2019, Zimmermann, Julian, Langbehn, Bruno, Cucini, Riccardo, Di Fraia, Michele, Finetti, Paola, LaForge, Aaron C., Nishiyama, Toshiyuki, Ovcharenko, Yevheniy, Piseri, Paolo, Plekan, Oksana, Prince, Kevin C., Stienkemeier, Frank, Ueda, Kiyoshi, Callegari, Carlo, Möller, Thomas, Rupp, Daniela

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.

2018, Langbehn, Bruno, Sander, Katharina, Ovcharenko, Yevheniy, Peltz, Christian, Clark, Andrew, Coreno, Marcello, Cucini, Riccardo, Drabbels, Marcel, Finetti, Paola, Di Fraia, Michele, Giannessi, Luca, Grazioli, Cesare, Iablonskyi, Denys, LaForge, Aaron C., Nishiyama, Toshiyuki, Oliver Álvarez de Lara, Verónica, Piseri, Paolo, Plekan, Oksana, Ueda, Kiyoshi, Zimmermann, Julian, Prince, Kevin C., Stienkemeier, Frank, Callegari, Carlo, Fennel, Thomas, Rupp, Daniela, Möller, Thomas

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.