The measurement of scatter and absorption using three spectrophotometric techniques

Three methods for scattering and absorption measurements were compared for correlation; Kubelka-Munk, 4pi and an in transmission compartment scattering measurement method. The results indicated highest correlation between the 4pi and Kubelka-Munk absorption measurements. The 4pi and Kubelka-Munk scattering measurements had the highest correlation for scattering, and almost no correlation was found between Kubelka-Munk and in transmission compartment scattering measurements

Modified Kubelka-Munk Equations for Localized Waves Inside a Layered Medium

We present a pair of coupled partial differential equations to describe the evolution of the average total intensity and intensity flux of a wave field inside a randomly layered medium. These equations represent a modification of the Kubelka-Munk equations, or radiative transfer. Our modification accounts for wave interference (e.g., localization), which is neglected in radiative transfer. We numerically solve the modified Kubelka-Munk equations and compare the results to radiative transfer as well as to simulations of the wave equation with randomly located thin layers

Correspondence Between Continuous and Discrete 2 Flux Models for Reflectance and Transmittance of Diffusing Layers

This paper provides a theoretical connection between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The Kubelka–Munk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogeneous layer (continuous two-flux model). On the other hand, Kubelka's layering model describes the multiple reflections and transmissions of light taking place between various superposed diffusing layers (discrete two-flux model). The compatibility of these two models is shown. In particular, the Kubelka–Munk reflectance and transmittance expressions are retrieved, using Kubelka's layering model, with mathematical arguments using infinitely thin sublayers. A new approach to the Kubelka–Munk expressions is thus obtained, giving, moreover, new details for physical interpretation of the Kubelka–Munk theory

Radiative transfer in highly scattering materials - numerical solution and evaluation of approximate analytic solutions

Numerical solutions for radiative transport in a class of anisotropically scattering materials are presented. Conditions for convergence and divergence of the iterative method are given and supported by computed results. The relation of two flux theories to the equation of radiative transfer for isotropic scattering is discussed. The adequacy of the two flux approach for the reflectance, radiative flux and radiative flux divergence of highly scattering media is evaluated with respect to solutions of the radiative transfer equation

Analiza oblika Kubelka–Munk spektralnih funkcija superionskih vodiča CuI, AgI, Cu2HgI4 i Ag2HgI4, u velikom intervalu temperatura

The changing shapes of the Kubelka-Munk spectral function of different solid phases of CuI, AgI, Cu2HgI4 and Ag2HgI4 were studied in a wide temperature range. The spectra consist generally of a single, light absorption like, band. The parameters of the spectra were compared. Their distribution as functions of frequency or temperature in the case of the phases of CuI and AgI are similar. Distributions of parameters related to the phases of Cu2HgI4 and Ag2HgI4 are alike only in the case of the full width at half maximum. The existence of already reported phases of the investigated compounds is confirmed.Pokazano je da oblik Kubelka–Munk spektralne funkcije istraživanih spojeva ovisi o kristalnoj fazi u kojoj se nalaze. Potvrđeno je postojanje faza tih spojeva navedenih u literaturi

Analiza oblika Kubelka–Munk spektralnih funkcija superionskih vodiča CuI, AgI, Cu2HgI4 i Ag2HgI4, u velikom intervalu temperatura

The changing shapes of the Kubelka-Munk spectral function of different solid phases of CuI, AgI, Cu2HgI4 and Ag2HgI4 were studied in a wide temperature range. The spectra consist generally of a single, light absorption like, band. The parameters of the spectra were compared. Their distribution as functions of frequency or temperature in the case of the phases of CuI and AgI are similar. Distributions of parameters related to the phases of Cu2HgI4 and Ag2HgI4 are alike only in the case of the full width at half maximum. The existence of already reported phases of the investigated compounds is confirmed.Pokazano je da oblik Kubelka–Munk spektralne funkcije istraživanih spojeva ovisi o kristalnoj fazi u kojoj se nalaze. Potvrđeno je postojanje faza tih spojeva navedenih u literaturi

Investigating synthesis of Cu2ZnSn(Se1-x,Sx)4 for values of 0≤x≤1 by S for Se substitution and direct sulphidisation of metallic precursors

Thin layers of Cu2ZnSn(Se1-x,Sx)4 were produced by selenisation and subsequent sulphur substitution of DC sputter-deposited metallic CZT precursors on soda-lime glass. Values of x=(0, 0.07, 0.12, 0.17, 0.28, 1) were measured by EDS. Samples were characterised optically and analysed using the Kubelka-Munk function, and found to have 0.96eV ≤Eg≤ 1.47eV, varying approximately linearly with x. Samples underwent X-ray diffraction characterisation and substituted samples were found to comprise of multiple phase kesterite material with different levels of S substitution, averaging to the values obtained by EDS. The spectra were found to conform to Vegard's law, as peak location shifted linearly between x=0 and x=1. Binary phases are suspected to exist, because of some unusual behaviour at the location of the (200) peak. Lattice parameters for all phases were calculated and found to vary linearly between (a=b=5.692, c=11.338) for x=0 and (a=b= 5.393, c= 10.863) for x=1, which are in excellent agreement with previously published figures

Two-flux and multiflux matrix models for colored surfaces

International audienceThis paper presents various extensions of the so-called two-flux models for prediction of reflectance and transmittance of diffusing media, i.e. the ubelka-Munk model, and the extension of Kubelka-Munk for stacks of diffusing layers. A first matrix formulation of the Kubelka-Munk differential equations leads to a matrix framework based on transfer matrices, which can be extended to stacks of diffusing layers, stacks of nonscattering films, and stacks of scattering and non-scatterings films as a generalization of the Williams-Clapper model for prediction of the reflectance of paper photographs, each of these configurations being illustrated through various examples. This paper also exposes the limitsof the two flux approach and shows that the matrix formalism extends in a straightforward manner to multiflux models, where the size of the matrices is increased