Grating-based Wavefront Metrology

The ever increasing demand on X-ray optical elements to preserve the wavefront shape and coherence requires new instruments that can measure the wavefront shape in-situ, at-wavelength and under experimental conditions. Due to its high angular sensitivity on the order of 10 nrad and its single-shot capability, hard X-ray grating interferometry is ideally suited to observe the wavefront downstream of X-ray optical components and assess the aberrations they introduce.

Figure 1: Sketch of the X-ray free electron laser and the grating interferometry setup.
Figure 2: Aspherical component of the hard X-ray offset mirror profile deduced from single shots (lines with markers) and comparison of a fifty-pulse average (blue line) with an ex-situ measurement (solid red line).
Figure 3: The source distance, which is equivalent to the wavefront radius of curvature as the free electron laser LCLS is driven into saturation.

The first applications of X-ray grating interferometry to optics metrology were in the metrology of an X-ray multilayer mirror [1] and in analyzing the distortions of a single beryllium focusing lens of long focal length [2]. The technique has also been applied to in-situ observations of heatload induced distortions on a double crystal monochromator [3]. As no reference scan can be recorded, a high placement accuracy of the microfabricated grating structures is essential.

We have implemented a grating interferometer to analyze the wavefront at a hard X-ray free electron laser, the Linac Coherent Light Source (LCLS) [4] and the japanese XFEL SACLA [5]. The experimental setup is outlined in figure 1. Like the future free electron laser SwissFEL at PSI, LCLS produces x-ray pulses of unprecedented intensity, high spatial coherence and extremely short pulse duration. This enables new and exciting experiments in many areas of science. Many of these experiments rely fundamentally on a clean, well-defined and reproducible wavefront from one pulse to the next.

Using grating interferometry, we have shown that the harmonic offset mirrors (figure 1) are slightly collimating the radiation in horizontal direction. The experimental data from a grating interferometer also enables a spatially resolved analysis of the wavefront distortions introduced by the optical elements, such as the aspherical components of the mirror profile shown in figure 2.

Due to its high sensitivity, even the location of the source point in the 130 m long undulator of LCLS can be determined with grating interferometry [3]. Absolute radius of curvature measurement are possible, once the grating alignment angles have been determined [5]. These source point position measurements are illustrated an observation of the source position of LCLS as it is driven into saturation (figure 3).


  1. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, X-ray wavefront analysis and optics characterization with a grating interferometer, Applied Physics Letters 86 (2005), 054101. DOI: 10.1063/1.1857066
  2. S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer, Applied Physics Letters 99 (2011), 221104. DOI: 10.1063/1.3665063 PDF
  3. S. Rutishauser, A. Rack, T. Weitkamp, Y. Kayser, C. David, and A. T. Macrander, Heat bump on a monochromator crystal measured with X-ray grating interferometry, Journal of Synchrotron Radiation 20 (2013), 300 DOI: 10.1107/S0909049513001817 PDF
  4. S. Rutishauser, L. Samoylova, J. Krzywinski, O. Bunk, J. Grünert, H. Sinn, M. Cammarata, D. M. Fritz, and C. David, Exploring the wavefront of hard x-ray free electron laser radiation, Nature Communications 3 (2012), 947. DOI: 10.1038/ncomms1950 PDF Suppl. Mat.
  5. Y. Kayser, S. Rutishauser, T. Katayama, T. Kameshima, H. Ohashi, U. Flechsig, M. Yabashi, and C. David, Wavefront metrology measurements at SACLA by means of x-ray grating interferometry, Optics Express 22 (2014) p. 9004-9015
  6. C. David, S. Rutishauser, M. Sprung, I. Zanette, T. Weitkamp, X-Ray Grating Interferometry - Applications in Metrology and Wave Front Sensing, AIP Conference Proceedings 1466 (2012), 23-28. DOI: 10.1063/1.4742264