Appl Opt. 2021 May 1;60(13):3964-3970. doi: 10.1364/AO.422012.
By analyzing Newton's rings, often encountered in interferometry, the parameters of spherical surfaces such as the rings' center and the curvature radius can be estimated. First, the classical convolutional neural networks, visual geometry group (VGG) network and U-Net, are applied to parameter estimation of Newton's rings. After these models are trained, the rings' center and curvature radius can be obtained simultaneously. Compared with previous analysis methods of Newton's rings, it is shown that the proposed method has higher precision, better immunity to noise, and lower time consumption. For a Newton's rings pattern of ${{640}} \times {{480}}$ pixels comprising ${-}{{5}};{\rm{dB}}$ Gaussian noise or 60% salt-and-pepper noise, the parameters can be estimated by the VGG model in 0.01 s, the error of the rings' center is less than one pixel, and the error of curvature radius is lower than 0.5%.
通过分析干涉仪中常见的牛顿环，可以估计环的中心和曲率半径等球面参数。首先，将经典卷积神经网络、视觉几何组（VGG）网络和 U-Net 应用于牛顿环的参数估计。在这些模型经过训练后，就可以同时得到环的中心和曲率半径。与之前的牛顿环分析方法相比，所提出的方法具有更高的精度、更好的抗噪能力和更低的时间消耗。对于一个包含 ${-}{{5}};{\rm{dB}}$ 高斯噪声或 60%椒盐噪声的 ${640} \times {{480}}$ 像素的牛顿环图案，VGG 模型可以在 0.01 秒内估计出参数，环中心的误差小于一个像素，曲率半径的误差低于 0.5%。
