## 3 Results  
Figure 3 shows the assessment of de-noised signals in all three channels and at all wavelengths in terms of the cross-subject averaged temporal correlation (first and second rows), temporal logarithmic signal means (third row, used for the data quality assessment), and temporal standard deviations (fourth row). Figure 3: Hyperspectral signal analysis: cross-subject averaged correlation, temporal means, and temporal standard deviations for signals from 1 cm, 3 cm, and 4 cm channels. Blue color shows the cross-subject standard deviations. Since the noise was filtered out, the latter represent the average magnitude of changes at different wavelengths. The correlation coefficient maps (first row) show that signals at all wavelengths from 700 nm to over 900 nm and in all channels were positively correlated. The latter means that there were no pairs of signals at any wavelengths from 700 nm to 900 nm and in any channels where temporal changes occurred simultaneously in opposite directions. Also from the correlation maps and same-wavelength correlation plots (second row) one could see that all signals between 750 nm and 900 nm were highly correlated (correlation coefficient > 0.6). This high correlation occurred because, as shown in [3], at both 3 and 4 cm the optical pathlength in the extracerebral tissue was several times longer than in the brain, and therefore the scalp contribution was high at both 4 and 3 cm channels. Correlations were low for the wavelengths longer than 900 nm in the 4 cm channel. While the mean signal value in the 4 cm channel at these wavelengths was high (third row), the amplitude of changes (fourth row) was small. This lack of changes should be due to fact that at longer wavelengths the partial optical pathlengths in the tissues where the changes occurred (scalp and brain) was shorter than at wavelengths below 900 nm, and at the 4 cm source-detector separation the light of wavelengths greater than 900 nm mostly interrogated the volume which belongs to the skull where no changes occurred. For the above reasons the further analysis was performed using the waveband from 750 nm to 900 nm. Figure 4 shows the cross-subject averaged changes in [HbO\({}_{2}\)], [HHb], [rCCO], and [rSO\({}_{2}\)] measured at 1 cm, 3 cm, and 4 cm using the homogeneous tissue model and 750-900 nm waveband. One could see that the hemoglobin signals showed responses to BHs in all channels, while rCCO exhibited clear responses only at 4 cm. Table 1 presents the average amplitude, p-values, and temporal values characteristic for the chromophore responses to BHs. In addition to Figures 4 and 5 provides a direct comparison of the hemoglobin time-courses at 1 cm and 4 cm and shows a return to the baseline 4 min after BHs. As shown in Figures 4 and 5, and also from the peak times for HbO\({}_{2}\) in Table 1 the time-courses of HbO\({}_{2}\) responses appeared similar in all channels. The common features of HHb responses to BHs in 1 cm and 3 cm channels were the initial dips followed by quick increases peaking up 4-10 s after the end of BH. The depth of initial dips was much greater in the 1 cm channel than in 3 cm and 4 cm channels (Figure 5b). However, the magnitudes of these dips measured from the HHb levels just before BH were statistically insignificant (\(p\) > 0.05). The HHb peak times were longest for the 1 cm channel (about 9 s after the end of BH, see Table 1). Much earlier peaks and faster falls in the HHb responses at 4 cm compared to those features at 1 cm (Figure 5b, Table 1) might indicate a prevalence of the cerebral component in the 4 cm HHb responses. In particular, the faster falls of HHb at 4 cm than at 1 cm could be due to the cerebral autoregulation restoring the oxygen concentration in the brain faster than in extracerebral tissues. In Figure 4 one can also see that at 3 cm the HHb responses were intermediate between those measured at 1 cm and 4 cm. The rCCO signals from the 1 cm and 3 cm channels showed no clear responses to BHs.