Mode With High-order Parameter Of The Biological Tissue Optical Diffuse Reflectance

With the development of the application of the optical diagnosis in biomedicine,optical diffuse spectroscopy is crucial in non-invasive measurements and quickanalysis of biological tissues. The diffusion approximation (DA) is a successful theoryfor solving the radiative transport equation. However, the DA model is not accurate todescribe the light transmission of small region near the light source, this limits theeffective application of the optical diffuse spectroscopy. Therefore, there is asignificant need to establish a more accurate theory to describe the light transmissionin the small region near the light source, to obtain the reliable optical parameters ofbiological tissue.In this paper, a semi-empirical formula of diffuse reflectance is elaborated on thebasis of the photon migration theory and the second-order similarity relation, and theinfluence of second-order parameter γ on the semi-empirical formula is studied byuse of Monte Carlo method. Based on a theoretical model for spatial diffusionreflection, the optical absorption coefficientμ a, reduced scattering coefficient μ’s, andthe second-order parameterγ of the medium are recovered from the measurementdata of the reflectance by the nonlinear least squares method. The problem aboutthe diffuse reflectance has been studied with theoretical, simulated and experimentalmethods. The main work as following:Firstly, the exponential model, photon migration model, diffusion approximationmodel and Monte Carlo numerical model are summarized in this paper. What’s more,in the diffusion approximation model, we derived the total diffuse reflectance of thesemi-infinite medium is a function ofμ μ’as.Secondly, on the basis of the photon migration theory and the second-ordersimilarity relation， we get an analytical expressions containing higher-orderparameters γ based on the MC simulated data. This model has a simplemathematical form, and is suitable for the measurements of the diffuse reflectance inlow albedo and the small region near the light source. Studies show that when we usesmall aperture to collect diffuse light, the reflectance is a quadratic function ofγ.Compared with other analytical model contained a high-order parameter, thesemi-empirical analytical model presented in this paper has a simple mathematicalform. This provides a new theoretical and technical support to the measurements ofoptical parameters of biological tissue and the application of diffuse reflectance spectroscopy.Finally, Using nonlinear least squares method, we inverse the optical parametersof biological tissues from the measured reflectance data, demonstrating thesemi-empirical formula with high-order parameters could give a better description ofoptical radiation near the light source. These studies have important implications formeasure the optical properties of biological tissues and applications of diffusereflectance spectroscopy.