Simultaneous misalignment and mode mismatch sensing in resonant optical cavities using intensity-only measurements

Precise sensing and control of spatial mode content is essential for the performance of precision optical systems, particularly interferometric gravitational-wave detectors, where misalignment and mode mismatch can lead to significant optical losses and degraded quantum noise suppression. Conventional approaches, including heterodyne wavefront sensing and phase camera techniques, are effective but can be limited by hardware complexity and systematic uncertainties arising from restricted reference-beam overlap. This paper presents what we believe to be a novel two-step deep learning pipeline for robust beam diagnostics based solely on beam intensity images. In the first stage, a multi-intensity-image convolutional neural network (CNN) performs accurate mode decomposition, recovering the complex modal content of distorted beams. In the second stage, the predicted mode coefficients are fed into a downstream regression network that simultaneously estimates all eight degrees of freedom (DoFs) associated with misalignment and mode mismatch, including beam tilt, lateral offset, and waist size and position mismatches in both transverse directions. The proposed CNN-based framework achieves a mean absolute error (MAE) of 0.0034 in the mode decomposition stage, which propagates to a total MAE of 0.0062 in the recovered beam imperfection parameters at the final stage on a numerically generated synthetic dataset. This corresponds to an average residual optical loss of 39 ppm per DoF (310 ppm total). This approach relies only on standard CCD imaging and is robust to random intensity noise, eliminating the need for complex interferometric hardware. The results demonstrate that the proposed deep learning pipeline enables real-time, high-accuracy wavefront sensing and mode-mismatch diagnostics, providing a hardware-efficient tool for improving the stability and sensitivity of precision optical systems.