## 3 Results  
### Determination of the Optimal Spectral Configuration of the Hyperspectral Camera  
In Figure 6, the quantification errors in \(\Delta C_{Hb\Omega_{2}}\), \(\Delta C_{Hb}\) and \(\Delta C_{oxCCO}\) (see Equation (10)) obtained for the best simulation-based deconvolution systems of \(N\) spectral bands (\(N\in[3;25]\)) are represented. The solid lines stand for the mean quantification error. The colored areas represent the dispersion range of the quantification errors. The vertical dashed lines indicate the optimal number of spectral bands for the deconvolution of each chromophore. Both corrected (in green) and uncorrected spectral configuration (in red) are represented. Note that these data were obtained using noisy measurements; zeros mean Gaussian noises were added to the camera intensities and to the Monte Carlo quantities (mean path length and reflection spectra); see Section 2.6.1. For the three chromophores, the quantification errors are important when a small number of spectral bands are used, but the quantification errors decrease with a larger number of bands. The quantification errors in \(\Delta C_{Hb\Omega_{2}}\) are on average 30% lower when the spectral correction is applied than when it is not applied. The quantification errors in \(\Delta C_{Hb}\) are on average 20% lower when the spectral correction is applied than when it is not applied. The quantification errors in \(\Delta C_{oxCCO}\) are  
Figure 6: Quantification errors (see Equation (10)) in \(\Delta C_{Hb\Omega_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\) obtained for the best simulation-based deconvolution systems of \(N\) spectral bands (\(N\in[3;25]\)). The solid lines stand for the mean quantification error. The colored areas represent the dispersion range of the quantification errors. The vertical dashed lines indicate the optimal number of spectral bands for the deconvolution of each chromophore. Both corrected (in green) and uncorrected spectral configuration (in red) are represented. equivalent with and without spectral correction. We can notice that the quantification errors reach a plateau when 15 corrected and uncorrected spectral bands are used. These spectral bands are indicated by violet points in Figure 7 and will be named optimal reduced spectral bands in the rest of the paper. For each chromophore, different optimal spectral combinations are found. For the quantification of \(\Delta C_{HbO_{2}}\), the best spectral configuration of our hyperspectral camera is composed of 25 spectral bands if the spectral correction is applied and of 16 spectral bands if the spectral correction is not applied. These spectral bands are indicated by black vertical lines in the HbO\({}_{2}\) molar extinction spectra in Figure 7. For these configurations, the quantification error (with Monte Carlo and intensity noise  
systems. When inspecting the spectral band used in the optimal reduced multiple systems, twenty-one different spectral bands are used with and without spectral correction. Thus, a single system can be designed using these spectral bands to quantify \(\Delta C_{HbO_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\) in a single measurement. In the same way, when inspecting the spectral variables used in the optimal multiple systems, all spectral bands of the hyperspectral camera are used. The accuracy of the quantification of the chromophore \(n\) can be measured using the mean and the standard deviation of the quantification error (see Equation (10)). According to ISO 5725-1 standards, the term \"accuracy\" stands for the trueness of the measurement (mean quantification errors close to 0%) and the repeatability of the measurement (standard deviation of quantification errors close to 0%). The mean and standard deviation values were calculated on \(10^{3}\) noisy measurements.