Image-Based Laser Beam Diagnostics Using Statistical Analysis and Machine Learning Regression

This study is a comprehensive experimental and computational investigation into high-resolution laser beam diagnostics, combining classical statistical techniques, numerical image processing, and machine learning-based predictive modeling. A dataset of 50 sequential beam profile images is collected from a femtosecond fiber laser operating at a central wavelength of 780 nm with a pulse duration of approximately 125 fs. These images are analyzed to extract spatial and temporal beam characteristics, including centroid displacement, full width at half maximum (FWHM), ellipticity ratio, and asymmetry index. All parameters are derived using intensity-weighted algorithms and directional cross-sectional analysis to ensure accurate and consistent quantification of the beam's dynamic behavior. Linear regression models are applied to horizontal and vertical intensity distributions to assess long-term beam stability. The resulting predictive trends revealed a systematic drift in beam centroid position, most notably along the vertical axis, and a gradual broadening of the horizontal FWHM. The modeling further showed that vertical intensity increased over time while horizontal intensity displayed a slight decline, reinforcing the presence of axis-specific fluctuations. These effects are attributed to minor optical misalignments or thermally induced variations in the beam path. By integrating deterministic analysis with data-driven forecasting, this methodology offers a robust framework for real-time beam quality evaluation. It enhances sensitivity to subtle distortions and supports the future development of automated, self-correcting laser systems. The results underscore the critical role of continuous, high-resolution monitoring in maintaining beam stability and alignment precision in femtosecond laser applications.