This paper presents the numerical and experimental study of a multimode optical fiber (MMF) sensor based on Fresnel reflection at the fiber tip. Considering different modal power distributions (uniform mode distribution, gaussian and equilibrium mode distribution), the effective fraction of the incident light reflected at the interface between the end of the fiber and the surrounding medium is first calculated numerically with a ray model. Even when considering modal power distribution and non-normal incidence influence, simplifying assumptions such as normal incidence hypothesis can be made to facilitate experimental data exploitation, with a maximum error on the deduced medium refractive index of the ${10}^{-4}$ order. A statistical analysis of noise is then made, to study the influence of a random noise between 0.1% and 5% noise level: results show that the approximation error made by using normal incidence formula for a Fresnel sensor based on a MMF is significantly smaller than the repeatability error. These assumptions are then verified experimentally with two experimental setups by measuring the refractive index at 1550 nm of reference solutions (distilled water-isopropanol and distilled water-sodium chloride mixtures) with a Fresnel based on a multimode fiber, and a Fresnel based on single-mode fiber for comparison. Good agreement is found with refractive index values from the literature with a maximum relative difference of only 0.1%, and the maximum experimental uncertainties in this work is $1.1\times {{10}^{-4}}_{}$. Differences between refractive index measured with a Fresnel based on single-mode and multimode fiber are found to be in accordance with values from the statistical study.

本文介绍了基于光纤尖端菲涅尔反射的多模光纤 (MMF) 传感器的数值和实验研究。考虑到不同的模式功率分布（均匀模式分布、高斯和平衡模式分布），在光纤末端和周围介质之间的界面处反射的入射光的有效分数首先用射线模型进行数值计算。即使在考虑模态功率分布和非垂直入射影响时，也可以做出简化假设，如垂直入射假设，以促进实验数据的利用，推导出的介质折射率误差最大。${10}^{——4}$命令。然后对噪声进行统计分析，研究0.1%~5%噪声水平的随机噪声的影响：结果表明，基于MMF的菲涅耳传感器使用法向入射公式得出的近似误差明显小于重复性误差。然后，通过使用基于多模光纤的菲涅耳和基于单模光纤的菲涅耳测量参比溶液（蒸馏水-异丙醇和蒸馏水-氯化钠混合物）在 1550 nm 处的折射率，通过两个实验装置对这些假设进行了实验验证。模式光纤进行比较。与文献中的折射率值具有良好的一致性，最大相对差异仅为 0.1%，本工作中的最大实验不确定度为$1.1\times {{10}^{——4}}_{}$. 发现使用基于单模和多模光纤的菲涅耳测量的折射率之间的差异与统计研究中的值一致。