Fig. 1. Principle of solving optical parameters using MC-NMS algorithm (μat and μst' are ideal values and μap and μsp' are calculated values)

Fig. 2. Schematic diagrams of biological tissue models. (a) Single-layer biological tissue model, where L represents the thickness of the SL-BTM layer; (b) double-layer biological tissue model, where SDS1 represents the fixed near SDS, SDS2 represents the varying far SDS, L₁ represents the thickness of the upper tissue layer, and L₂ represents the thickness of the lower tissue layer; (c) a schematic of measuring skin thickness using T₁W₁ image obtained by magnetic resonance imaging

Fig. 3. Inversion error of SL-BTM optical parameters for different algorithms. (a) Mean relative error in μ_a ; (b) mean relative error in μs'

Fig. 4. Inversion results of SL-BTM optical parameters for MC-NMS alogrithm when SDS is 3 mm. (a) Inversion result of μ_a; (b) inversion result of μs'

Fig. 5. Inversion error of DL-BTM optical parameters for MC-NMS algorithm under different SDS combinations when the thickness of the upper layer changes, where d₁‒d₅ represent the thickness of the upper layer. (a) Mean relative error in μa1; (b) mean relative error in μa2; (c) mean relative error in μs'

Fig. 6. Inversion mean relative error of DL-BTM optical parameters for MC-NMS algorithm under different SDS combinations. (a) Inversion mean relative errors in μa1; (b) inversion mean relative error in μa2; (c) inversion mean relative error in μs'

Fig. 7. Numerical simulation results of DL-BTM optical parameters, where μa1t, μa2t and μst' are respectively the true values of shallow absorption coefficient, deep absorption coefficient and reduced scattering coefficient, and μa1p,μa2p and μsp' are respectively the calculated values of shallow absorption coefficient, deep absorption coefficient and reduced scattering coefficient. (a) Inversion results of MC-NMS; (b) inversion results of TDIA; (c) inversion results of SDIA

Fig. 8. Diagrams of experimental devices. (a) Schematic of time-domain measurement system; (b) IRF and TPSF curves; (c) IRF measuring device; (d) SL-BTM liquid phantom experimental facility; (e) DL-BTM liquid phantom experimental facility

Fig. 9. Inversion results of SL-BTM optical parameters of liquid phantom, where μat and μst' are respectively the true values of absorption coefficient and reduced scattering coefficient, and μap and μsp' are respectively the calculated values of absorption coefficient and reduced scattering coefficient. (a) Inversion result of μa; (b) inversion result of μs'

Fig. 10. Inversion results of DL-BTM optical parameters of liquid phantom,where μa1t, μa2t and μst' are respectively the true values of shallow absorption coefficient, deep absorption coefficient and reduced scattering coefficient, and μa1p, μa2p and μsp' are respectively the calculated values of shallow absorption coefficient, deep absorption coefficient and reduced scattering coefficient. (a) Inversion result of μa1; (b) inversion result of μa2; (c) inversion result of μs'