中文摘要：

研究一种高精度曲线拟合方法，用于评价超小梯度折射率光纤探针的聚焦性能。首先，概述梯度折射率光纤探针模型；其次，根据高斯光束通过梯度折射率光纤探针进行聚焦的特点，提出利用多项式拟合的方法评价聚焦的束腰位置和光斑尺寸；最后，进行评价方法的验证分析。结果显示，由曲线拟合方法得到的工作距离为0．93mm，束腰直径为28．2μm，与实验测得的工作距离1mm和束腰直径28μm基本一致。表明所研究的基于多项式拟合的曲线拟合方法适于梯度折射率光纤探针聚焦性能的评价。

英文摘要：

A high-precision curve fitting method was investigated so evaluate the focusing performance of an ultra-small gradient-index （GRIN） fiber probe. Firstly, an overview of the GRIN fiber probe model is given. Secondly,according to the characteristics of Gaussian beam focusing through the GRIN fiber probe ,the polynomial fitting method is proposed to evalu- ate the waist position and spot size of the focused beam. Finally,the evaluation method is analyzed for validation. The re- sults show that, with the curve fitting method, the obtained working distance and waist diameter are 0.93 mm and 28.2 μm, respeetively. Under the same conditions, the experimentally measured working distance and waist diameter are 1 mm and 28 13μn,accordingly. The fitting results are in good agreement with the experiment data. Therefore,the proposed polynomial curve fitting method is applicable to evaluate the focusing performance of GRIN fiber probe.