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Stitching interferometry is performed by collecting interferometric data from overlapped sub-apertures and stitching these data together to provide a full surface map. The propagation of the systematic error in the measured subset data is one of the main error sources in stitching interferometry for accurate reconstruction of the surface topography. In this work, we propose, using the redundancy of the captured subset data, two types of two-dimensional (2D) self-calibration stitching algorithms to overcome this issue by in situ estimating the repeatable high-order additive systematic errors, especially for the application of measuring X-ray mirrors. The first algorithm, called CS short for "Calibrate, and then Stitch", calibrates the high-order terms of the reference by minimizing the de-tilted discrepancies of the overlapped subsets and then stitches the reference-subtracted subsets. The second algorithm, called SC short for "Stitch, and then Calibrate", stitches a temporarily result and then calibrates the reference from the de-tilted discrepancies of the measured subsets and the temporarily stitched result. In the implementation of 2D scans in x - and y -directions, step randomization is introduced to generate nonuniformly spaced subsets which can diminish the periodic stitching errors commonly observed in evenly spaced subsets. The regularization on low-order terms enables a highly flexible option to add the curvature and twist acquired by another system. Both numerical simulations and experiments are carried out to verify the proposed method. All the results indicate that 2D high-order repeatable additive systematic errors can be retrieved from the 2D redundant overlapped data in stitching interferometry.

An alternate multilayer (AML) grating has been prepared by coating an ion etched lamellar grating with a B4C/Mo2C multilayer (ML) having a layer thickness close to the groove depth. Such a structure behaves as a 2D synthetic crystal and can reach very high efficiencies when the Bragg condition is satisfied. This AML coated grating has been characterized at the SOLEIL Metrology and Tests Beamline between 0.7 and 1.7 keV and at the four-crystal monochromator beamline of Physikalisch-Technische Bundesanstalt (PTB) at BESSY II between 1.75 and 3.4 keV. A peak diffraction efficiency of nearly 27% was measured at 2.2 keV. The measured efficiencies are well reproduced by numerical simulations made with the electromagnetic propagation code CARPEM. Such AML gratings, paired with a matched ML mirror, constitute efficient monochromators for intermediate energy photons. They will extend the accessible energy for many applications as x-ray absorption spectroscopy or x-ray magnetic circular dichroism experiments.