Data Driven Drift Correction For Complex Optical Systems

TL;DR

Drifts degrade beam trajectory stability over long X-ray experiments. The authors apply Time Varying Bayesian Optimization (TVBO) with a sliding window of size $w=40$ and a Gaussian Process surrogate to actively re-optimize a high-dimensional HXRSND drift-correction problem. They demonstrate TVBO on continuous linear drift, discontinuous episodic drift, and constrained multi-objective drift correction, achieving sub-micron beam-position stability and preserving beam intensity. The approach offers a scalable, data-driven alternative to traditional feedback loops, enabling near-autonomous optimization of complex beam conditioning hardware and applicability to other beamlines for sustained sub-micron and nanoradian stability over hours.

Abstract

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.

Figures (5)

• Figure 1: Schematic of the HXRSND with the CC (Channel Cut) branch in blue and the delay branch in red. The x-ray beam propagates from right to left. The arrows indicate the motorized degrees of the system. In addition, each crystal along the delay branch has "chi" adjustment which corresponds to rotation about the tangential vector of the crystal surface (not shown). The red and blue dots correspond to locations of beam diagnostics, as noted in the legend on the top right of the figure. Figure re-used with permission from Zhu2017.
• Figure 2: Comparison of the predictions of the Beam Position Error from the wave-optical simulations code used in this investigation against experimental results on the HXRSND (delay branch only). Between each sample various degrees of freedom were adjusted both in experiment and also as inputs to the simulator.
• Figure 3: Visualization of the drift for the horizontal Beam Position Error in the Channel Cut (labeled as cc) and the Delay (labeled as delay) branches observed in an experiment using the HXRSND, without adjustment of any of the degrees of freedom. The rate of drift is observed to be $\approx$300 nm in 1 minute, and the standard deviation after subtracting the linear drift is 108 nm rms.
• Figure 4: Results using Time Varying Bayesian Optimization (TVBO) for Drift Correction with a constant, linear drift model, for the Beam Position Error in $\mu m$. The solid line reports the change in performance of the initial optimum setting due to drift. Each semi-transparent circle represents the Beam Position Error for a single sample generated using TVBO. The transparency in the circles is used to assist the reader visualize the location and density of the points even in areas of high overlap.
• Figure 5: Results using Time Varying Bayesian Optimization (TVBO) for Drift Correction with a Discontinuous, episodic drift model. The solid line reports the change in performance of the initial optimum setting due to drift. Each semi-transparent circle represents the Beam Position Error for a single sample generated using TVBO.