Star W M, Marijnissen J P, van Gemert M J
Dr Daniel den Hoed Cancer Centre, Rotterdam, The Netherlands.
Phys Med Biol. 1988 Apr;33(4):437-54. doi: 10.1088/0031-9155/33/4/004.
This is the first of two papers on the quantitative measurement of light energy fluence rates in optical phantoms and in tissues, in vitro and in vivo. The theory discussed in the present paper will be used in a forthcoming experimental paper to quantitatively check measurements of light energy fluence rates. A simple multiple flux model, which is equivalent to the diffusion approximation, is derived from the equation of transfer in a plane as well as in a spherical geometry. The equations obtained are similar to those of the Kubelka-Munk and related heuristic models. This permits conclusions regarding the limitations of these models and the values of their constants. The heuristic models are equivalent to diffusion theory for diffuse incident light, but not for collimated incident light. We also present a simple calculation of the radiance as a function of direction in the diffusion domain. This, together with the effective attenuation coefficient, permits indirect experimental determination of both the albedo and the anisotropy factor (g) of the scattering function. Similarity relations are discussed, as they result from the so called delta-Eddington approximation, leading to the conclusion that far from boundaries and sources light propagation characteristics do not change very much when g and omega s are varied, provided omega s (1-g) is kept constant (omega s = scattering coefficient). Therefore, only two optical constants are required to approximately describe light propagation in homogeneous and isotropic media in the diffusion approximation.
这是关于在光学体模以及体外和体内组织中定量测量光能注量率的两篇论文中的第一篇。本文所讨论的理论将用于即将发表的实验性论文中，以定量检验光能注量率的测量结果。一个简单的多通量模型，它等同于扩散近似，是从平面以及球形几何结构中的传输方程推导出来的。所得到的方程与库贝尔卡 - 芒克及相关启发式模型的方程相似。这使得能够得出关于这些模型的局限性及其常数取值的结论。启发式模型对于漫射入射光等同于扩散理论，但对于准直入射光则不然。我们还给出了在扩散区域中作为方向函数的辐亮度的简单计算。这与有效衰减系数一起，允许通过实验间接确定散射函数的反照率和各向异性因子（g）。讨论了相似性关系，这些关系源自所谓的δ - 爱丁顿近似，从而得出结论：在远离边界和源的情况下，当g和ωs变化时，只要ωs(1 - g)保持恒定（ωs = 散射系数），光传播特性不会有太大变化。因此，在扩散近似中，只需要两个光学常数就可以近似描述均匀各向同性介质中的光传播。
