提出了基于曲线拟合的光纤透镜聚焦常数的测试方法，用于超小自聚焦光纤探头研制过程中聚焦常数的直接测试。基于自聚焦光纤透镜模型及其折射率分布特征，研究了测量自聚焦光纤透镜聚焦常数的二次多项式拟合和线性化拟合算法。论述了聚焦常数对超小自聚焦光纤探针传光性能的影响。利用光纤端面折射率测试仪测试自聚焦光纤的折射率分布轮廓曲线，根据二次多项式拟合和线性化拟合算法分别求得聚焦常数和中心折射率。实验结果显示，利用二次多项式拟合算法和线性拟合算法求出的聚焦常数分别为5.587 mm-1和5.513 mm-1，与厂家的标称值5.5 mm-1基本吻合，表明曲线拟合算法适用于对自聚焦光纤透镜聚焦常数的测量与分析。

The curve-fitting algorithms were proposed to measure directly the focusing constant of a gradient-index (GRIN) fiber lens to further design ultra-small GRIN fiber probes. The quadratic polynomial algorithm and linear fitting method for measuring the focusing constant of GRIN fiber lens were investigated based on the characteristics of refractive index profile of the GRIN fiber lens and its model. Then,the effect of the focusing constant on the light-transporting characteristics of ultra-small GRIN fiber probes was discussed. The refractive index profile of the GRIN fiber lens was acquired by using an optical fiber refractive index profile tester. And then the focusing constant and center refractivity were obtained by the quadratic polynomial algorithm and linear fitting method. The results show that the fitted values of the focusing constant are calculated to be 5.587 mm-1and 5.513 mm-1 respectively with the quadratic polynomial algorithm and linear fitting method, which agree well with the nominal value of 5.5 mm-1 provided by the manufacturer. The fitting results show that the proposed curve fitting algorithms are feasible to measure and analyze the focusing constants of GRIN fiber lenses.