We proposed a new method for the radius of curvature (ROC) of spherical wave measurement based on vortex beam interference and Fermat's spiral fitting, which can not only provide a large measurement range but also have high precision. Theoretical analysis showed that the maximum distribution of the interference light intensity is in accordance with the Fermat's spiral, and the spiral coefficient is proportional to the ROC of spherical wave. For a concave spherical mirror with a ROC of 899.89mm and a convex spherical lens with a ROC of 59.99mm, the average measurement error of five measurements are 0.080% and 0.083%, respectively. Controlled experiments showed that, our proposed method has a higher measurement accuracy and a larger measurement range than Newton's rings method, it has almost equal measurement accuracy for large and small ROC. This research provides a theoretical basis for the development of a ROC measurement system with large measurement range and high precision.

提出了一种基于涡流干涉和费马螺旋拟合的球面波曲率半径（ROC）测量新方法，该方法不仅可以提供较大的测量范围，而且具有较高的精度。理论分析表明，干涉光强的最大分布与费马螺旋线一致，螺旋系数与球面波的ROC成正比。对于ROC为899.89mm的凹球面镜和ROC为59.99mm的凸球面透镜，五次测量的平均测量误差分别为0.080％和0.083％。对照实验表明，与牛顿环法相比，我们提出的方法具有更高的测量精度和更大的测量范围，无论大小，ROC的测量精度几乎相等。该研究为大量程，高精度ROC测量系统的开发提供了理论依据。