In situ fast measurement of the radius of curvature for the plano-convex lens with deep-learning based on the point spread functions

As one of the most basic optical elements, lenses are widely used in lots of high-tech fields such as optical lithography, photoelectric detection, biological and medical engineering. The radius of curvature (ROC) is one of the key parameters determining the performances of the lens such as imaging, phase transform and spatial Fourier transform. In the process of lens manufacturing, the ROC needs to be measured to make sure the lens can meet the requirements for use. In this paper, we first develop a method to measure the ROC of plano-convex lens in situ by using deep-learning based on the point spread functions (PSFs). Through simulation, we utilize the convolutional neural network to establish the nonlinear mapping between the error of ROC and corresponding focus and defocus PSFs generated by the lens, and the ROC can be directly estimated from the actual PSFs generated by the lens under test by means of the network of simulation training in practical application. The experimental proofs show that our method could achieve a relative measurement error of 0.029% for the plano-convex lens at high measurement speed. This method can realize the in situ fast measurement of the ROC with the significant advantages of no damage, simple operation and non-interferometric technique.