Rapid in situ X-ray position stabilization via extremum seeking feedback.

X-ray beam stability is crucial for acquiring high-quality data at synchrotron beamline facilities. When the X-ray beam and defining apertures are of similar dimensions, small misalignments driven by position instabilities give rise to large intensity fluctuations. This problem is solved using extremum seeking feedback control (ESFC) for in situ vertical beam position stabilization. In this setup, the intensity spatial gradient required for ESFC is determined by phase comparison of intensity oscillations downstream from the sample with pre-existing vertical beam oscillations. This approach compensates for vertical position drift from all sources with position recovery times <6 s and intensity stability through a 5 µm aperture measured at 1.5% FWHM over a period of 8 hours.