Impact of ultrafast electronic damage in single-particle x-ray imaging experiments

In single-particle coherent x-ray diffraction imaging experiments, performed at x-ray free-electron lasers (XFELs), samples are exposed to intense x-ray pulses to obtain single-shot diffraction patterns. The high intensity induces electronic dynamics on the femtosecond time scale in the system, which can reduce the contrast of the obtained diffraction patterns and adds an isotropic background. We quantify the degradation of the diffraction pattern from ultrafast electronic damage by performing simulations on a biological sample exposed to x-ray pulses with different parameters. We find that the contrast is substantially reduced and the background is considerably strong only if almost all electrons are removed from their parent atoms. This happens at fluences of at least one order of magnitude larger than provided at currently available XFEL sources.

Figure 1

Averaged two-dimensional diffraction patterns of the biological sample in logscale for an x-ray pulse of 5-fs FWHM and 3.1-keV photon energy. (a) Diffraction pattern of the neutral sample without electronic damage at a fluence of 10${}^{14}$ photons$/\mu$m${}^2$. [(b) and (c)] Diffraction patterns of the ionized sample at a fluence of 10${}^{14}$ photons$/\mu$m${}^2$ (b) and 10${}^{16}$ photons$/\mu$m${}^2$ (c). (d) Intensity profiles for (a)–(c) along the black lines. The intensities in (d) have been rescaled to be equal at $q=0$.

Figure 2

[(a) and (c)] Contrast $\zeta \left(q_{\text{max}}\right)$ and [(b) and (d)] relative background contribution $\Gamma \left(q_{\text{max}}\right)$ calculated at $q_{\text{max}}$ corresponding to a resolution of 5.2 Å at 3.1-keV photon energy [(a) and (b)] and a resolution of 0.95 Å at 12.4-keV photon energy [(c) and (d)]. The labels indicate the approximate fluences for the saturation of the ionization of the respective shells: $1s$ of neutral carbon, $2s$ of C${}^{2+}\left(1s^{0}2s^{2}2p^2\right)$, and $2p$ of C${}^{4+}\left(1s^{0}2s^{0}2p^2\right)$. The dashed line in all figures corresponds to a fluence of 10${}^{14}$ photons$/\mu$m${}^2$.

Figure 3

[(a) and (c)] Angular averaged scattered signal ${\langle I_{\text{W}}\left(\mathbf{q}\right)\rangle }_{\varphi }$ and [(b) and (d)] relative background contribution $\Gamma \left(q\right)$ for a 5-fs FWHM x-ray pulse at different fluences; [(a) and (b)] 3.1-keV [(c) and (d)] 12.4-keV photon energy. Dashed curves in (a) and (c) correspond to the intensity scattered by a sample without electronic damage. Thin dashed horizontal lines in (a) and (c) denote the cutoff of ${10}^{-2}$ photons per Shannon angle, and the labels denote the achievable resolution. The curves have been smoothed with a Gaussian filter to remove high-frequency oscillations from the speckle pattern.

Figure 4

Form factors of the respective shells of (a) carbon and (b) oxygen. Black line: $1s$ shell; red (dark gray) line: $2s$ shell; green (light gray) line: $2p$ shell. Solid lines refer to the neutral atom, and dashed lines are those of the hollow atom (i.e., without electrons in the $1s$ shell).