## 3 Results
### Phantom Experimental Results  
Figures 11 and 12 show the broadband \(\mu_{a}\) and \(\mu_{s}\)' spectra of the inclusion and substrate optical properties reconstructed from the two heterogeneous tissue-simulating phantoms. Each panel of Figures 11 and 12 compares the broadband results from hybrid DOI technique to the topographic DOI results and the true (\(\mu_{a}\), \(\mu_{s}\)') values of the phantom. Broadband optical properties for substrate \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Depths** & \multicolumn{6}{c}{**Tumor**} \\ \multicolumn{2}{c}{**(mm)**} & \multicolumn{2}{c}{**Hybrid DOI**} & \multicolumn{6}{c}{**Topographic DOI**} \\ \hline  & \multicolumn{2}{c}{**Mean Difference from**} & \multicolumn{2}{c}{**Mean\% Change**} & \multicolumn{2}{c}{**Mean Difference from**} & \multicolumn{2}{c}{**Mean\% Change**} \\  & \multicolumn{2}{c}{**True Over all**} & \multicolumn{2}{c}{**from True Over all**} & \multicolumn{2}{c}{**True Over all**} & \multicolumn{2}{c}{**from True Over all**} \\  & \multicolumn{2}{c}{**Wavelengths (mm\({}^{-1}\))**} & \multicolumn{2}{c}{**Wavelengths (\%)**} & \multicolumn{2}{c}{**Wavelengths (mm\({}^{-1}\))**} & \multicolumn{2}{c}{**Wavelengths (\%)**} \\ \hline  & \multicolumn{2}{c}{\(\mu_{a}\)} & \(\mu_{s}\)’ & \(\mu_{a}\) & \(\mu_{s}\)’ & \(\mu_{a}\) & \(\mu_{s}\)’ & \(\mu_{a}\)’ \\ \hline
0 & \(3.9\times 10^{-4}\) & 0.13 & 3.87 & 7.86 & \(2.2\times 10^{-3}\) & 0.03 & 22.35 & 1.78 \\ \hline
5 & \(7.2\times 10^{-4}\) & 0.25 & 7.49 & 15.34 & \(2.6\times 10^{-3}\) & 0.16 & 26.52 & 10.38 \\ \hline
10 & \(1.2\times 10^{-3}\) & 0.75 & 8.39 & 47.86 & \(3.2\times 10^{-3}\) & 0.21 & 32.26 & 13.04 \\ \hline \multicolumn{6}{c}{**Normal**} \\ \hline  & \multicolumn{2}{c}{**Hybrid DOI**} & \multicolumn{6}{c}{**Topographic DOI**} \\ \hline  & \multicolumn{2}{c}{**Mean difference from**} & \multicolumn{2}{c}{**Mean\% change from**} & \multicolumn{2}{c}{**Mean difference from**} & \multicolumn{2}{c}{**Mean\% change from**} \\  & \multicolumn{2}{c}{**true over all**} & \multicolumn{2}{c}{**true over all**} & \multicolumn{2}{c}{**true over all**} & \multicolumn{2}{c}{**true over all**} \\  & \multicolumn{2}{c}{**wavelengths (mm\({}^{-1}\))**} & \multicolumn{2}{c}{**wavelengths (\%)**} & \multicolumn{2}{c}{**wavelengths (mm\({}^{-1}\))**} & \multicolumn{2}{c}{**wavelengths (\%)**} \\ \hline  & \multicolumn{2}{c}{\(\mu_{a}\)} & \(\mu_{s}\)’ & \(\mu_{a}\)’ & \(\mu_{s}\)’ & \(\mu_{a}\)’ & \(\mu_{s}\)’ & \(\mu_{a}\)’ \\ \hline
0 & \(1.1\times 10^{-4}\) & 0.03 & 1.64 & 1.9 & \(1.9\times 10^{-4}\) & 0.04 & 3.65 & 3.14 \\ \hline
5 & \(1.0\times 10^{-4}\) & 0.02 & 1.50 & 1.76 & \(2.1\times 10^{-4}\) & 0.04 & 3.89 & 3.30 \\ \hline
10 & \(1.0\times 10^{-4}\) & 0.02 & 1.35 & 1.64 & \(2.2\times 10^{-4}\) & 0.04 & 4.10 & 3.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean difference and mean percentage difference of recovered (\(\mu_{a}\), \(\mu_{s}\)′) from true (\(\mu_{a}\), \(\mu_{s}\)′) over all wavelengths. Figure 10: Hyperspectral normal (row 1) and tumor \(\mu_{s}\)′ (row 2) at wavelengths 650 nm to 1000 nm at different tumor depths (columns). and inclusion were reconstructed for 71 wavelengths from 650 to 1000 nm on each side of phantoms A and B. Measurements on different sides of the phantoms corresponds to different depths of the inclusion from the phantom surface. The top and bottom row correspond to the substrate and inclusion absorption of the phantoms, respectively. The true spectra for the substrate was measured on the inclusion phantoms (A and B), by acquiring a measurement away from the inclusion. This was done to ensure that the optical path does not interrogate the inclusion. The true spectra for the inclusions of phantoms A and B were acquired by measuring a separate homogenous phantoms that were made from the same batch material/composition of the inclusions in A and B.