Abstract
In this paper is demonstrated a complete algorithm for determining the electron density of an individual particle from diffraction patterns of many particles, randomly oriented about a single axis. The algorithm operates on angular correlations among the measured intensity distributions. We also demonstrate the ability to recover the angular correlation functions of a single particle from measured diffraction patterns.
Highlights
The reconstruction of a high-resolution image of a single particle from scattering by several symmetrically equivalent ones has been demonstrated recently [1]
Demonstrated in this paper only for an artificial object of rectangular projection, these results suggest the possibility of deducing the diffraction pattern of a single particle from the angular correlations of a diffraction pattern from the scattering of radiation from multiple identical particles in random orientations
It should be possible to reconstruct an image of an individual particle via an iterative phasing algorithm applied to an oversampled reconstructed single-particle diffraction pattern
Summary
The reconstruction of a high-resolution image of a single particle from scattering by several symmetrically equivalent ones has been demonstrated recently [1]. If the scattered intensities from a single molecule could be measured at their (finer) Shannon angular sampling rate, the structure of the scatterer could be determined by iterative phasing algorithms [3] These advantages of signal amplification, damage reduction for high resolution, and access to oversampled intensities (allowing solution of the phase problem) may be combined if the structure of a single particle may be determined from diffraction patterns from many identical particles in random orientations. This is possible if scattering is recorded either from stationary particles or for a recording time less than the rotational diffusion time.
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