The diffusion approximation has been one of the central topics in near-infrared spectroscopy (NIRS). When NIRS measurements are analyzed by the diffusion theory, the measurements must be performed in the diffusive regime. However, since most of past researches have focused on theoretical or qualitative nature of the diffusion approximation, it is not easy to know if each measurement is designed in the diffusive regime. In this paper, we consider the diffusion approximation quantitatively and propose indicators that quantify the degree of validness of the diffusion approximation. The difference between the measurement and diffusion theory can be evaluated with the χ ² value, ℓ ¹ and ℓ ² norms, and Kullback-Leibler divergence. We conduct a liquid phantom experiment to test the proposed χ ² value. Moreover, the χ ² value is further investigated by Monte Carlo simulations. We find the χ ² value becomes significantly large when measurements are performed in the nondiffusive or transport regime. The proposed indicators similarly work. In particular, the χ ² value is shown to work as an indicator which evaluates the degree of validness of the diffusion approximation. These indicators are general and can be used for different numerical, experimental, and clinical measurements in NIRS.

扩散近似已成为近红外光谱（NIRS）的中心主题之一。当NIRS测量值通过扩散理论进行分析时，必须在扩散状态下进行测量。但是，由于过去的大多数研究都集中在扩散近似的理论或定性性质上，因此不容易知道每种测量是否在扩散体系中进行设计。在本文中，我们定量地考虑了扩散近似，并提出了量化扩散近似有效程度的指标。测量和扩散理论之间的差异可以与被评估χ ²值，ℓ ¹和ℓ ²规范和Kullback-Leibler分歧。我们进行的液体幻像实验来测试提出的χ ²的值。此外，χ ²值进一步由Monte Carlo模拟研究。我们发现χ ²时测量的nondiffusive或运输制度执行值变大显著。拟议的指标类似地起作用。特别地，χ ²值被示出为工作作为评估扩散近似的区分有效性的程度的指标。这些指标是通用的，可用于NIRS中的不同数值，实验和临床测量。