Classification of continuous diffraction patterns: a numerical study

The very intense and short pulses of future X-ray free electron lasers may allow the atomic resolution imaging of small, non-periodic objects. Preliminary estimates show that images obtained from single pulses do not contain statistically enough photons to allow successful reconstruction. Therefore multiple exposures of randomly oriented identical replicas have to be taken and the individual images have to be classified according to the object's orientation. The classification has been analytically treated by Huldt et al. [Huldt, G., Szoke, A., Hajdu, J., 2003. J. Struct. Biol. 144, 219.]. In this paper we extend the analytical results with numerical model calculations. This allows us to simulate realistic situations, which we will face in real experiments. We find significant deviations from the analytical expectations, even in the ideal case of spherical particles with random atomic distributions. We introduce a new norm for the individual scattering patterns and describe a criterion to select images belonging to similar orientation, which makes the classification more reliable in practice. We also discuss the effects of particle shape and size, partial orientational ordering, the measurement's resolution and the charge error caused by the Coulomb explosion.