Fig. 4
Comparison of \({\langle {l}_{i}\rangle }_{\phi }\) obtained with MCX and DT according to Eq. (29), and \({\langle {l}_{i}\rangle }_{R\_MC}\). A cube of side 1 mm was scanned along the \(x\) axis at three different depths: \(z=6.5, 12.5, 20.5 \text{ mm}\) (top, middle and bottom row, respectively) and for the three detectors of Fig. 1 at the distance \(\rho =15, 25, 35\text{ mm}\) (1st, 2nd, and 3rd column, respectively). The symbols refer to MCX results for: \({\langle {l}_{i}\rangle }_{R\_MC}\) (\({\langle {l}_{i}\rangle }_{R\_MCX}\)), \({\langle {l}_{i}\rangle }_{\phi }\) obtained with an isotropic point source at \(\mathbf{r}=(\rho ,0,s/2)\) (\({\langle {l}_{i}\rangle }_{\phi \_MCX(z=\frac{s}{2})}\)), and for \({\langle {l}_{i}\rangle }_{\phi }\) obtained with a pencil beam at \(=(\rho ,\text{0,0})\) (\({\langle {l}_{i}\rangle }_{\phi \_MCX(z=1/{\mu }_{s}^{\prime})}\)) for the adjoint calculations. The lines refer to DT calculations of \({\langle {l}_{i}\rangle }_{\phi }\) with \(\mathbf{r}=(\rho ,0,s/2)\) (\({\langle {l}_{i}\rangle }_{\phi (z=\frac{s}{2})}\)), and with \(\mathbf{r}=(\rho ,\text{0,1}/{\mu }_{s}^{\prime})\) (\({\langle {l}_{i}\rangle }_{\phi (z=1/{\mu }_{s}^{\prime})}\)). The optical properties are: \(\left({\mu }_{a},{\mu }_{s}^{\prime}\right)=\left(0.02, 0.5\right){\text{ mm}}^{-1}\). A double arrow indicating the maximum discrepancy between \({\langle {l}_{i}\rangle }_{R\_MCX}\) and \({\langle {l}_{i}\rangle }_{\phi \_MCX(z=\frac{s}{2})}\) (i.e.,\(\left({\langle {l}_{i}\rangle }_{R\_MCX}-{\langle {l}_{i}\rangle }_{\phi \_MCX(z=\frac{s}{2})}\right)/{\langle {l}_{i}\rangle }_{\phi \_MCX(z=\frac{s}{2})}\)) is shown in panel (a).
