How 100-pm figure errors in x-ray mirrors affect the image of 100-keV undulator radiation

Double multilayer monochromators for high-flux, high-energy x-ray imaging have been developed at SPring-8. Although state-of-the-art mirrors are fabricated with root-mean-square (RMS) figure errors of 100 pm, they still introduce horizontal stripes in beam images. Suppressing these stripes remains a significant challenge, as it requires controlling figure errors to levels well beyond current fabrication capabilities. To evaluate the impact of such errors on high-energy x-ray beams, given the partially coherent nature of the 100 keV pink beam, we performed coherent mode decomposition to represent realistic radiation fields. Wave field propagation was computed using the angular spectrum method, which is computationally efficient. The simulation results were in agreement with the measured beam image in terms of beam size and intensity variation. Further simulations using modulated spatial spectra of figure errors demonstrated that suppressing mid-spatial-frequency components (2-50 mm) to below 10 pm RMS reduced the intensity variation to 1%.