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

Abstract

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 TiO 2 particles in a lowabsorbing 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.

Inversión de los modelos de transferencia radiativa de dos flujos y de cuatro flujos para determinar los coeficientes de dispersión y de absorción para cristales líquidos dispersos en polímero

“…Other works [27,28,29,30,31] combine direct and inverse problems for this task. However, recent advances in the inverse problem with new equations determined for intrinsic and extrinsic coefficients were recently carried out [32,33,34,35,36] by differentiating two average crossing parameters (for forward and backward light senses) and four forward scattering ratios (for forward and backward light senses and for collimated and diffuse light beams).…”