Self-calibrated stitching metrology for X-ray flat mirrors with the power- <i>x</i> term calibrated by grazing-incidence absolute testing

Shear-shift self-calibration stitching interferometry for long X-ray flat mirrors cannot reliably recover the meridional power-<i>x</i> term (<i>x</i>²). Calibrating the reference-flat power term and then stitching amplifies any residual power error to an unacceptable level for extreme X-ray optics. We demonstrate a hybrid absolute metrology in which a full-field grazing-incidence absolute test directly measures the power-<i>x</i> term, while a two-dimensional self-calibration stitching procedure determines the remaining surface components at high spatial resolution. This hybrid strategy removes the power-term ambiguity in self-calibration stitching and prohibits the power-error amplification in traditional stitching for long flats. On a 300 × 60 mm mirror (288 × 40 mm clear aperture), the reconstructed absolute surface shows 0.75 nm PV and 0.07 nm RMS repeatability, and the central profile agrees with a slope profiler at the sub-nanometer level.