[论文解读] Drift-Free Fabry-Perot-Cavity-based Optical Refractometry -- Accurate Expressions for Assessments of Gas Refractivity and Density

Ove Axner, Isak Silander+2 more|arXiv (Cornell University)|Apr 3, 2017

Spectroscopy and Laser Applications参考文献 2被引用 4

一句话总结

本文提出了显式、无漂移的解析表达式，将法布里-珀罗腔基光学折射计中的气体折射率和密度与激光频率漂移关联起来。该研究量化了腔体形变、色散非线性性以及重新锁定效应的贡献，表明在开放式腔体中形变可引入高达3×10⁻³的误差，但在设计良好的封闭式腔体中仅约10⁻⁴，从而实现高精度的气体表征。

ABSTRACT

Recent advancements in the field of Fabry-Perot cavity based optical refractometry (OR), FPC-OR, comprising the use of proposed novel methodologies based on drift-free Dual FPC-OR (DF-DFPC-OR), have alleviated much of earlier problems with FPC-OR, in particular drifts of the cavity spacer, and therefore open up for new levels of accurate characterization of gases. However, to be able to use these techniques for highly accurate assessments, general and explicit expressions are needed for how the gas density, ${ρ_n}$, is related to the refractivity of the gas, $n - 1$, and how the latter depends on the change in frequency of laser light that follows an evacuation of the cavity, $Δ{ν_l}$. This paper presents such relations that properly acknowledge the influence of all conceivable phenomena and higher order (non-linear) contributions to the assessment of these entities under drift-free conditions. The relative contributions of each of these phenomena to measurements of gas refractivity and density are individually assessed. It is shown, among other things, that, the influence of cavity deformation is larger for an open cavity (placed in a compartment in which gas is introduced) than a closed one; if not accounted for appropriately, under standard pressure and temperature conditions it can contribute to the accuracy of the technique with up to a few times 10$^{-3}$ if an open cavity is used, while it can be an order of magnitude smaller, i.e. in the order of 10$^{-4}$, for a well-designed closed cavity. It is also shown that the non-linearities from dispersion are smaller for the cases when relocking takes place than when it is not used. The expressions derived can serve as a basis for assessment of refractivity or gas density, and changes in such, in future realizations of OR in such a way that they can fully benefit from the extraordinary power of DF-DFPC-OR.

研究动机与目标

• 推导出无漂移法布里-珀罗腔基光学折射计中气体折射率和密度的精确、显式表达式。
• 量化腔体形变、色散非线性性以及重新锁定对测量精度的影响。
• 通过考虑DF-DFPC-OR系统中所有显著的物理现象，实现高精度气体表征。
• 为未来FPC-OR的实现提供理论基础，以充分发挥无漂移运行的潜力。

提出的方法

• 推导出气体折射率（n−1）和密度（ρₙ）与腔体抽空后激光频率漂移（Δνₗ）之间的一般性显式解析表达式。
• 将所有相关物理效应（包括腔体形变、色散和热膨胀）纳入理论模型。
• 显式建模腔体几何结构（开放式与封闭式）对形变引起的误差的影响。
• 分析在重新锁定与非重新锁定条件下非线性色散的贡献。
• 定量评估每种物理效应对总测量不确定度的相对贡献。
• 利用推导出的表达式评估实际实验配置中的精度极限。

实验结果

研究问题

• RQ1 在开放式与封闭式法布里-珀罗腔中，腔体形变效应对气体折射率和密度测量精度的影响如何？
• RQ2 非线性色散贡献的误差量级是多少？重新锁定如何影响这一误差？
• RQ3 腔体间隔层的热与机械不稳定性在多大程度上导致漂移和测量不确定度？
• RQ4 所推导的解析表达式如何提升无漂移FPC-OR中折射率和密度评估的精度？
• RQ5 DF-DFPC-OR中的主要误差来源是什么？如何实现其定量抑制？

主要发现

• 在标准条件下，腔体形变在开放式腔体中可导致高达3×10⁻³的测量误差，但在设计良好的封闭式腔体中仅约10⁻⁴。
• 在使用重新锁定时，色散非线性性的影响比未使用时更小。
• 由于压力和热梯度的影响，腔体形变对开放式腔体的影响远大于对封闭式腔体的影响。
• 所推导的解析表达式考虑了所有相关物理现象，从而能够实现对折射率和密度的精确评估。
• 这些表达式为未来DF-DFPC-OR系统实现高精度气体表征提供了稳健的理论基础。
• 本研究确立了：通过合理的腔体设计和操作规程，无漂移FPC-OR可实现折射率和密度测量的亚ppm级精度。