Improved Inverse Method for Radiative Characteristics of Closed-Cell Absorbing Porous Media

a = bubble radius, m b = corrective factor used in Eq. (10) cij = matrix elements of the sensitivity coefficients J e = sample thickness, m f1, f2 = spectral weights of the Henyey–Greenstein phase function HG g = spectral asymmetry factor g1, g2 = spectral parameters of the Henyey–Greenstein phase function HG I = spectral radiation intensity, W m 2 sr 1 J = matrix of the sensitivity coefficients k = volumetric absorption coefficient, m 1 Mb = quadrature order of the discrete ordinate method m = fused quartz refractive index Nb = number of measurement directions n = number of unknown parameters including !, , f1, g1, and/or g2 p = unknown parameter such as !, , f1, g1, or g2 Q = ratio of the measured scattered to the incident radiation fluxes r = interface reflectivity S = minimization function T = spectral transmittance or reflectance, sr 1 T = average spectral transmittance or reflectance, sr 1 w = angular weight of the discrete ordinate method w0 = angular weight of the two Gaussian quadratures associated to the experimental directions x = bubble size parameter y = spatial coordinate along the sample thickness, m = angle between incident radiation and measurement directions, rad = volumetric extinction coefficient, m 1 = relaxation factor used in Eq. (5) = divergence angle of the incident radiation, rad = solid angle, sr = Kronecker delta function "0, "1, "2, "3 = coefficients of the third order polynomial estimating Tsca in Eq. (17) = cosine of the angle = scattering angle defined in Eq. (21), rad = angle between incident radiation direction and radiation inside the porous medium, rad = fused quartz absorption index = radiation wavelength, m = cosine of the angle