Diffuse photon remission from thick opaque media of the high absorption/scattering ratio beyond what is accountable by the Kubelka–Munk function
Daqing Piao, Tengfei Sun
Abstract
The Kubelka–Munk (KM) theory of diffuse photon remission from opaque media is widely applied to quality-control processes. Recent works based on radiative transfer revealed that the KM function as the backbone parameter of the method may saturate at strong absorption to cause the KM approach to be unfit to predict the change of diffuse reflectance from the medium at strong absorption. We demonstrate by empirical means based on Monte Carlo results that diffuse photon remission from a strong-absorbing medium depends simply upon the absorption/scattering ratio when evaluated over a large area centered at the point of illumination differing in geometry from those convenient for the KM approach. Our empirical prediction gives <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>∼</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>11</mml:mn> </mml:mrow> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> mean errors of the diffuse photon remission from thick opaque medium having an absorption coefficient ranging 0.001 to up to 1000 times stronger than the reduced-scattering coefficient. A slight modification to the KM function in terms of the absorption weighting and absorption-scattering coupling for use within the KM approach also noticeably improves the prediction of diffuse photon remission from thick opaque medium of strong absorption. Our empirical model and the KM approach using the modified KM function were compared against measurements from a thick opaque medium, of which the absorption coefficient was changed over four orders of magnitude.