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Unambiguous derivation of the effective refractive index of biological suspensions and an extension to dense tissue such as blood
Journal of the Optical Society of America A ( IF 1.9 ) Pub Date : 2021-05-07 , DOI: 10.1364/josaa.420136
Alexander Nahmad-Rohen , Augusto García-Valenzuela

The van de Hulst formula provides an expression for the effective refractive index or effective propagation constant of a suspension of particles of arbitrary shape, size, and refractive index in an optically homogeneous medium. However, its validity for biological matter, which often consists of very dense suspensions of cells, is unclear because existing derivations of the formula or similar results rely on far-field scattering and/or on the suspension in question being dilute. We present a derivation of the van de Hulst formula valid for suspensions of large, tenuous scatterers—the type biological suspensions are typically made of—that does not rely on these conditions, showing that they are not strictly necessary for the formula to be valid. We apply these results specifically to blood and epithelial tissue. Furthermore, we determine the true condition for the formula to be valid for these types of tissues. We finally provide a simple way to estimate—and, more importantly, correct—the error incurred by the van de Hulst formula when this condition is not met.

中文翻译:

生物悬浮液的有效折射率的明确推导以及对致密组织(如血液)的扩展

van de Hulst 公式提供了在光学均匀介质中任意形状、尺寸和折射率的颗粒悬浮液的有效折射率或有效传播常数的表达式。然而,它对通常由非常密集的细胞悬浮液组成的生物物质的有效性尚不清楚,因为该公式的现有推导或类似结果依赖于远场散射和/或所讨论的悬浮液被稀释。我们提出了 van de Hulst 公式的推导,该公式适用于大的、稀薄的散射体的悬浮液(生物悬浮液通常由这种类型的悬浮液制成),它不依赖于这些条件,表明它们对于公式有效并不是绝对必要的。我们将这些结果专门应用于血液和上皮组织。此外,我们确定公式对这些类型的组织有效的真实条件。我们最终提供了一种简单的方法来估计——更重要的是,纠正——当这个条件不满足时 van de Hulst 公式产生的误差。
更新日期:2021-06-02
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