Intrinsic and Extrinsic Scattering and Absorption Coefficients New Equations in Four-flux and Two-flux Models Used for Determining Light Intensity Gradients

Abstract

Collimated, diffuse, and total light intensity gradients, for forward and backward light senses, were determined in a three substrate layers – glass/electrolyte/glass – almost transparent sample, using optical constants and new equations for intrinsic and extrinsic scattering and absorption coefficients. These new equations were obtained for the inner electrolyte layer from the systems of differential equations of the four-flux and two-flux radiative transfer models, used for determining intrinsic and extrinsic coefficients, respectively, once knowing the optical constants of outer glass layers, from a single glass substrate sample measured in advance. Extinction coefficients were determined from optical constants and considering the wavelength compression of light when it enters into a material, decreasing its speed with respect to the vacuum. The same extinction coefficients for glass and electrolyte layers were computed in three different ways. First, from optical constants, they were determined using collimated transmittance and reflectance solutions of four-flux model. From them, collimated interface reflectance and attenuation due to extinction were computed. These intermediate parameters for glass and electrolyte layers were required for determining inner collimated light intensities at the interfaces, which were used at the collimated forward and backward differential equations, solving for the forward and backward extinction coefficients. The three-extinction matching requirement was successfully satisfied for the glass and electrolyte layers. Two average crossing parameters equations, for each sense, and four forward scattering ratios equations, for collimated and for diffuse light intensities for each sense, were used in the system of diffuse differential equations (DDE) for intrinsic coefficients. For them, intuitive equations were proposed based on collimated and diffuse light intensities at each interface. New equations for extrinsic parameters were determined by equalizing the system of total differential equations of the two-flux model to the sum of the systems of collimated and DDE of the four-flux model.

Received: 9 December 2023 | Revised: 4 March 2024 | Accepted: 25 April 2024

Conflicts of Interest

The author declares that he has no conflicts of interest to this work.

Data Availability Statement

Data are available from the corresponding author upon reasonable request.