High-precision interferometric measurement method for the radius of curvature with a computer-aided adjustment model

In order to achieve high-precision measurement of the radius of curvature, this paper proposes an interferometric measurement method with a computer-aided adjustment model. This model is based on the principle of light propagation and derives the parameters of the adjustment error caused by the misalignment. According to the relationship between the adjustment error and the surface change at the null point positions, the adjustment amount of the tested sphere is calculated. By adjusting the position of the tested sphere several times, the measurement error is reduced. Then, an interferometer model is established to simulate and validate the mathematical model, which is further validated through experiments. The proposed method is applied to measure the sphere with a nominal radius of -146.0076 mm. The experimental results show that the repeatability of the radius measurement is improved from 4.0 ppm to 1.7 ppm with the computer-aided adjustment model, which is nearly 2.3 times improved in precision. It also helps to improve the efficiency of the radius measurement.