Fluorescence intensity correlations enable 3D imaging without sample rotations

TL;DR

The paper introduces incoherent diffractive imaging (IDI), a lensless 3D imaging approach that uses intensity correlations of X-ray fluorescence excited by ultrafast FEL pulses to retrieve the 3D structure of non-periodic samples without rotating them. By measuring the second-order correlation $g^{(2)}$ between fluorescence signals recorded across a detector and applying the Siegert relation, the authors access the Fourier magnitudes $| ilde{S}(\vec{q})|^2$ over a broad $\vec{q}$ range, enabling 3D tomography from stationary emitters. They experimentally demonstrate 16 distinct projections of a vanadium foil by translating the fluorescing volume through an astigmatic sub-200 nm FEL focus, using 5,000–10,000 exposures per position to map $g^{(2)}$ across detector tiles and reveal focal-spot geometry and astigmatism; pulse durations were estimated to be $2$–$3$ fs, with potential improvements from sub-fs pulses. IDI offers a practical route to combine 3D structural information with spectroscopic fingerprints without sample rotation, with implications for materials science, chemistry, and nanotechnology.

Abstract

Lensless X-ray imaging provides element-specific nanoscale insights into thick samples beyond the reach of conventional light and electron microscopy. Coherent diffraction imaging (CDI) methods, such as ptychographic tomography, can recover three-dimensional (3D) nanoscale structures but require extensive sample rotation, adding complexity to experiments. X-ray elastic-scattering patterns from a single sample orientation are highly directional and provide limited 3D information about the structure. In contrast to X-ray elastic scattering, X-ray fluorescence is emitted mostly isotropically. However, first-order spatial coherence has traditionally limited nanoscale fluorescence imaging to single-crystalline samples. Here, we demonstrate that intensity correlations of X-ray fluorescence excited by ultrashort X-ray pulses contain 3D structural information of non-periodic, stationary objects. In our experiment, we illuminated a vanadium foil within a sub-200 nm X-ray laser beam focus. Without changing the sample orientation, we recorded 16 distinct specimen projections using detector regions covering different photon incidence angles relative to the X-ray free-electron laser (FEL) beam. The projections varied systematically as the fluorescing volume was translated along an astigmatism, confirming that FEL-induced fluorescence reflects real-space structural changes. Our results establish a new approach for lensless 3D imaging of non-periodic specimens using fluorescence intensity correlations, with broad implications for materials science, chemistry, and nanotechnology.

Figures (6)

• Figure 1: Basic principle of incoherent diffractive imaging and its three-dimensional imaging capabilities. a An object $S(\vec{r})$ is illuminated by the FEL pulse and subsequently emits X-ray fluorescence. The fluorescence photons are recorded on a detector (here indicated by the light-gray curve). The second-order intensity correlation is calculated between different pixels on the detector corresponding to different wavevectors $\vec{k}_1,\vec{k}_2$ of the detected photons. b Due to the random phase relation between individual emitters, fluorescence produces speckle patterns. The structure factor of the emitting object $\left|\tilde{S}(\vec{q})\right|^2$ can be retrieved from these speckle patterns via the second-order intensity correlation $g^{(2)}(\vec{q})$. The retrieval of the structure factor $\left|\tilde{S}(\vec{q})\right|^2$ then allows the reconstruction via phase retrieval akin to the process in CDI. c Opposed to CDI, IDI is not restricted by the scattering signal at high angles, as fluorescence is emitted isotropically. Hence, IDI can record several projections of the sample simultaneously, while CDI is limited to a single projection per sample orientation.
• Figure 2: Description of the experimental setup and visualization of the focus astigmatism. a Schematic representation of the experimental setup at the CXI endstation at LCLS. The few-femtosecond X-ray pulses provided by LCLS were focused using CXI's KB mirror system to a sub-200 focus spot size. The 4$\;$µm thick vanadium foil was placed in the X-ray beam at varying distances from the focus spot. The emitted fluorescence was recorded on a Jungfrau 4M detector placed 50 downstream from the sample. b The focus spot has a different shape on the vanadium foil when the foil is shifted relative to the nominal focus position within an astigmatic focal volume. c The fluorescing volume appears as a long needle from the perspective of the detector. Regions close to the center of the detector see a mostly two-dimensional Gaussian spot as the needle is viewed point-on. Regions closer to the edge of the detector see a more elongated volume because the needle is viewed from the side.
• Figure 3: Experimental results of the $g^{(2)}$ measurement. a Resulting $g^{(2)}$ with the vanadium foil at the nominal focus position. Every Jungfrau 4M detector tile has a different perspective on the fluorescing volume. b Schematic representation of the different perspectives onto the fluorescing needle as seen by the different detector tiles. c Fitted focal spot size at different foil positions along the beam axis with a guide to the eye (blue lines). The insets at the top show the measured $g^{(2)}$ at respective foil positions. The tile chosen for the fitting procedure was the upper-left center tile in \ref{['fig:results']} (a), which is the closest to the point-on perspective. d Simulated cross section of an astigmatic Gaussian beam at positions similar to those in the experiment. The orange arrows represent the tilt of the major axes of the ellipses.
• Figure 4: Comparison between the measured and simulated $g^{(2)}$ from the fluorescing foil volume at the nominal focus and 250 upstream and downstream from the focus. a A sketch of the fluorescing volume at the respective foil position shifted along the astigmatism of the FEL. b Measured $g^{(2)}$ upstream (left), downstream (right) of the nominal position and at the nominal focus (center). c Simulated $g^{(2)}$ at the same conditions as in the experiment displayed in (b). The simulation closely reproduces the experimental data, especially in the shape and defocusing effect along the astigmatism.
• Figure 5: Histogram of the detected photon energies over 24000 shots. The black lines mark the energies of one (dashed) and two (dash-dot) detected vanadium $\text{K}_\alpha$ photons at 4.95. The red line marks the energy of potential elastically scattered photons at 10.48. No significant number of elastically scattered photons is observed.