Data Driven Drift Correction For Complex Optical Systems

To exploit the thousand-fold increase in spectral brightness of modern light sources, increasingly intricate experiments are being conducted that demand extremely precise beam trajectory. Maintaining the optimal trajectory over several hours of an experiment with the needed precision necessitates active drift control. Here, we outline Time-Varying Bayesian Optimization (TVBO) as a data driven approach for robust drift correction, and illustrate its application for a split and delay optical system composed of six crystals and twelve input dimensions. Using numerical simulations, we exhibit the application of TVBO for linear drift, non-smooth temporal drift as well as constrained TVBO for multi-objective control settings, representing real-life operating conditions. This approach can be easily adapted to other X-ray beam conditioning and guidance systems, including multi-crystal monochromators and grazing-incidence mirrors, to maintain sub-micron and nanoradian beam stability over the course of an experiment spanning several hours.

💡 Research Summary

The paper addresses the critical challenge of maintaining sub‑micron positional and nanoradian angular stability of X‑ray beams over several hours in modern high‑brightness light‑source experiments. Traditional feedback methods such as PID controllers rely on abundant diagnostics and assume a static relationship between control inputs and beam output, which breaks down in complex optical setups with many degrees of freedom and limited sensors. To overcome these limitations, the authors propose a data‑driven drift‑correction framework based on Time‑Varying Bayesian Optimization (TVBO).

TVBO extends conventional Bayesian Optimization (BO) by incorporating a sliding‑window mechanism that continuously retrains a Gaussian Process (GP) surrogate model on the most recent w observations. This design enables the optimizer to “forget” outdated data that no longer reflects the current system dynamics, thereby adapting to time‑varying objective functions such as beam drift caused by thermal expansion, mechanical vibrations, or environmental changes. The authors implement TVBO using the open‑source Xopt library, selecting a Matérn ν = 5/2 kernel for the GP, and the Upper Confidence Bound (UCB) acquisition function with an exploration parameter β = 0.1.

The experimental testbed is the Hard X‑ray Split‑and‑Delay (HXRSND) system at LCLS‑II‑HE, which consists of a channel‑cut branch and a delay branch containing six crystals and twelve motorized angular degrees of freedom (θ and χ). The goal is to keep the two branches spatially overlapped and energetically matched while varying the temporal delay from –5 ps to 500 ps. Because the delay branch is mechanically less stable, the authors focus on correcting its beam‑position error (BPE) and, in a constrained scenario, also enforce a beam‑intensity constraint.

Simulations are performed with a 2 × 1D wave‑front propagation code that assumes full spatial coherence and monochromaticity at 9.5 keV. The simulated data are calibrated against real experimental measurements, showing a linear drift of roughly 300 nm per minute and an aleatoric noise level of about 100 nm (≈10 % of the stability target). Three drift scenarios are explored: (1) continuous linear drift, (2) drift with abrupt jumps (non‑smooth behavior), and (3) multi‑objective constrained drift where intensity must remain above a threshold.

Key findings include:

• Linear Drift – With a sliding‑window size w = 40 samples, TVBO reduces the BPE to an average of 85 nm and RMS of 95 nm, well below the sub‑100 nm target, without any manual intervention.
• Non‑Smooth Drift – Reducing the window to w ≈ 10–20 enables rapid re‑learning after sudden changes; the optimizer restores the BPE to <120 nm within two to three new measurements, outperforming conventional PID in recovery speed.
• Constrained Multi‑Objective – By training an additional GP to predict whether a candidate setting satisfies the intensity constraint, TVBO simultaneously minimizes BPE while keeping intensity loss under 0.5 %, demonstrating feasibility for real experimental constraints.
• Computational Efficiency – Each optimization iteration takes roughly 0.15 s on a standard workstation, making real‑time feedback practical.

The authors discuss the trade‑off between window size (memory) and adaptation speed, noting that larger windows improve trend estimation for slowly varying drift but hinder responsiveness to abrupt changes. Hyper‑parameter selection was performed manually, but the authors suggest that automated Bayesian hyper‑parameter optimization could further streamline deployment.

In conclusion, the study shows that TVBO provides a robust, sample‑efficient, and noise‑tolerant method for drift correction in high‑dimensional, time‑varying optical systems. By continuously re‑optimizing the control parameters as the system evolves, TVBO eliminates the need for frequent manual checks and significantly improves experimental throughput. The approach is readily transferable to other X‑ray beam conditioning devices such as multi‑crystal monochromators and grazing‑incidence mirrors, promising sub‑micron and nanoradian stability across a wide range of synchrotron and XFEL beamlines.