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Reconstruction algorithms for x-ray nanocrystallography via solution of the twinning problem


X-ray nanocrystallography is an emerging technique for imaging nanoscale objects that alleviates the large crystallization requirement of conventional crystallography by collecting diffraction patterns from a large ensemble of smaller and easier to build nanocrystals, which are typically delivered to the x-ray beam via a liquid jet. In order to determine the structure of an imaged object, several parameters must first be determined, including the crystal sizes, incident photon flux densities, and crystal orientations. Autoindexing techniques, which have been used extensively to orient conventional crystals, only determine the orientation of the nanocrystals up to symmetry of the crystal lattice, which is often greater than the symmetry of the diffraction information, resulting in what is known as the twinning problem. In addition, the image data is corrupted by large degrees of shot noise due to low collected signal, background signal due to the liquid jet and detector electronics, as well as other sources of noise. Furthermore, diffraction only measures the magnitudes of the Fourier transform of the object and, thus, one must recover phase information in order to invert the data and recover a three-dimensional reconstruction of the constituent molecular structure. Previous approaches for handling the twinning problem have mainly relied on having a known similar structure available, which may not be present for fundamentally new structures. We present a series of techniques to determine the crystal sizes, incident photon flux densities, and crystal orientations in the presence of large amounts of noise common in experiments. Additionally, by using a new sampling strategy, we demonstrate that phase information can be computed from nanocrystallographic diffraction images using only Fourier magnitude information, via a compressive phase retrieval algorithm. We demonstrate the feasibility of this new approach by testing it on simulated data with parameters and noise levels common in current experiments.

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