Mudgett P S, Richards L W
Appl Opt. 1971 Jul 1;10(7):1485-502. doi: 10.1364/AO.10.001485.
A many-flux (discrete ordinate) radiative transfer calculation procedure is described with the goal of making the mathematics easy to learn and use. The major approximation is the neglect of polarization. Emission within the scattering medium is not included, and the formulas are restricted to a scattering medium bounded by parallel planes. The boundary conditions allow for a variety of kinds of illumination, and the surface reflection coefficients at the boundaries of the scattering medium are accurately determined. A comparison is made with the two-flux (Kubelka-Munk) and four-flux calculation methods, and this leads to empirical expressions for the scattering and absorption coefficients in these simple theories, which make them give nearly the same results as exact theories. These empirical expressions provide a very simple method for estimating the absolute reflectance and transmittance of turbid media and greatly increase the utility of the two-flux and four-flux calculation methods. The two-flux equations give excellent results provided the absorption is small compared to scattering and the optical thickness is greater than 5. A comparison with experimental data taken with collimated illumination shows that the four-flux equations give good results at any optical thickness even if the absorption is strong.
描述了一种多流（离散坐标）辐射传输计算程序，目的是使数学内容易于学习和使用。主要近似是忽略偏振。不包括散射介质内的发射，并且公式限于由平行平面界定的散射介质。边界条件允许各种照明情况，并且准确确定了散射介质边界处的表面反射系数。与二流（库贝尔卡 - 蒙克）和四流计算方法进行了比较，这导致了这些简单理论中散射和吸收系数的经验表达式，使它们给出与精确理论几乎相同的结果。这些经验表达式提供了一种非常简单的方法来估计浑浊介质的绝对反射率和透射率，并大大提高了二流和四流计算方法的实用性。如果吸收与散射相比很小且光学厚度大于5，则二流方程给出优异的结果。与准直照明下的实验数据比较表明，即使吸收很强，四流方程在任何光学厚度下都能给出良好的结果。
