Self-Calibrated Stitching Test of X-Ray Flat Mirrors for Achieving Single-Nanometer and Nanoradian Long-Term Reproductivity

X-ray flat surfaces utilized in most advanced light sources have posed challenges to achieving form accuracy of peak-to-valley (PV) 2 nm, root mean square (rms) 0.2 nm, and rms 50 nrad. Measurement of the form error with high long-term reproductivity, i.e., repeatability over time of at least one day and with test surface remounted, is the key to a direct deterministic figuring process. To this end, the models of two main error sources—long-term environment disturbance and retrace error—have been established. The different error period components of the long-term environment disturbance and their influence on the full-aperture test accuracy have been investigated. The method of determining the adequate subaperture size, overlapping ratio, and tilt misalignment threshold for decreasing the influence of the long-term environment disturbance and the retrace error is reported. The PV value standard uncertainty is evaluated to be 0.092 nm. Experiments on an X-ray flat with a clear aperture (CA) of $250\times 30$ mm were tested with the optimized test parameters and other sets of parameters for comparisons. Self-consistency experiments have been conducted to verify the long-term reproductivity can reach PV 0.908 nm, rms 0.076 nm, and rms 32 nrad, which meet the typical test accuracy posed by the fourth-generation synchrotron radiation and free electron lasers.