Incoherent Diffractive Imaging via Intensity Correlations of Hard X Rays

Nanoscale x-ray imaging with high spectral sensitivity using fluorescence intensity correlations

This paper introduces spectral incoherent diffractive imaging (SIDI) as a novel method for achieving dark-field imaging of nanostructures with heterogeneous oxidation states. With SIDI, shifts in photoemission profiles can be spatially resolved, enabling the independent imaging of the underlying emitter distributions contributing to each spectral line. In the x-ray domain, this approach offers unique insights beyond the conventional combination of diffraction and x-ray emission spectroscopy. When applied at x-ray free-electron lasers, SIDI promises to be a versatile tool for investigating a broad range of systems, offering unprecedented opportunities for detailed characterization of heterogeneous nanostructures for catalysis and energy storage, including of their ultrafast dynamics.

Ab initio spatial phase retrieval via intensity triple correlations

Second-order intensity correlations from incoherent emitters can reveal the Fourier transform modulus of their spatial distribution, but retrieving the phase to enable completely general Fourier inversion to real space remains challenging. Phase retrieval via the third-order intensity correlations has relied on special emitter configurations which simplified an unaddressed sign problem in the computation. Without a complete treatment of this sign problem, the general case of retrieving the Fourier phase from a truly arbitrary configuration of emitters is not possible. In this paper, a general method for ab initio phase retrieval via the intensity triple correlations is described. Simulations demonstrate accurate phase retrieval for clusters of incoherent emitters which could be applied to imaging stars or fluorescent atoms and molecules. With this work, it is now finally tractable to perform Fourier inversion directly and reconstruct images of arbitrary arrays of independent emitters via far-field intensity correlations alone.

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.

Single-shot generalized Hanbury Brown-Twiss experiments using a polarization camera for target intensity reconstruction in scattering media

To see through a random light field in real-time, single-shot generalized Hanbury Brown-Twiss experiments using a polarization camera are proposed. The target intensity distribution is obtained from a complex coherence function which is calculated from auto-correlation and cross correlation functions of phase-shifted speckle intensity distributions. The phase-shifted speckle intensity distributions are simultaneously obtained through a strategy of parallel phase-shifting digital holography. Experimental results show that the proposed method can image a moving object in a random light field using a measured complex coherence function through the van Cittert-Zernike theorem.

Speckle contrast of interfering fluorescence X-rays

With the development of X-ray free-electron lasers (XFELs), producing pulses of femtosecond durations comparable with the coherence times of X-ray fluorescence, it has become possible to observe intensity-intensity correlations due to the interference of emission from independent atoms. This has been used to compare durations of X-ray pulses and to measure the size of a focusedX-ray beam, for example. Here it is shown that it is also possible to observe the interference of fluorescence photons through the measurement of the speckle contrast of angle-resolved fluorescence patterns. Speckle contrast is often used as a measure of the degree of coherence of the incident beam or the fluctuations of the illuminated sample as determined from X-ray diffraction patterns formed by elastic scattering, rather than from fluorescence patterns as addressed here. Commonly used approaches to estimate speckle contrast were found to suffer when applied to XFEL-generated fluorescence patterns due to low photon counts and a significant variation of the excitation pulse energy from shot to shot. A new method to reliably estimate speckle contrast under such conditions, using a weighting scheme, is introduced. The method is demonstrated by comparing the speckle contrast of fluorescence observed with pulses of 3 fs to 15 fs duration.

