X-ray pulse wavefront metrology using speckle tracking

Abstract

An instrument allowing the quantitative analysis of X-ray pulsed wavefronts is presented and its processing method explained. The system relies on the X-ray speckle tracking principle to accurately measure the phase gradient of the X-ray beam from which beam optical aberrations can be deduced. The key component of this instrument, a semi-transparent scintillator emitting visible light while transmitting X-rays, allows simultaneous recording of two speckle images at two different propagation distances from the X-ray source. The speckle tracking procedure for a reference-less metrology mode is described with a detailed account on the advanced processing schemes used. A method to characterize and compensate for the imaging detector distortion, whose principle is also based on speckle, is included. The presented instrument is expected to find interest at synchrotrons and at the new X-ray free-electron laser sources under development worldwide where successful exploitation of beams relies on the availability of an accurate wavefront metrology.

State of the Art of X-ray Speckle-Based Phase-Contrast and Dark-Field Imaging

“…The information from the differential phase signals in the two orthogonal directions can then be combined via phase integration to obtain the phase shift Φ of the wavefront. This can be done with various methods, e.g., Fourier-based approaches [64,[139][140][141], two-dimensional numerical integration using least-squares minimisation [91,142] or matrix inversion [135].…”

“…This can be reduced by a shorter propagation distance, which, however, also affects the sensitivity of the measurement; see Section 3.4. Furthermore, methods have been investigated to mitigate these artefacts, e.g., by considering the effect of the second derivative of the wavefront [91] or attempting to eliminate the edge effect from the image before reconstruction [151].…”

“…However, it has been shown that considering the distortions of the analysis subset can improve the robustness and accuracy of the reconstruction algorithm and furthermore delivers additional information, e.g., on the local curvature of the X-ray wavefront [91]. The coefficients of the higher-order distortions can be obtained from a minimisation approach after determining the rigid translation of the subset.…”

“…This method, however, requires the beam to remain stable over the course of the two image acquisitions. For cases where the X-ray beam is fluctuating in time, it is more appropriate to record the two images simultaneously and a different variation of this type of measurement was demonstrated for this purpose [91]. The setup consists of a diffuser and one camera with a semi-transparent mirror and scintillator that records an image, but at the same time transmits part of the X-rays, which is recorded by a second camera further downstream.…”

High-accuracy wavefront sensing for x-ray free electron lasers

“…In addition to the photon energy, pulse duration, and spectral characteristics, it is important to have an accurate knowledge of the single pulse x-ray wavefront, which affects focal plane intensity and profile, spot size, and spatial resolution, as well as centroid location within the focal plane. Among techniques currently in use are the following: burn patterns that ablate material as a function of intensity across the focal plane [5,6]; Hartmann masks, which track localized wavefront vectors [7,8]; double grating interferometers, each grating having a two-dimensional checkerboard pattern, where the second grating produces a spatially downshifted Moiré pattern [9,10]; and x-ray speckle tracking techniques [11].…”