Research on high-precision angular measurement based on machine learning and optical vortex interference technology

Abstract The distortion degree of the interference pattern of vortex light is measured to achieve high-precision measurement of small angles. In this paper, a regression prediction model based on the Stacking ensemble learning algorithm is constructed. Firstly, by altering the optical axis at small angles within the range of 0.0006° to 0.3° in a vortex optical conjugate interference system, corresponding interference patterns were obtained. The angle formed by the centroids of the upper two petals of the deformed interference patterns and the center was extracted as a feature for dataset construction. The dataset was randomly split into training and testing sets in a 7:3 ratio. Secondly, four models, including SVR, PSO-BP, GPR, and Stacking ensemble algorithm, were optimized for hyperparameters, trained, and evaluated. Comparative analysis of prediction performance was conducted using coefficients of determination, root mean square errors, and mean absolute errors. Based on multiple random splits of the dataset for training and prediction, it was observed that compared to single learners, the ensemble model reduced the average relative error by 0.2829%, demonstrating better prediction performance and stronger stability by combining the advantages of primary learners. Additionally, the Stacking model achieved a measurement accuracy of 0.0006°, with the relative error maintained within 0.6%, indicating the feasibility of high-precision measurement of optical axis micro-angles using machine learning and vortex optical conjugate interference systems.