Investigation of total diffuse-photon-density-wave field in semi-infinite turbid media based on the extrapolated Beer–Lambert law

The accurate description of the total diffuse-photon-density-wave field inside turbid media, especially in the near-field region, is extremely critical but challenging for many decades. Here, the total diffuse-photon-density-wave field of semi-infinite turbid media was calculated by the third-order simplified spherical harmonics approximation (SP3) and compared with Monte Carlo simulations. To improve the SP3 approximation, the extrapolated Beer–Lambert law model considering the contribution of the coherent-photon-density-wave in the near-field region was proposed and implemented by Levenberg–Marquardt and universal global optimization methods. Last, we demonstrated the superiority of the proposed model over the existing model in fitting the accuracy and applicable source–detector distance range. The high accuracy and simplicity of the proposed model would be extremely helpful for biomedical applications involving photothermal radiometry, and rapidly determining optical properties of media, along with photoacoustic imaging and photodynamic therapy.