A novel procedure for a robust assessment of cavity deformation in Fabry–Perot (FP) refractometers is presented. It is based on scrutinizing the difference between two pressures: one assessed by the uncharacterized refractometer and the other provided by an external pressure reference system, at a series of set pressures for two gases with dissimilar refractivity (here, He and N 2). By fitting linear functions to these responses and extracting their slopes, it is possible to construct two physical entities of importance: one representing the cavity deformation and the other comprising a combination of the systematic errors of a multitude of physical entities, viz., those of the assessed temperature, the assessed or estimated penetration depth of the mirror, the molar polarizabilities, and the set pressure. This provides a robust assessment of cavity deformation with small amounts of uncertainties. A thorough mathematical description of the procedure is presented that serves as a basis for the evaluation of the basic properties and features of the procedure. The analysis indicates that the cavity deformation assessments are independent of systematic errors in both the reference pressure and the assessment of gas temperature and when the gas modulation refractometry methodology is used that they are insensitive to gas leakages and outgassing into the system. It also shows that when a high-precision (sub-ppm) refractometer is characterized according to the procedure, when high purity gases are used, the uncertainty in the deformation contributes to the uncertainty in the assessment of pressure of N 2 with solely a fraction (13%) of the uncertainty of its molar polarizability, presently to a level of a few ppm. This implies, in practice, that cavity deformation is no longer a limiting factor in FP-based refractometer assessments of pressure of N 2.

中文翻译：

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基于 Fabry-Pérot 的折射计中腔变形的稳健评估程序

提出了一种在法布里-珀罗 (FP) 折光仪中对空腔变形进行稳健评估的新程序。它基于仔细检查两个压力之间的差异：一个由未表征的折光仪评估，另一个由外部压力参考系统提供，在具有不同折射率的两种气体（此处为 He 和 N 2）的一系列设定压力下。通过将线性函数拟合到这些响应并提取它们的斜率，可以构建两个重要的物理实体：一个代表空腔变形，另一个包括多个物理实体的系统误差的组合，即评估温度、评估或估计的反射镜穿透深度、摩尔极化率和设定压力。这提供了具有少量不确定性的腔变形的稳健评估。提供了该程序的全面数学描述，作为评估该程序的基本属性和特征的基础。分析表明，腔变形评估与参考压力和气体温度评估中的系统误差无关，并且当使用气体调制折光率方法时，它们对气体泄漏和向系统中释气不敏感。它还表明，当根据程序对高精度（亚 ppm）折射计进行表征时，当使用高纯度气体时，变形的不确定性导致 N 2 压力评估的不确定性，仅占其摩尔极化率不确定性的一小部分 (13%)，目前达到几个 ppm 的水平。这意味着，在实践中，腔体变形不再是基于 FP 的折光仪评估 N 2 压力的限制因素。