Wavefield propagation simulation of a partially coherent 100keV pink beam to evaluate figure-error effects

Abstract

High-energy x-ray measurements often require a high photon-flux beam to compensate for their weak interaction with matter. While a double-multilayer monochromator (DMM) provides a high-flux beam with a broad (pink) bandwidth at 100keV at SPring-8 BL05XU, the beam profile exhibits fine-scale horizontal stripe patterns, despite the fact that the substrate surfaces of the multilayer mirrors have been processed to current technological limits (approximately 0.1nm RMS figure error). To identify the primary cause of these variations, we performed wavefield propagation simulations by rigorously modeling the spatially partially coherent undulator radiation with a finite energy bandwidth using the coherent mode decomposition. The overall shape and the root-mean-square (RMS) intensity variation of our simulations were in agreement with the measured beam profile, demonstrating that both energy bandwidth and spatial coherence must be considered to avoid overestimating figure-error effects. Furthermore, by applying spatial-frequency band-stop filters to the measured figure-error profiles in the simulations, we identified that mid-spatial-frequency errors (0.02 to 0.5mm-1) are the dominant cause of the intensity variations. The results suggest that reducing the figure errors in this specific frequency range to below 10 pm RMS could decrease beam intensity variations from 3% to 1%.