Decreasing ultrafast x-ray pulse durations with saturable absorption and resonant transitions

Saturable absorption is a nonlinear effect where a material's ability to absorb light is frustrated due to a high influx of photons and the creation of electron vacancies. Experimentally induced saturable absorption in copper revealed a reduction in the temporal duration of transmitted x-ray laser pulses, but a detailed account of changes in opacity and emergence of resonances is still missing. In this computational work, we employ nonlocal thermodynamic equilibrium plasma simulations to study the interaction of femtosecond x rays and copper. Following the onset of frustrated absorption, we find that a K-M resonant transition occurring at highly charged states turns copper opaque again. The changes in absorption generate a transient transparent window responsible for the shortened transmission signal. We also propose using fluorescence induced by the incident beam as an alternative source to achieve shorter x-ray pulses. Intense femtosecond x rays are valuable to probe the structure and dynamics of biological samples or to reach extreme states of matter. Shortened pulses could be relevant for emerging imaging techniques.

Numerical Simulation of Heat Load for Multilayer Laue Lens under Exposure to XFEL Pulse Trains

Multilayer Laue lenses (MLLs) made from WC and SiC were previously used to focus megahertz X-ray pulse trains of the European XFEL free-electron laser, but suffered damage with trains of 30 pulses or longer at an incident fluence of about 0.13 J/cm2 per pulse. Here, we present numerical simulations of the heating of MLLs of various designs, geometry and material properties, that are exposed to such pulse trains. We find that it should be possible to focus the full beam of about 10 J/cm2 fluence of XFEL using materials of a low atomic number. To achieve high diffraction efficiency, lenses made from such materials should be considerably thicker than those used in the experiments. In addition to the lower absorption, this leads to the deposition of energy over a larger volume of the multilayer structure and hence to a lower dose, a lower temperature increase, and an improved dissipation of heat.

Non-Poissonian Ultrashort Nanoscale Electron Pulses

The statistical character of electron beams used in current technologies, as described by a stream of particles, is random in nature. Using coincidence measurements of femtosecond pulsed electron pairs, we report the observation of sub-Poissonian electron statistics that are nonrandom due to two-electron Coulomb interactions, and that exhibit an antibunching signal of 1 part in 4. This advancement is a fundamental step toward observing a strongly quantum degenerate electron beam needed for many applications, and in particular electron correlation spectroscopy.

On incoherent diffractive imaging

Incoherent diffractive imaging (IDI) promises structural analysis with atomic resolution based on intensity interferometry of pulsed X-ray fluorescence emission. However, its experimental realization is still pending and a comprehensive theory of contrast formation has not been established to date. Explicit expressions are derived for the equal-pulse two-point intensity correlations, as the principal measured quantity of IDI, with full control of the prefactors, based on a simple model of stochastic fluorescence emission. The model considers the photon detection statistics, the finite temporal coherence of the individual emissions, as well as the geometry of the scattering volume. The implications are interpreted in view of the most relevant quantities, including the fluorescence lifetime, the excitation pulse, as well as the extent of the scattering volume and pixel size. Importantly, the spatiotemporal overlap between any two emissions in the sample can be identified as a crucial factor limiting the contrast and its dependency on the sample size can be derived. The paper gives rigorous estimates for the optimum sample size, the maximum photon yield and the expected signal-to-noise ratio under optimal conditions. Based on these estimates, the feasibility of IDI experiments for plausible experimental parameters is discussed. It is shown in particular that the mean number of photons per detector pixel which can be achieved with X-ray fluorescence is severely limited and as a consequence imposes restrictive constraints on possible applications.

Fluorescence intensity correlation imaging with high spatial resolution and elemental contrast using intense x-ray pulses

We theoretically investigate the fluorescence intensity correlation (FIC) of Ar clusters and Mo-doped iron oxide nanoparticles subjected to intense, femtosecond, and sub-femtosecond x-ray free-electron laser pulses for high-resolution and elemental contrast imaging. We present the FIC of K α and K α h emission in Ar clusters and discuss the impact of sample damage on retrieving high-resolution structural information and compare the obtained structural information with those from the coherent diffractive imaging (CDI) approach. We found that, while sub-femtosecond pulses will substantially benefit the CDI approach, few-femtosecond pulses may be sufficient for achieving high-resolution information with the FIC. Furthermore, we show that the fluorescence intensity correlation computed from the fluorescence of the Mo atoms in Mo-doped iron oxide nanoparticles can be used to image dopant distributions in the nonresonant regime.

