Data requirements for single-particle diffractive imaging

• Single-shot diffractive imaging with ultra-short and very intense coherent X-ray pulses has become a routine experimental technique at new free-electron-laser facilities. Extension to three-dimensional imaging requires many diffraction pat- terns from identical objects captured in different orientations. These can then be combined into a full three-dimensional Fourier transform of the object. The ori- entation of the particle intercepted by the pulsed X-ray beam is usually unknown. This makes it hard to predict the number of patterns required to fully cover the Fourier space. In this paper we provide formulae to estimate the number of expo- sures required to achieve a given coverage of Fourier space as a function of parti- cle size, resolution and shot noise. 

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