Pulse-to-pulse wavefront sensing at free-electron lasers using ptychography

Abstract

The pressing need for knowledge of the detailed wavefront properties of ultra-bright and ultra-short pulses produced by free-electron lasers has spurred the development of several complementary characterization approaches. Here a method based on ptychography is presented that can retrieve high-resolution complex-valued wavefunctions of individual pulses without strong constraints on the illumination or sample object used. The technique is demonstrated within experimental conditions suited for diffraction experiments and exploiting Kirkpatrick-Baez focusing optics. This lensless technique, applicable to many other short-pulse instruments, can achieve diffraction-limited resolution.

Keywords: X-ray free-electron lasers; XFELs; ptychography; ultra-short pulses; wavefronts.

Figure 1

Diagram of the experimental setup. Adjustable slits form an aperture that admits the central part of the FEL beam. KB mirrors focus the beam onto a small area of the sample, which is scanned with a translation stage in the xy plane. The intensities of the resulting free-space-propagated exit waves (i.e. the diffraction patterns) are recorded by a detector downstream along z.

Figure 2

(a) SEM image of the Siemens star test pattern; the scale bar is in (b). (b) Amplitude of the ptychographic reconstruction; the color bar represents transmission between 0 and 1. (c) Probe positions recovered via our position-correction algorithm; the scale bar is in (b). The area covered by the motor positions used for the ptychographic scan is indicated with rectangles in (a) and (c). (d) Position correction for each scanning point; null correction (0, 0) at the center. The main axis of this two-dimensional correction distribution is indicated, revealing a dominant vibration component along the x axis.

Figure 3

(a)–(j) Ten components of reconstructed probes obtained via OPRP reconstruction. Singular values are annotated on each component. (k)–(t) Back-propagation of the same components to the virtual secondary source plane, neglecting the spherical wave term. Amplitude is mapped to brightness and phase is mapped to hue according to the color wheel in (a); the brightness scale is such that its maximum has been adjusted for every frame individually to match its brightest pixel.

Figure 4

(a)–(d) Amplitude of four of the N = 937 retrieved probes obtained via OPRP reconstruction. (e) Amplitude of a probe retrieved from Hartmann sensor data. (f)–(j) Back-propagation of (a)–(e) to the virtual secondary source plane, neglecting the spherical wave term. Color scales are shared among (a)–(e) and among (f)–(j), revealing intensity variations.

Figure 5

Histograms of (a) the intensity of each probe relative to the median intensity and (b) the radial displacement of the center of mass of each probe relative to the center of the detector. Inset in (b) is a rescaled version of a portion of the same histogram.

Figure 6

Horizontal (a) and vertical (b) sections of ptychographic reconstruction of the main component propagated around the focal position (±20 mm). Image scaling is different in its two dimensions according to the scale bars in (a). Amplitude is mapped to brightness and phase is mapped to hue according to the color wheel in (a).