Decay behavior and optical parameter identification for spatial-frequency domain imaging by the radiative transport equation

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) of the Top Layer of the Two-Layer Medium by RTE for ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) of the Top Layer of the Two-Layer Medium by RTE for ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Three-Layer Model^a

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 1.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) of the Top Layer of the Two-Layer Medium by RTE for ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 2.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) of the Top Layer of the Two-Layer Medium by RTE for ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 3.

Three-Layer Model^a

Table 4.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 5.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 6.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 7.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 8.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 9.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 10.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.01\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 11.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.02\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer

Table 12.

Reconstructed ${\mu }_a$ and ${\mu }_s^{\mathrm{\prime }}$ ($\mathrm{m}{\mathrm{m}}^{-1}$) by RTE, DA1, and DA2 When ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Top Layer and ${\mu }_a=0.03\mathrm{m}{\mathrm{m}}^{-1}$ in the Bottom Layer