Imaging Trapped Ion Structures via Fluorescence Cross-Correlation Detection

Cross-correlation signals are recorded from fluorescence photons scattered in free space off a trapped ion structure. The analysis of the signal allows for unambiguously revealing the spatial frequency, thus the distance, as well as the spatial alignment of the ions. For the case of two ions we obtain from the cross-correlations a spatial frequency f_{spatial}=1490±2_{stat}±8_{syst}  rad^{-1}, where the statistical uncertainty improves with the integrated number of correlation events as N^{-0.51±0.06}. We independently determine the spatial frequency to be 1494±11  rad^{-1}, proving excellent agreement. Expanding our method to the case of three ions, we demonstrate its functionality for two-dimensional arrays of emitters of indistinguishable photons, serving as a model system to yield structural information where direct imaging techniques fail.

Light of Two Atoms in Free Space: Bunching or Antibunching?

Photon statistics divides light sources into three different categories, characterized by bunched, antibunched, or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record spatially resolved the autocorrelation function g^{(2)}(τ) with a movable Hanbury Brown and Twiss detector. Varying the detector position we find a minimum value for antibunching, g^{(2)}(0)=0.60(5) and a maximum of g^{(2)}(0)=1.46(8) for bunching, demonstrating that this source radiates fundamentally different types of light alike. The observed variation of the autocorrelation function is understood in the Dicke model from which the observed maximum and minimum values can be modeled, taking independently measured experimental parameters into account.

Determination of X-ray pulse duration via intensity correlation measurements of X-ray fluorescence

A simple method using X-ray fluorescence is proposed to diagnose the duration of an X-ray free-electron laser (XFEL) pulse. This work shows that the degree of intensity correlation of the X-ray fluorescence generated by irradiating an XFEL pulse on metal foil reflects the magnitude relation between the XFEL duration and the coherence time of the fluorescence. Through intensity correlation measurements of copper Kα fluorescence, the duration of 12 keV XFEL pulses from SACLA was evaluated to be ∼10 fs.

X-Ray Free-Electron Lasers for the Structure and Dynamics of Macromolecules

X-ray free-electron lasers provide femtosecond-duration pulses of hard X-rays with a peak brightness approximately one billion times greater than is available at synchrotron radiation facilities. One motivation for the development of such X-ray sources was the proposal to obtain structures of macromolecules, macromolecular complexes, and virus particles, without the need for crystallization, through diffraction measurements of single noncrystalline objects. Initial explorations of this idea and of outrunning radiation damage with femtosecond pulses led to the development of serial crystallography and the ability to obtain high-resolution structures of small crystals without the need for cryogenic cooling. This technique allows the understanding of conformational dynamics and enzymatics and the resolution of intermediate states in reactions over timescales of 100 fs to minutes. The promise of more photons per atom recorded in a diffraction pattern than electrons per atom contributing to an electron micrograph may enable diffraction measurements of single molecules, although challenges remain.

Rayleigh-scattering microscopy for tracking and sizing nanoparticles in focused aerosol beams

Ultra-bright femtosecond X-ray pulses generated by X-ray free-electron lasers (XFELs) can be used to image high-resolution structures without the need for crystallization. For this approach, aerosol injection has been a successful method to deliver 70-2000 nm particles into the XFEL beam efficiently and at low noise. Improving the technique of aerosol sample delivery and extending it to single proteins necessitates quantitative aerosol diagnostics. Here a lab-based technique is introduced for Rayleigh-scattering microscopy allowing us to track and size aerosolized particles down to 40 nm in diameter as they exit the injector. This technique was used to characterize the 'Uppsala injector', which is a pioneering and frequently used aerosol sample injector for XFEL single-particle imaging. The particle-beam focus, particle velocities, particle density and injection yield were measured at different operating conditions. It is also shown how high particle densities and good injection yields can be reached for large particles (100-500 nm). It is found that with decreasing particle size, particle densities and injection yields deteriorate, indicating the need for different injection strategies to extend XFEL imaging to smaller targets, such as single proteins. This work demonstrates the power of Rayleigh-scattering microscopy for studying focused aerosol beams quantitatively. It lays the foundation for lab-based injector development and online injection diagnostics for XFEL research. In the future, the technique may also find application in other fields that employ focused aerosol beams, such as mass spectrometry, particle deposition, fuel injection and three-dimensional printing techniques.

