Imaging via Correlation of X-Ray Fluorescence Photons

We demonstrate that x-ray fluorescence emission, which cannot maintain a stationary interference pattern, can be used to obtain images of structures by recording photon-photon correlations in the manner of the stellar intensity interferometry of Hanbury Brown and Twiss. This is achieved utilizing femtosecond-duration pulses of a hard x-ray free-electron laser to generate the emission in exposures comparable to the coherence time of the fluorescence. Iterative phasing of the photon correlation map generated a model-free real-space image of the structure of the emitters. Since fluorescence can dominate coherent scattering, this may enable imaging uncrystallised macromolecules.

Figure 1

(a) Simplified sketch of the experimental setup. (b) Simulated intensity distribution in the focal plane with the phase grating. (c) Photon counts at the AGIPD, measured with the phase grating, averaged over 58 million patterns. This is a flat distribution without any apparent structural information. The mean photon count per pixel per frame was $⟨I⟩=0.0077$.

Figure 2

$g^{(2)}$ signal of Cu $\mathrm{K}\alpha$ fluorescence with the Cu foil located in the focal plane ($z=0$), without the phase grating. An offset of $1\times {10}^{-4}$ was added for the logarithmic representation. The rms width of a fitted Gaussian is marked, with ${\sigma }_1=(272\pm 17)\mathrm{nm}$ and ${\sigma }_2=(204\pm 13)\mathrm{nm}$. See Appendix B for details.

Figure 3

(a) Measured $g^{(2)}-1$ signal in logarithmic representation. (b) Cut through the $g^{(2)}-1$ signal along $q_{y^{\prime }}$ and integrated along $q_{x^{\prime }}$ within the boundaries indicated in (a). The distance between the boundaries was optimized to achieve maximum fringe visibility. (c) Reconstructed fluorescence emitter distribution at the Cu disk, to be compared with the simulation in Fig. 1.

Figure 4

Simulated $g^{(2)}-1$ signal for the intensity distribution displayed in Fig. 1 with an assumed visibility of $\beta =0.018$.

Figure 5

Inverse of the focal area $1/({\sigma }_1{\sigma }_2)$, and the fitted visibility $\beta$, versus defocus $z$. The data were measured during two different scans.