 2, and Figure 8 shows the simulation results using MMC-OCT. When using the method described in [6], it can be approximated that the scattering coefficient is not affected by the wavelength, so we set the scattering coefficient for each wavelength to 70 mm\({}^{-1}\). The simulation results for the 560 nm wavelength are summarized in Figure 8. Figure 8a shows the continuous wave (CW) fluence extracted at plane \(y=0\)\(\upmu\)m, and the black dotted box in the figure indicates the position of the blood vessel. The blue curve in Figure 8b is the backscattered signal, and the signal in the depth range of 70 \(\upmu\)m-100 \(\upmu\)m is selected to calculate the extinction coefficient by exponential fitting, the results of which are shown in Figure 8c. The fitting coefficients and goodness are shown in the picture, and the \(R^{2}\) value of the fitting results is 0.9969. The fitting results of two combinations and \(C\), \(Y\), and \(S\) calculated from the fitting results are listed in Table 3. The parameters marked \"The\" in Table 3 are the theoretical calculation values, and those labeled \"Rea\" are the simulation values. It can be seen that the two are basically the same, and the maximum error  
Figure 6: Calculation errors of three parameters when \(dC\) is small (**a**) and when \(dY\) is small (**b**). is 0.06 mm\({}^{-1}\). Of course, this does not mean that the error in the actual experiment is also at this level, but rather illustrates the feasibility of the MMC-OCT in simulating the process of obtaining the extinction coefficient. The errors of \(C\), \(Y\), and \(S\) obtained by the optimized combination of wavelengths are much smaller than those obtained by the worst combination, and the calculation errors of \(C\), \(Y\), and \(S\) are reduced by 160, 16.75, and 238.8 times, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \(\Lambda\) (nm) & \(\epsilon_{O}\) (mmol\({}^{-1}\).mm\({}^{-1}\)) & \(\epsilon_{D}\) (mmol\({}^{-1}\).mm\({}^{-1}\)) & \(S\) (mm\({}^{-1}\)) \\ \hline \multicolumn{4}{c}{Optimal Combination} \\ \hline
560 & 4.1519 & 5.7674 & 70 \\
575 & 5.8742 & 4.5500 & 70 \\
590 & 2.1107 & 3.0857 & 70 \\ \hline \multicolumn{4}{c}{Worst Combination} \\ \hline
553 & 4.7611 & 5.7666 & 70 \\
568 & 4.8988 & 5.2246 & 70 \\
583 & 4.7178 & 3.8402 & 70 \\ \hline \end{tabular}
\end{table} 
Table 2: Optical parameters of optimal and worst wavelength combinations for functional sensing. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Combinations** & **The \(\mu_{1}\)** & **The \(\mu_{2}\)** & **The \(\mu_{3}\)** & **Rea \(\mu_{1}\)** & **Rea \(\mu_{2}\)** & **Rea \(\mu_{3}\)** & \(C\) & \(Y\) & \(S_{1}\) \\ \hline
560, 575, 590 & 91.352 & 95.222 & 81.067 & 91.338 & 95.268 & 81.047 & 2.003 & 0.704 & 69.978 \\
553, 568, 583 & 93.315 & 93.01 & 90.514 & 93.291 & 93.171 & 90.531 & 2.482 & 0.767 & 64.746 \\ \hline \end{tabular}
\end{table} 
Table 3: Fitting results and calculated \(C\), \(Y\), and \(S\) for two combinations. Figure 7: **(a)** The sum of the errors of the three parameters calculated using different wavelength combinations; calculation errors of \(C\) (**b**), \(Y\) (**c**), and \(S\) (**d**) calculated using the optimal wavelength combination and the worst wavelength combination. The results in Table 3 show that we can obtain very accurate optical parameters of blood vessels by reasonably selecting three wavelengths.