Dichography: Two-frame Ultrafast Imaging from a Single Diffraction Pattern

Abstract

We experimentally demonstrate that pairs of time-delayed ultrabright and ultrashort X-ray pulses of two different colors, delivered by modern X-ray Free Electron Lasers, can provide two time-delayed snapshots of a sample. We introduce Dichography, a method that algorithmically separates the diffraction signals overlapping on the detector and independently retrieves the two images of the specimen. We employ Dichography to reconstruct two views of individual xenon-doped helium nanodroplets with 20 nm spatial resolution. The consistency of structures observed in both images at delays up to 750 fs provides evidence that, under these illumination conditions, significant structural damage only occurs at longer timescales. We further validate the method by imaging pairs of silver nanoparticles intercepted by the same light pulse. Dichography enables a new class of experiments across physics, chemistry, and materials science, making a significant step toward the original promise of X-ray free-electron lasers to capture ultrafast movies of nanomatter.

Figures (7)

• Figure 1: Intuitive representation of the difference between conventional single-particle CDI, Holography, and Dichography in terms of a double-slit experiment. In a), the incoming radiation intercepts a single slit, and the recorded scattering image encodes its size. In b), the fields scattered by two apertures interfere with each other. The far-field intensities thus encode the information on the size of both slits and their relative distance. In c), the fields produced by the two apertures do not interfere. The diffraction signal, thus, only encodes the independent properties of the two slits.
• Figure 2: Reconstructions from two-color diffraction patterns acquired at the European XFEL, produced by superfluid helium nanodroplets doped with xenon. Two experimental diffraction patterns are reported in a) and d), on which the diffraction signals produced by two different photon energies, 1.0keV and 1.2keV, are superimposed. The intensity is encoded as reported by the color bar at the bottom. The intensity values are translated into numbers of 1.2keV photons per pixel. The inset plot is a zoomed-in region of the diffraction image, to better appreciate the photon statistics, and thus the statistical noise, that affects the experimental data. The two colors are delayed by 50fs for the pattern in a) and 750fs for the pattern in d). The two reconstructed frames, corresponding to the two time-delayed projections of the particle density, are reported in b), c) and e), f) for the patterns in a) and d), respectively. The reconstructed density of the xenon doping follows the color bar in Fig. \ref{['fig:SFEL_examples']}. The shape of the helium droplets, independently retrieved before the imaging process and constrained using the DCDI method, are superimposed in blue color.
• Figure 3: Example of dichographic reconstruction from a single diffraction pattern produced by a "double-hit". The experimental diffraction data from an individual light pulse delivered by SwissFEL is shown in a). The two particle densities retrieved from a) via Dichography are shown in b) and c). The two reconstructions correspond to two silver nanocubes, with edge length of around 100nm. Once the two particles have been reconstructed, the corresponding single-particle diffraction patterns can be calculated, shown in d) for the reconstruction in b), and in e) for the one reported in c). The central parts of the disentangled diffraction images in d) and e) are magnified in f) and g), respectively. The white arrows point at the same region of the diffraction image. All diffraction data in a), d), e), f) and g) are plotted with logarithmic color scale.
• Figure 4: Further Dichography reconstructions of silver nanoparticles from individual diffraction patterns acquired at SwissFEL. Each sub-figure, from a) to d), reports different imaging results on a single diffraction pattern. The experimental data are shown in the leftmost column. The central and rightmost columns report the two frames of the reconstruction. Similar to Fig. \ref{['fig:SFEL_single']}, within the same sub-figure the two reconstructed densities are reported with common color scale and scale bar, such that their size and brightness can be compared.
• Figure 5: Scheme of the iterative phase retrieval algorithm for Dichography. The approach corresponds, in most steps, to the execution of two independent reconstruction procedures, $A$ and $B$, using conventional iterative phase retrieval algorithms. The two densities, $\rho^A$ and $\rho^B$, are randomly initialized. Two constraints -- the support function in real space and the experimental intensities in Fourier space -- are cyclically enforced. The application of the real-space constraint (shown on the right and left sides of the figure) is independent for $A$ and $B$, each with its own support function. This step is thus equivalent to conventional methods for two independent reconstructions. The Fourier intensity constraint, depicted in the center of the figure, is shared between $A$ and $B$. Here, the sum of the two Fourier amplitudes is replaced by the experimentally measured values. This information is then back-propagated to the two separate densities, $\rho^A$ and $\rho^B$. The two reconstruction outcomes are returned once the total number of iterations is reached. The support function is periodically updated and refined, based on the current density estimate, completely independently between the two frames, as discussed in Sec. \ref{['sec:suppconstraint']}