  Single particle imaging (SPI) at X-ray free electron lasers (XFELs) is a
technique to determine the 3D structure of nanoscale objects like biomolecules
from a large number of diffraction patterns of copies of these objects in
random orientations. Millions of low signal-to-noise diffraction patterns with
unknown orientation are collected during an X-ray SPI experiment. The patterns
are then analyzed and merged using a reconstruction algorithm to retrieve the
full 3D-structure of particle. The resolution of reconstruction is limited by
background noise, signal-to-noise ratio in diffraction patterns and total
amount of data collected. We recently introduced a reference-enhanced
holographic single particle imaging methodology [Optica 7,593-601(2020)] to
collect high enough signal-to-noise and background tolerant patterns and a
reconstruction algorithm to recover missing parameters beyond orientation and
then directly retrieve the full Fourier model of the sample of interest. Here
we describe a phase retrieval algorithm based on maximum likelihood estimation
using pattern search dubbed as MaxLP, with better scalability for fine sampling
of latent parameters and much better performance in the low signal limit.
Furthermore, we show that structural variations within the target particle are
averaged in real space, significantly improving robustness to conformational
heterogeneity in comparison to conventional SPI. With these computational
improvements, we believe reference-enhanced SPI is capable of reaching sub-nm
resolution biomolecule imaging.
