A significant fraction of superfluid helium nanodroplets produced in a free-jet expansion has been observed to gain high angular momentum resulting in large centrifugal deformation. We measured single-shot diffraction patterns of individual rotating helium nanodroplets up to large scattering angles using intense extreme ultraviolet light pulses from the FERMI free-electron laser. Distinct asymmetric features in the wide-angle diffraction patterns enable the unique and systematic identification of the three-dimensional droplet shapes. The analysis of a large data set allows us to follow the evolution from axisymmetric oblate to triaxial prolate and two-lobed droplets. We find that the shapes of spinning superfluid helium droplets exhibit the same stages as classical rotating droplets while the previously reported metastable, oblate shapes of quantum droplets are not observed. Our three-dimensional analysis represents a valuable landmark for clarifying the interrelation between morphology and superfluidity on the nanometer scale.
Coherent diffractive imaging of individual free nanoparticles has opened routes for the in situ analysis of their transient structural, optical, and electronic properties. So far, single-shot single-particle diffraction was assumed to be feasible only at extreme ultraviolet and X-ray free-electron lasers, restricting this research field to large-scale facilities. Here we demonstrate single-shot imaging of isolated helium nanodroplets using extreme ultraviolet pulses from a femtosecond-laser-driven high harmonic source. We obtain bright wide-angle scattering patterns, that allow us to uniquely identify hitherto unresolved prolate shapes of superfluid helium droplets. Our results mark the advent of single-shot gas-phase nanoscopy with lab-based short-wavelength pulses and pave the way to ultrafast coherent diffractive imaging with phase-controlled multicolor fields and attosecond pulses.
Intense short-wavelength pulses from free-electron lasers and high-harmonic-generation sources enable diffractive imaging of individual nano-sized objects with a single x-ray laser shot. The enormous data sets with up to several million diffraction patterns represent a severe problem for data analysis, due to the high dimensionality of imaging data. Feature recognition and selection is a crucial step to reduce the dimensionality. Usually, custom-made algorithms are developed at a considerable effort to approximate the particular features connected to an individual specimen, but facing different experimental conditions, these approaches do not generalize well. On the other hand, deep neural networks are the principal instrument for today's revolution in automated image recognition, a development that has not been adapted to its full potential for data analysis in science. We recently published in [Langbehn et al. Phys. Rev. Lett. 121, 255301 (2018)] the first application of a deep neural network as a feature extractor for wide-angle diffraction images of helium nanodroplets. Here we present the setup, our modifications and the training process of the deep neural network for diffraction image classification and its systematic benchmarking. We find that deep neural networks significantly outperform previous attempts for sorting and classifying complex diffraction patterns and are a significant improvement for the much-needed assistance during postprocessing of large amounts of experimental coherent diffraction imaging data.
Single-shot coherent diffraction imaging (CDI) is a powerful approach to characterize the structure and dynamics of isolated nanoscale objects such as single viruses, aerosols, nanocrystals and droplets. Using X-ray wavelengths, the diffraction images in CDI experiments usually cover only small scattering angles of a few degrees. These small-angle patterns represent the magnitude of the Fourier transform of the 2D projection of the sample's electron density, which can be reconstructed efficiently but lacks any depth information. In cases where the diffracted signal can be measured up to scattering angles exceeding ∼10°, i.e. in the wide-angle regime, some 3D morphological information of the target is contained in a single-shot diffraction pattern. However, the extraction of the 3D structural information is no longer straightforward and defines the key challenge in wide-angle CDI. So far, the most convenient approach relies on iterative forward fitting of the scattering pattern using scattering simulations. Here the Scatman is presented, an approximate and fast numerical tool for the simulation and iterative fitting of wide-angle scattering images of isolated samples. Furthermore, the open-source software implementation of the Scatman algorithm, PyScatman, is published and described in detail. The Scatman approach, which has already been applied in previous work for forward-fitting-based shape retrieval, adopts the multi-slice Fourier transform method. The effects of optical properties are partially included, yielding quantitative results for small, isolated and weakly interacting samples. PyScatman is capable of computing wide-angle scattering patterns in a few milliseconds even on consumer-level computing hardware, potentially enabling new data analysis schemes for wide-angle coherent diffraction experiments.
Single-shot coherent diffraction imaging of isolated nanosized particles has seen remarkable success in recent years, yielding in-situ measurements with ultra-high spatial and temporal resolution. The progress of high-repetition-rate sources for intense X-ray pulses has further enabled recording datasets containing millions of diffraction images, which are needed for the structure determination of specimens with greater structural variety and dynamic experiments. The size of the datasets, however, represents a monumental problem for their analysis. Here, we present an automatized approach for finding semantic similarities in coherent diffraction images without relying on human expert labeling. By introducing the concept of projection learning, we extend self-supervised contrastive learning to the context of coherent diffraction imaging and achieve a dimensionality reduction producing semantically meaningful embeddings that align with physical intuition. The method yields substantial improvements compared to previous approaches, paving the way toward real-time and large-scale analysis of coherent diffraction experiments at X-ray free-electron lasers.
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