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

Abstract The paper innovatively constructs a regression prediction model based on the Stacking ensemble learning algorithm by utilizing the distortion degree of vortex optical interference patterns, achieving high-precision measurement of small angles. It constructs a regression prediction model based on the Stacking ensemble learning algorithm. Initially, in the spiral optical conjugate interference system, minute variations in the optical axis yield corresponding interference patterns, within an angle range of 0.0006° to 0.3°. The angle formed between the centroids of the upper two petals in the deformed interference patterns and the center is extracted as a feature for feature extraction. A dataset is established and randomly divided into training, validation, and testing sets in a 6:2:2 ratio. Subsequently, four models—support vector regression, particle swarm optimization back propagation, Gaussian process regression, and the stacking ensemble algorithm—are optimized for hyperparameters, trained, and evaluated based on coefficients of determination, root mean square error, and mean absolute error to compare their predictive performance. Through multiple rounds of training and prediction on randomly partitioned datasets, it is evident that the ensemble model exhibits a reduction in relative error compared to single learners, demonstrating that the Stacking-based ensemble algorithm can combine the strengths of base learners, showcasing superior predictive performance and enhanced stability. Moreover, the Stacking ensemble model achieves a measurement precision of 0.0006°, with a relative error maintained within 0.6%, indicating the feasibility of achieving high-precision measurement of tiny angles in the optical axis using machine learning and spiral optical conjugate interference systems.