Structure Determination from Single Molecule Ultrafast X-Ray Scattering using Three Photons per Image
Financial Support: Federal Ministry of Education and Research through the joint research project 05K20EGA Fluctuation XFEL, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - CRC 1456/1 - 432680300 Mathematics of Experiments
The main challenges of single molecule scattering experiments are the unknown random orientation of the molecule in each shot and the extremely low signal to noise ratio due to the very low expected photon count per scattering image, typically well below the number of over 100 photons required by available analysis methods. Photon correlations are a summary statistic of the scattering images that can be collected from few photons without the need to determine the corresponding molecular orientations of each image.
We have developed a correlation-based approach that can determine the molecular structure de novo from as few as three coherently scattered photons per image. The method expresses Fourier intensities with spherical harmonics expansion that facilitate the analytic calculation of the three-photon correlations.
A Monte Carlo simulated annealing approach is used to solve the inverse problem of finding an intensity that fits the experimentally observed triple correlations. The size of the search space is reduced by using information from the analytic inversion of the two-photon correlation and the electron density is retrieved by applying an iterative phase retrieval method to the determined intensity.