Simultaneous Misalignment and Mode Mismatch Sensing in Optical Cavities Using Intensity-Only Measurements

TL;DR

This paper introduces a deep learning-based method for diagnosing misalignment and mode mismatch in optical cavities using only intensity images, achieving high accuracy and robustness without complex hardware.

Contribution

A novel two-step CNN pipeline for accurate, real-time beam diagnostics based solely on intensity images, eliminating the need for interferometric hardware.

Findings

Achieved a mode decomposition MAE of 0.0034, leading to a total parameter MAE of 0.0062.

Residual optical loss of 39 ppm per degree of freedom on average.

Demonstrated robustness to intensity noise and real-time capability.

Abstract

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 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. 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 scalable and hardware-efficient tool for improving the stability and sensitivity of precision optical systems.