Identification of radiative characteristics of fused quartz containing bubbles using discrete ordinates method with Fresnel interfaces

Radiation characteristics of fused quartz containing bubbles (10 % porosity) are determined using inverse method based on theoretical and experimental bi-directional transmittances and reflectances. The Discrete Ordinates Method is used to solve the RTE. The internal and external interfaces are assumed to be optically smooth. The importance of the choice of the interpolation law has been shown, exponential law is appropriate in directions near the normal where there are large variations of intensity. The influence of thickness on the results are studied. Nomenclature g Henyey-Greenstein phase function parameter I intensity of the collimated incident beam I spectral intensity of radiation y sample thickness n real part of the complex index of refraction of the quartz continuous phase P phase function r12 reflectivity at the interface air-foam r21 reflectivity at the interface foam-air T transmittance or reflectance Greek symbols volumetric extinction coefficient i, j Kronecker's delta function i, j =1 if i= j and 0 otherwise volumetric absorption coefficient cosine of the polar angle angle defined between the incident and scattering direction divergence angle of incident beam volumetric scattering coefficient volumetric scattering albedo coefficient Subscripts e experimental t theoretical monochromatic wavelength