Abstract
Single-shot x-ray imaging of short-lived nanostructures such as clusters and nanoparticles near a phase transition or non-crystalizing objects such as large proteins and viruses is currently the most elegant method for characterizing their structure. Using hard x-ray radiation provides scattering images that encode two-dimensional projections, which can be combined to identify the full three-dimensional object structure from multiple identical samples. Wide-angle scattering using XUV or soft x-rays, despite yielding lower resolution, provides three-dimensional structural information in a single shot and has opened routes towards the characterization of non-reproducible objects in the gas phase. The retrieval of the structural information contained in wide-angle scattering images is highly non-trivial, and currently no efficient rigorous algorithm is known. Here we show that deep learning networks, trained with simulated scattering data, allow for fast and accurate reconstruction of shape and orientation of nanoparticles from experimental images. The gain in speed compared to conventional retrieval techniques opens the route for automated structure reconstruction algorithms capable of real-time discrimination and pre-identification of nanostructures in scattering experiments with high repetition rate—thus representing the enabling technology for fast femtosecond nanocrystallography.
Highlights
Sources of soft and hard X-rays with large photon flux such as free electron lasers [1, 2] have enabled the high-resolution imaging of unsupported nanosystems such as viruses [3], helium droplets [4, 5, 6], rare-gas clusters [7], or metallic nanoparticles [8]
For the wavelength range for which wide-angle scattering is realized, the refractive index of most materials deviates substantially from unity, and multiple scattering, absorption, backpropagating waves, and refraction all have to be accounted for. All these constraints can only be met by solving the full three-dimensional scattering problem by, e.g., finite-difference timedomain (FDTD) methods, gridless discrete-dipole approximation (DDA) techniques, or appropriate approximate solutions based on multislice Fourier transform (MSFT) techniques [6, 12]
We have shown that, using a deep-learning technique based on augmented theoretical scattering data, neural networks enable the accurate and fast reconstruction of wide-angle scattering images of individual icosahedral nanostructures
Summary
Sources of soft and hard X-rays with large photon flux such as free electron lasers [1, 2] have enabled the high-resolution imaging of unsupported nanosystems such as viruses [3], helium droplets [4, 5, 6], rare-gas clusters [7], or metallic nanoparticles [8]. For the wavelength range for which wide-angle scattering is realized, the refractive index of most materials deviates substantially from unity, and multiple scattering, absorption, backpropagating waves, and refraction all have to be accounted for All these constraints can only be met by solving the full three-dimensional scattering problem by, e.g., finite-difference timedomain (FDTD) methods, gridless discrete-dipole approximation (DDA) techniques, or appropriate approximate solutions based on multislice Fourier transform (MSFT) techniques [6, 12]. The task of pre-classifying scattering patterns has been successfully tackled with neural networks [6], and reinforcement learning techniques have provided further insights into experimental features of X-ray scattering patterns [26] In these previous applications, the neural networks were either trained and tested solely on theoretical data or were used for feature extraction from experimental diffraction images. In our work we take the decisive step by training a neural network on augmented theoretical data and use it for predictions on experimental scattering data
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