Model to subtract contributions of scattered radiation from measured direct transmittance and specular reflectance by light diffusing materials

Abstract

The formalism of the Lorenz–Mie (LM) theory is used to estimate the contributions of radiation being scattered into the detector acceptance angle of spectrophotometers (with or without an integrating sphere) to the apparent direct transmittance and specular reflectance measurements. These contributions are subtracted from the measurements before doing the inversion to obtain the spectral variation of the scattering and absorption (S&A) coefficients of optically particulate liquid samples, decoupling the contribution to extinction from these two mechanisms. The method is applied to transmittance spectra of Pickering emulsions of dodecane oil (DO) and DO micelles with saturated dissolved Nile red dye, stabilized with anatase ( T i O 2 ) in water. What we believe to be novel expressions are given to estimate the forward and backward average path-length parameters of propagating diffuse radiation from its equivalent quantities defined within the formalism of the LM theory and to relate these single particle average path-length parameters with the forward scattering ratio, asymmetry parameter, and higher-order coefficients in the expansion of the LM phase function. This novel approach makes it possible to avoid the underestimation of the S&A coefficients, which arises when the correction is not made by subtracting that contribution due to scattered radiation that is reaching the detectors from the directional reflectance and transmittance measurements.