Surface shape fitting for x-ray mirror characterization

X-ray mirrors play a pivotal role in beamline operation as they are the key optical components for the transport, the focusing of the incoming radiation to the sample under study. To ensure high beam quality, the accuracy of the surface shape of these mirrors is critical. Therefore, it is essential to precisely evaluate measured mirror surfaces using shape fitting in synchrotron mirror inspection. This study focuses on developing a comprehensive approach for fitting measured x-ray mirror surface shapes to their target shapes, with several typical mirror geometries summarized for x-ray reflective optics characterization. A general framework for mirror shape fitting enables the implementation of reusable and maintainable fitting code across diverse mirror shapes, facilitating adaptation to new target shapes. Furthermore, the study incorporates parameter tolerance into the shape-fitting process, addressing its significance in synchrotron mirror applications. This integration ensures that the mirror surface aligns not only with the nominal target shape but also with allowable deviations critical for the performance in beamline experiments.