Effective backscattering and absorption coefficients of light diffusing materials retrieved from reflectance and transmittance spectra of diffuse radiation

Solutions of the differential equations for the diffuse components of the four-flux model are obtained, including explicit expressions for the collimated-diffuse and diffuse-diffuse reflectance and transmittance for an optical three-layer system. We establish a method to invert collimated-diffuse reflectance and transmittance in order to obtain the spectral variation of all average pathlength parameters and forward scattering ratios, by applying a spectral simulated annealing method. The inversion procedure was tested with synthetic collimated-diffuse reflectance and transmittance spectra and showed very good convergence. Subsequently, the method was applied to measured spectra of a light scattering and absorbing medium containing TiO2 particles in a low-absorbing matrix, which was enclosed between two glass slides. Hence the present paper, together with our previous one, wherein we inverted collimated-collimated reflectance and transmittance spectra to obtain scattering and absorption coefficients, establishes a reliable inversion method for obtaining all parameters in the most general version of the four-flux theory from experimental data.

Automated summary

The paper presents an inversion method for the differential equations of the diffuse components of the four-flux model in an optical three-layer system, which was tested with synthetic spectra to show its reliability.