Real-Time-Capable Betatron Tune Measurement from Schottky Spectra Using Deep Learning and Uncertainty-Aware Kalman Filtering

TL;DR

The paper tackles real-time betatron tune estimation in compact proton-therapy synchrotrons under very low SNR by introducing a lightweight, uncertainty-aware pipeline. It combines a self-calibrating frequency normalization, a dual-branch attention-based CNN that outputs both the tune $q \in [0,0.5)$ and a calibrated uncertainty $\sigma$, and an uncertainty-aware Kalman filter that adaptively weights measurements. Training with a Laplace NLL loss yields well-calibrated uncertainty estimates, which are then used to suppress outliers and stabilize tracking in time series. On synthetic data spanning $0$ to $-20$ dB SNR, the approach outperforms traditional peak-detection and achieves sub-millisecond end-to-end latency on commodity GPUs; preliminary beam-data validation from SAPT shows stable tracking without retraining, supporting practical deployment in clinical facilities.

Abstract

Betatron tune measurement is essential for beam control in compact proton-therapy synchrotrons, yet conventional peak-detection techniques are not robust under the low signal-to-noise ratio (SNR) conditions typical of these machines. This work presents a lightweight convolutional neural network that performs real-time tune extraction from Schottky spectra with sub-millisecond inference latency and calibrated uncertainty estimates. The model uses attention-based pooling for reliable peak localization and a dual-branch architecture that jointly predicts the tune and its associated uncertainty. Trained with a Laplace negative log-likelihood loss, it produces uncertainty estimates whose magnitude tracks the instantaneous prediction error, which enables uncertainty-aware Kalman filtering for temporal smoothing. Experiments on a large synthetic dataset spanning SNR levels from 0 to $-20$\,dB demonstrate substantial performance gains over traditional peak-detection baselines, while the Kalman filter further suppresses transient outliers in time-series operation. Preliminary validation on operational beam data confirms stable tune tracking without retraining. With only about $2.0\times 10^{4}$ trainable parameters and real-time inference on commodity GPU hardware, the proposed diagnostic offers a practical solution for rapid and accurate betatron tune monitoring in compact medical synchrotrons and similar accelerators.

Figures (8)

• Figure 1: Mapped PSD (left) and corresponding weight map (right) after frequency normalization and soft binning. The betatron tune $q = 0.3$ appears as a localized peak in the normalized representation. SNR = $-20$ dB.
• Figure 2: Overall architecture of the proposed neural network. Multi-scale feature extraction processes the two-channel input through parallel fine-grained and coarse-grained paths. After shared residual processing, the network splits into dual branches: the tune prediction branch uses sharp attention pooling for precise localization, while the uncertainty estimation branch employs softer attention to assess measurement difficulty.
• Figure 3: Detailed structure of the modules presented in Fig. \ref{['fig:overall_architecture']}, where $k$ denotes the kernel size and $C$ denotes the number of channels.
• Figure 4: Failure cases for the peak-detection baseline on simulated Schottky spectra from the static test set. Each panel shows a PSD snapshot in tune units. Vertical lines indicate the true tune (black dotted line), the peak-detection estimate (green dashed line), and the CNN prediction (blue dash-dotted line). The six examples are selected such that the peak-detection error is larger than $10^{-2}$, while the CNN prediction error is below $10^{-3}$ with predicted uncertainty $\sigma < 3\times 10^{-3}$, highlighting typical low-SNR failure modes of the classical algorithm.
• Figure 5: Mean absolute error within each uncertainty quartile (Q1--Q4) as a function of SNR. The strict monotonic ordering (Q1 $<$ Q2 $<$ Q3 $<$ Q4) at all SNR ranges confirms robust calibration across operating conditions.