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

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.

Figures (11)

• Figure 1: Impact of optical loss on observed squeezing and quantum noise spectrum. Left: Illustration of a squeezed vacuum state, where fluctuations are suppressed in one quadrature at the expense of increased fluctuations in the orthogonal quadrature. Right: Broadband quantum noise reduction achieved with frequency-dependent squeezing, shown as a function of increasing optical loss. This is a simplified model meant only for illustration. More realistically, depending on where they occur, most of the losses are shaped by the different cavity bandwidths in the interferometer and therefore exhibit a clear frequency dependence. The inset highlights the observed squeezing level as a function of optical loss.
• Figure 2: Amplitudes of Hermite-Gaussian modes, $\mathrm{HG}_{n,m}$, evaluated at the beam waist for mode indices $n,m \leq 2$. The higher-order modes, beyond the fundamental $\mathrm{HG}_{0,0}$, arise from beam misalignment and mode mismatch within the system.
• Figure 3: Illustration of beam misalignment (left) and mode mismatch (right) when coupling a laser beam into an optical cavity. Misalignment is described by two orthogonal DoFs: lateral offset and beam axis tilt. Mode mismatch is similarly described by two orthogonal DoFs: waist size mismatch and waist position mismatch.
• Figure 4: Example intensity images showing scattered modal content from random misalignment and mode mismatch. Six representative cases are shown. The lower-left subpanel (titled "Imperfection") summarizes the applied misalignment (MA) and mode mismatch (MM) along the $X$ and $Y$ directions: the horizontal axis represents lateral offset (MA) and waist size mismatch (MM), while the vertical axis represents beam tilt (MA) and waist position mismatch (MM). The lower-right subpanel (titled "HG Modes") shows the resulting first-order modes ($\mathrm{HG}_{1,0}$ and $\mathrm{HG}_{0,1}$) and second-order modes ($\mathrm{HG}_{2,0}$ and $\mathrm{HG}_{0,2}$), with axes corresponding to the real and imaginary parts of the complex mode amplitudes.
• Figure 5: Schematic of the two-step machine learning pipeline for mode decomposition and beam diagnostics. In the first stage, an adapted VGG16-based convolutional neural network (CNN) takes three beam intensity images measured at different locations as input and outputs the complex mode amplitudes up to order 2. In the second stage, these mode coefficients are fed into a separate neural network that predicts all eight misalignment and mode mismatch degrees of freedom simultaneously.