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Deep neural networks for classifying complex features in diffraction images
Intense short-wavelength pulses from free-electron lasers and high-harmonic-generation sources enable diffractive imaging of individual nanosized objects with a single x-ray laser shot. The enormous data sets with up to several million diffraction patterns present a severe problem for data analysis because of 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 because they face 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 [Langbehn et al., Phys. Rev. Lett. 121, 255301 (2018)] the 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 bench marking. 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.
Application of Matched-Filter Concepts to Unbiased Selection of Data in Pump-Probe Experiments with Free Electron Lasers
Pump-probe experiments are commonly used at Free Electron Lasers (FEL) to elucidate the femtosecond dynamics of atoms, molecules, clusters, liquids and solids. Maximizing the signal-to-noise ratio of the measurements is often a primary need of the experiment, and the aggregation of repeated, rapid, scans of the pump-probe delay is preferable to a single long-lasting scan. The limited availability of beamtime makes it impractical to repeat measurements indiscriminately, and the large, rapid flow of single-shot data that need to be processed and aggregated into a dataset, makes it difficult to assess the quality of a measurement in real time. In post-analysis it is then necessary to devise unbiased criteria to select or reject datasets, and to assign the weight with which they enter the analysis. One such case was the measurement of the lifetime of Intermolecular Coulombic Decay in the weakly-bound neon dimer. We report on the method we used to accomplish this goal for the pump-probe delay scans that constitute the core of the measurement; namely we report on the use of simple auto- and cross-correlation techniques based on the general concept of “matched filter”. We are able to unambiguously assess the signal-to-noise ratio (SNR) of each scan, which then becomes the weight with which a scan enters the average of multiple scans. We also observe a clear gap in the values of SNR, and we discard all the scans below a SNR of 0.45. We are able to generate an average delay scan profile, suitable for further analysis: in our previous work we used it for comparison with theory. Here we argue that the method is sufficiently simple and devoid of human action to be applicable not only in post-analysis, but also for the real-time assessment of the quality of a dataset.
Three-Dimensional Shapes of Spinning Helium Nanodroplets
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.