Advanced vortex beam interference system enhanced by CNN for micro-displacement detection

This paper introduces an innovative conjugate vortex beam interference system that significantly enhances micro-displacement measurement capabilities by incorporating a deep learning model for processing and analyzing interference patterns. The theoretical foundation of this system is based on the petal-like interference pattern graduated when two conjugate vortex beams interact, where the rotation of the fringe orientation exhibits a strict linear correlation with displacement. The system fully exploits the sensitivity of vortex beams to minute changes in optical paths, along with the conjugate interference effect, to capture precisely angular variations in the interference pattern. This results in a measurement accuracy better than 0.84 nm across the 0–500 nm range, with a mean absolute error (MAE) approximately 0.5 nm, while achieving sub-nanometer precision across an extensive measurement range. By innovatively applying deep learning to analyze vortex beam interference data, the system effectively utilizes the unique properties of vortex beams alongside the powerful feature learning capabilities of convolutional neural networks (CNNs), enhancing robustness against fringe distortion and noise, thereby improving the accuracy of displacement detection. This method provides an accurate, efficient, and non-contact approach to displacement measurement, showcasing distinct advantages in the precision and stability of micro-displacement assessments.