Imaging of highly inhomogeneous strain field in nanocrystals using x-ray Bragg ptychography: A numerical study

X-ray ptychography is a lensless microscopy method able to provide extended field of view with spatial resolution above the diffraction limit. A series of intensity coherent diffraction patterns measured in the far field is used to obtain the numerical deconvolution between the sample scattering contrast and the illumination function. The measurements are performed with a finite-size beam spot scanned across the sample. The scan step, smaller than the beam size, ensures a high redundancy in the data set, which allows for the convergence of the iterative inversion algorithm. This work explores the possibility to use ptychography for the investigation of strained crystals by means of coherent x-ray Bragg diffraction, taking advantage of the high sensitivity to the atomic displacement fields. The Bragg diffraction scattering contrast is described by an effective complex-valued electron density, where the phase holds the information on the displacement field. The detailed two-dimensional numerical study of Bragg ptychography is presented, both for the known and unknown illumination cases. It demonstrates the high robustness of the ptychographical iterative engine for highly nonhomogeneous strain fields. In particular, the local information is extracted from the individual diffraction patterns to calculate the modulus and phase estimates of the electron density, which are further used to constrain the newly derived algorithm. From this work, it is foreseen that Bragg ptychography when experimentally feasible, will open the way to the nondestructive imaging of strain fields at the nanoscale.