## 3 Results
### Simulated Results of Topographic DOI Method
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Depths**} & \multicolumn{6}{c}{**Tumor**} \\ \multicolumn{2}{c}{**(mm)**} & \multicolumn{6}{c}{**Hybrid DOI**} & \multicolumn{6}{c}{**Topographic DOI**} \\ \hline \multicolumn{2}{c}{} & \multicolumn{6}{c}{**Difference from True (mm\({}^{-1}\))**} & \multicolumn{2}{c}{**\% Difference of**} & \multicolumn{2}{c}{**Difference from True (\%)**} & \multicolumn{2}{c}{**\% Difference of**} \\ \multicolumn{2}{c}{} & \multicolumn{2}{c}{**Difference from True (mm\({}^{-1}\))**} & \multicolumn{2}{c}{**mean from true (\%)**} & \multicolumn{2}{c}{**(mm\({}^{-1}\))**} & \multicolumn{2}{c}{**Mean from True (\%)**} \\ \hline \multirow{3}{*}{0} & \(\mu_{a}\) & \(\mu_{s}\) & \(\mu_{a}\) & \(\mu_{s}\) & \(\mu_{a}\) & \(\mu_{s}\) & \(\mu_{a}\) & \(\mu_{s}\)\({}^{{}^{\prime}}\) \\ \cline{2-10}  & \(4.4\times 10^{-4}\pm\) & \(-0.25\pm 7.9\) & \multirow{3}{*}{\(4.4\)} & \(-12.0\) & \(-2.3\times 10^{-3}\) & \(-0.08\pm 2.6\) & \multirow{3}{*}{\(-22.6\)} & \multirow{3}{*}{\(-3.9\)} \\  & \(6.3\times 10^{-5}\) & \(\times 10^{-3}\) & & & \(\pm 1.6\times 10^{-5}\) & & \\ \hline \multirow{3}{*}{5} & \(8.9\times 10^{-4}\pm\) & \(-0.49\pm\) & \multirow{3}{*}{\(8.9\)} & \(-23.5\) & \(-2.8\times 10^{-3}\) & \(-0.32\pm 2.4\) & \multirow{3}{*}{\(-28.0\)} & \multirow{3}{*}{\(-15.3\)} \\  & \(1.5\times 10^{-4}\) & & \(0.02\) & & \(\pm 2.3\times 10^{-5}\) & & \\ \hline \multirow{3}{*}{10} & \(3.5\times 10^{-4}\pm\) & \multirow{3}{*}{\(-1.3\pm 0.02\)} & \multirow{3}{*}{\(3.5\)} & \(-62.0\) & \(-3.5\times 10^{-3}\) & \(-0.38\pm 1.9\) & \multirow{3}{*}{\(-35.2\)} & \multirow{3}{*}{\(-18.2\)} \\  & \(1.9\times 10^{-4}\) & & & & \(\pm 2.1\times 10^{-5}\) & & \\ \hline \multicolumn{10}{c}{**Normal**} & \multicolumn{6}{c}{**Topographic DOI**} \\ \hline \multicolumn{2}{c}{} & \multicolumn{6}{c}{**Hybrid DOI**} & \multicolumn{6}{c}{**Topographic DOI**} \\ \hline \multicolumn{2}{c}{} & \multicolumn{6}{c}{**Difference from true (mm\({}^{-1}\))**} & \multicolumn{2}{c}{**\% Difference of**} & \multicolumn{2}{c}{**Difference from true (mm\({}^{-1}\))**} & \multicolumn{2}{c}{**\% Difference of**} \\ \multicolumn{2}{c}{} & \multicolumn{2}{c}{**mean from true (\%)**} & \multicolumn{2}{c}{**(mm\({}^{-1}\))**} & \multicolumn{2}{c}{**mean from true (\%)**} \\ \hline \multirow{3}{*}{0} & \(\mu_{a}\) & \(\mu_{s}\) & \(\mu_{a}\) & \(\mu_{s}\) & \(\mu_{a}\) & \(\mu_{s}\) \\ \cline{2-10}  & \(1.3\times 10^{-4}\pm\) & \(-0.05\pm 1.0\) & \multirow{3}{*}{\(2.1\)} & \(-3.1\) & \(-2.8\times 10^{-4}\) & \(0.07\pm 2.3\) & \multirow{3}{*}{\(-4.5\)} & \multirow{3}{*}{\(4.2\)} \\  & \(5.7\times 10^{-6}\) & \(\times 10^{-3}\) & & & \(\pm 1.6\times 10^{-5}\) & & \\ \hline \multirow{3}{*}{5} & \(1.2\times 10^{-4}\pm\) & \(-0.05\pm 1.2\) & \multirow{3}{*}{\(1.9\)} & \(-3.0\) & \(-2.9\times 10^{-4}\) & \(0.07\pm 3.5\) & \multirow{3}{*}{\(-4.5\)} & \multirow{3}{*}{\(4.3\)} \\  & \(3.5\times 10^{-6}\) & \(\times 10^{-3}\) & & & \(\pm 2.2\times 10^{-5}\) & & \\ \hline \multirow{3}{*}{10} & \(1.1\times 10^{-4}\pm\) & \(-0.05\pm 1.5\) & \multirow{3}{*}{\(1.7\)} & \(-2.9\) & \(-2.9\times 10^{-4}\) & \(0.07\pm 1.1\) & \multirow{3}{*}{\(-4.7\)} & \multirow{3}{*}{\(4.4\)} \\  & \(1.2\times 10^{-5}\) & \(\times 10^{-3}\) & & & \(\pm 1.1\times 10^{-5}\) & & \\ \hline \end{tabular}
\end{table} 
Table 2: Difference and percent difference of recovered \(\mu_{a}\) and \(\mu_{s}\)\({}^{{}^{\prime}}\) from true \(\mu_{a}\) and \(\mu_{s}\)\({}^{{}^{\prime}}\) at 650 nm. Figure 8: Bar plot representation of ground truth (gray), hybrid DOI, and conventional topographic DOI simulated recovery in \(\mu_{a}\) at 650 nm for (**a**) tumor and (**b**) normal tissue and \(\mu_{s}\)\({}^{{}^{\prime}}\) at 650 nm for (**c**) tumor and (**d**) normal tissue. The percentage difference of the hybrid DOI and topographic DOI recovered mean \(\mu_{a}\) and \(\mu_{s}\)', from the true \(\mu_{a}\) and \(\mu_{s}\)' for the normal tissue is below 5% for all tumor depths considered.