Phase retrieval in highly strained crystals

One of the hottest topics in X-ray structural analysis is coherent X-ray diffraction measurement to obtain real-space images of nanoscale crystals. The key here is the method of phase retrieval. Until now, iterative projective algorithms have been frequently employed to recover the phase information from the amplitude measured in reciprocal space. The analysis relies on experimental data to be oversampled, and there have been difficulties in the case of highly strained structures, where information is below the Nyquist frequency. A research team led by Professor I. K. Robinson (University College London, UK) has recently reported a new method, called a density modification phase reconstruction algorithm, to solve this problem. This is a successful extension of the recent compressive sensing theory and works well in solving the nonconvex phase retrieval problem for highly strained crystalline materials. For more information, see the paper, "Phase retrieval of diffraction from highly strained crystals", M. C. Newton et al., Phys. Rev. B 82, 165436 (2010).