Experimental calibration of grating period mismatch in Talbot interferometry for accurate x-ray wavefront and surface metrology

Thermal deformation of x-ray optical elements, especially the first element exposed to high thermal loads, can significantly degrade the performance of synchrotron radiation beamlines. Accurate wavefront measurement is essential for estimating such deformations and improving optical design. Talbot interferometry, employing phase and absorption gratings to produce moiré fringes, enables wide-field wavefront sensing across areas of several to tens of millimeters. However, mismatches in the designed period ratio between the gratings introduce systematic errors in wavefront curvature estimation and surface profile reconstruction. This study investigates the impact of such period mismatches on wavefront accuracy and presents a practical calibration method. Experiments with both minimally used and long-term exposed gratings show that calibration markedly improves the precision of surface profile measurements, reducing variation by up to 50%. These results emphasize the importance of precise grating period calibration for reliable wavefront and surface figure evaluation, particularly for optics subject to thermal deformation under high-power x-ray irradiation.