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High-brightness X-ray pulses, as generated at synchrotrons and X-ray freeelectron lasers (XFEL), are used in a variety of scientific experiments. Manyexperimental testbeds require optical equipment, e.g Compound Refractive Lenses(CRLs), to be precisely aligned and focused. The lateral alignment of CRLs to abeamline requires precise positioning along four axes: two translational, andthe two rotational. At a synchrotron, alignment is often accomplished manually.However, XFEL beamlines present a beam brightness that fluctuates in time,making manual alignment a time-consuming endeavor. Automation using classicstochastic methods often fail, given the errant gradient estimates. We presentan online correction based on the combination of a generalized finitedifference stencil and a time-dependent sampling pattern. Error expectation isanalyzed, and efficacy is demonstrated. We provide a proof of concept bylaterally aligning optics on a simulated XFEL beamline.

An Online Dynamic Amplitude-Correcting Gradient Estimation Technique to Align X-ray Focusing Optics