Single-particle incoherent diffractive imaging and amplified spontaneous emission in copper nanocubes

Abstract

We demonstrate element-specific incoherent diffractive imaging (IDI) of single copper nanocubes using intensity correlations of K$α$ fluorescence at a hard X-ray free-electron laser. Combining single particle diffraction classification with IDI, we retrieve the form factor of 88 nm cubes with 20 nm resolution, extending IDI to the destructive single-particle regime with a large gain in resolution. IDI visibility drops sharply above a fluence of $10^2$ J/cm$^2$, consistent with the assumption of amplified spontaneous emission. Our results reveal fundamental limits for high-fluence nanoimaging towards future single-particle X-ray imaging.

Figures (8)

• Figure 1: (a) Experimental schematic showing X-ray pulses incident on cubic copper oxide nanoparticles (not to scale) which were aerosolized and injected into the interaction region. A representative spectrum, which was measured for every pulse, is shown on the top left. The nickel foil filters the elastically scattered photons at high scattering angles, while letting the Cu-K$\alpha$ photons through. The coherent diffraction going through the Ni aperture was used for orientation determination and classification, while the fluorescence was studied in the filtered area of the detector. (b) Illustration of a region of the detector with individually measured photons. The wave-vector difference $\mathbf{q}$ as well as non-interfering photons are shown.
• Figure 2: Single particle coherent diffractive imaging analysis. The central region of detector frames (top left) were analyzed to detect those where a particle was hit by the XFEL. 2D classification was then performed on these hits to yield class average coherent intensities as well as estimates of the incident fluence and in-plane orientation for each frame.
• Figure 3: (a) Aligned $g^{(2)}(q_x, q_y)$ calculated from 1780 frames selected after 2D classification of the low-$q$ CDI signal. The single-frame $g^{(2)}(\mathbf{q})$ were rotated in-plane by the same amount required to align the CDI patterns. (b) Horizontal line profile $g^{(2)}(q_x, q_y=0)$ from (a), compared with the expected $|\mathcal{F}(\mathbf{q})|^2$ from an 88nm cube.
• Figure 4: (a) Visibility $\nu$ as a function of $\langle\mu\rangle$ for subsets of frames. The green line shows the expected visibility for 20 temporal modes with the experimental background level (dashed blue line). (b) Simulated intensity correlation, $g^{(2)}$ for the case where the random initial phases are partially dependent on the values of the neighbors with a correlation length, $\delta$. Uncorrelated initial phases ($\delta=0$) match well with the reference plot from the Siegert relation.
• Figure 5: Average second order correlation function $g^{(2)}(\Delta E)$. The full width at half maximum of the central feature is inversely proportional to the pulse duration.