Scattering and absorption cross sections of light diffusing materials retrieved from reflectance and transmittance spectra of collimated radiation

Abstract

Four-flux radiative transfer models have been extensively used to describe reflectance and transmittance (R&T) spectra of light scattering and absorbing (S&A) media. Solutions to the differential equations corresponding to the collimated fluxes are obtained by subsequent application of boundary conditions. Explicit expressions for the collimated R&T of light are reported, when considering a light S&A medium contained between two glass slides, an experimental arrangement which is appropriate for liquid suspensions and viscous matrices containing solid particles. A spectral simulated annealing method is applied to retrieve, from measured R&T spectra of collimated light under normal incident radiation, the scattering and absorption coefficients of the composite medium. First, the accuracy of the method is established by applying it to synthetic collimated R&T data. Secondly, we apply the method to experimental data and use it to determine the S&A coefficients of a layer of TiO 2 particles dispersed in a PVP/water matrix.

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

“…The four-flux theory [12,13] contains parameters related to angle-dependent scattering in a material, namely forward scattering ratios and average pathlength parameters and is an interesting option. The objective of our previous paper [14], as well as the present one, is to develop reliable inversion methods using this theory.…”

“…In the previous paper, we have considered a fourflux radiative transfer model (FFRTM) to fit reflection and transmission of radiation through a planeparallel light diffusing medium sandwiched between two glass slides. We obtained the average volume scattering and absorption cross sections of samples consisting of submicron sized anatase (TiO 2 ) particles dispersed in a weakly light-absorbing polyvinylpyrrolidone (PVP)water matrix between two glass slides, from inversion of their collimated-collimated components of reflectance and transmittance spectra [14]. The same approach was followed to obtain the instrinsic scattering and absorption coefficients of chlorophyll pigmented aqueous solutions at different concentrations [15].…”

“…The same approach was followed to obtain the instrinsic scattering and absorption coefficients of chlorophyll pigmented aqueous solutions at different concentrations [15]. This task required solutions to the two differential equations describing the variation of the collimated fluxes with depth through the light diffusing medium (Equation (1a) and (1b) in [14]) that satisfy the appropriate boundary conditions. A novel spectral version of the Acceptance-Probability-Controlled Simulated Annealing (APCSA) method was implemented to carry out the inversion process [16][17][18][19].…”

“…His formulation does not incorporate a priori the symmetry condition: the APPs and FSRs are a priori considered different for forward and backward diffuse radiation. Equation (1) shows the generalized version of the Equation (1c) and (1d) in [14] and are given by…”

“…Our aim is to report the solutions of the two differential equations (Equation ( 1)), under the appropriate boundary conditions to compare with spectrophotometric optical measurements, and accounting for the presence of the other layers (Figure 1) in the optical system containing the light diffusing medium. The present paper, taken together with our previous one [14] constitutes a complete solution of the inversion problem of the FFRTM. Thus, we show that it is possible to obtain all parameters of the FFRTM from measured collimated-collimated and collimated-diffuse reflectance and transmittance spectra.…”