Experimental 3D coherent diffractive imaging from photon-sparse random projections

Abstract

The routine atomic resolution structure determination of single particles is expected to have profound implications for probing structure–function relationships in systems ranging from energy-storage materials to biological molecules. Extremely bright ultrashort-pulse X-ray sources – X-ray free-electron lasers (XFELs) – provide X-rays that can be used to probe ensembles of nearly identical nanoscale particles. When combined with coherent diffractive imaging, these objects can be imaged; however, as the resolution of the images approaches the atomic scale, the measured data are increasingly difficult to obtain and, during an X-ray pulse, the number of photons incident on the 2D detector is much smaller than the number of pixels. This latter concern, the signal `sparsity', materially impedes the application of the method. An experimental analog using a conventional X-ray source is demonstrated and yields signal levels comparable with those expected from single biomolecules illuminated by focused XFEL pulses. The analog experiment provides an invaluable cross check on the fidelity of the reconstructed data that is not available during XFEL experiments. Using these experimental data, it is established that a sparsity of order 1.3 × 10−3 photons per pixel per frame can be overcome, lending vital insight to the solution of the atomic resolution XFEL single-particle imaging problem by experimentally demonstrating 3D coherent diffractive imaging from photon-sparse random projections.

3D diffractive imaging of nanoparticle ensembles using an x-ray laser

“…Each of these intensities represent an average of aligned copies of a subset of the patterns from the whole set. In addition to the EMC algorithm being highly noise-tolerant [7,29,30], one can also use it to examine the average models to understand what type of particles are in the dataset.…”

Reference-enhanced x-ray single-particle imaging

“…Simulations have been performed to illustrate the data produced and to demonstrate the reconstruction algorithm. For simplicity, a 2D toy model has been used which is rotated in-plane, similar to previous experiments to test the performance of the EMC algorithm with sparse data [4,28]. There is one parameter for the angle and two for the shift, but the qualitative structure of the problem remains the same.…”

“…Challenges still remain in collecting sufficient number of high quality diffraction patterns, where high quality refers to diffraction patterns with low background and high signal, enough to enable the orientation determination and merging of individual patterns into a 3D structure. Various studies have been performed on the minimum quality of patterns that are still tolerable [2][3][4][5], and they conclude that single proteins can be imaged with currently available XFEL sources as long as the background scattering is significantly less than the scattered signal from the particle and that 10 5 − 10 6 patterns from identical objects can be collected. Most experimental work [6][7][8] has been focussed on method development on much larger particles which scatter enough to be comfortably over the theoretical bounds.…”

Determination of the Structure of Biological Macromolecular Particles Using X-Ray Lasers. Achievements and Prospects

“…Перед тем, как применить метод главных компонент, было произведено сжатие данных. В недавней работе [127] было показано, что размытость (слабость) сигнала сама по себе не является проблемой. Видимо, основной проблемой является все же наличие изменяющегося шума.…”

“…В численных экспериментах, используя смоделированные данные, было показанo, что при современных параметрах лазеров на свободных электронах решение структур изолированных частиц является осуществимой задачей [159]. Кроме того, имеются и экспериментальные работы, проведенные на синхротронах, в которых была воссоздана геометрия эксперимента, соответствующая лазерам на свободных электронах, и было продемонстрировано, что даже несмотря на слабость и размазанность сигнала на детекторе, реконструкция трехмерного объекта вполне возможна [127]. Однако, в условиях реального эксперимента с единичными биологическими частицами появляется целый ряд факторов, сильно усложняющих эту задачу.…”