Simulating the photon stream of a real thermal light source

We present a computer algorithm capable of simulating the photon stream and the corresponding temporal photon statistics of thermal light sources. The algorithm implements realistic experimental conditions, incorporating the relevant parameters of the source as well as of the detection process. The code is verified by comparing the temporal photon autocorrelation function computed from the simulations to the one measured with a real thermal light source. In view of the renewed interest for intensity interferometry in astronomy and the life sciences, such simulations become increasingly relevant.

Ptychographical intensity interferometry imaging with incoherent light

Intensity interferometry (II), the landmark of the second-order correlation, enables very long baseline observations at optical wavelengths, providing imaging with microarcsecond resolution. However, the unreliability of traditional phase retrieval algorithms required to reconstruct images in II has hindered its development. We here develop a method that circumvents this challenge, which enables II to reliably image complex shaped objects. Instead of measuring the whole object, we measure it part by part with a probe moving in a ptychographic way: adjacent parts overlap with each other. A relevant algorithm is developed to reliably and rapidly recover the object in a few iterations. Moreover, we propose an approach to remove the requirement for a precise knowledge of the probe, providing an error-tolerance of more than 50% for the location of the probe in our experiments. Furthermore, we extend II to short distance scenarios, providing a lensless imaging method with incoherent light and paving a way towards applications in X-ray imaging.

DNA-based construction at the nanoscale: emerging trends and applications

The field of structural DNA nanotechnology has evolved remarkably-from the creation of artificial immobile junctions to the recent DNA-protein hybrid nanoscale shapes-in a span of about 35 years. It is now possible to create complex DNA-based nanoscale shapes and large hierarchical assemblies with greater stability and predictability, thanks to the development of computational tools and advances in experimental techniques. Although it started with the original goal of DNA-assisted structure determination of difficult-to-crystallize molecules, DNA nanotechnology has found its applications in a myriad of fields. In this review, we cover some of the basic and emerging assembly principles: hybridization, base stacking/shape complementarity, and protein-mediated formation of nanoscale structures. We also review various applications of DNA nanostructures, with special emphasis on some of the biophysical applications that have been reported in recent years. In the outlook, we discuss further improvements in the assembly of such structures, and explore possible future applications involving super-resolved fluorescence, single-particle cryo-electron (cryo-EM) and x-ray free electron laser (XFEL) nanoscopic imaging techniques, and in creating new synergistic designer materials.

Diffraction based Hanbury Brown and Twiss interferometry at a hard x-ray free-electron laser

X-ray free-electron lasers (XFELs) provide extremely bright and highly spatially coherent x-ray radiation with femtosecond pulse duration. Currently, they are widely used in biology and material science. Knowledge of the XFEL statistical properties during an experiment may be vitally important for the accurate interpretation of the results. Here, for the first time, we demonstrate Hanbury Brown and Twiss (HBT) interferometry performed in diffraction mode at an XFEL source. It allowed us to determine the XFEL statistical properties directly from the Bragg peaks originating from colloidal crystals. This approach is different from the traditional one when HBT interferometry is performed in the direct beam without a sample. Our analysis has demonstrated nearly full (80%) global spatial coherence of the XFEL pulses and an average pulse duration on the order of ten femtoseconds for the monochromatized beam, which is significantly shorter than expected from the electron bunch measurements.