Complex imaging of phase domains by deep neural networks

Single-particle imaging by using coherent X-ray diffraction was proposed more than a decade ago by the work of Fienup (1978), Miao et al. (1999), Robinson et al. (2001), Chao et al. (2005) and Sakdinawat & Attwood (2010). As a method of determining the inside complex structure of an individual particle, it records the diffracted coherent X-ray intensity by the particle in reciprocal space, where the phase information of the corresponding intensity is lost during the measurement (Williams et al., 2003; Chapman et al., 2006; Pfeifer et al., 2006). To provide this missing phase, one crucial step in an X-ray single-particle-imaging experiment, either by forward-scattering X-ray coherent diffraction imaging (Xu et al., 2014) or Bragg coherent diffraction imaging (BCDI) (Newton et al., 2010; Yang et al., 2013), is the reconstruction of the real-space complex information of the particle from its measured X-ray diffraction-pattern intensity. Because of the loss of the phase information of the recorded X-ray intensity, iterative phase-retrieval algorithms are widely applied to reconstruct the complex structure information of the measured particle. As shown originally by Bates (1982), this process, known as phase retrieval, depends on the diffraction data being oversampled by at least a factor of two with respect to the Shannon–Nyquist frequency.