3D strain imaging in sub-micrometer crystals using cross-reciprocal space measurements: Numerical feasibility and experimental methodology

Direct inversion of coherent X-ray diffraction patterns is a powerful method to image strains in individual crystals with a high spatial resolution, less than 10 nm. The possibility to invert the diffraction pattern is in principle ensured by the oversampling of the measurement. In addition, the resolution of the reconstructed object requires the measurement of the intensity distribution as far as possible in reciprocal space. Thus, fulfilling the oversampling and resolution constraints, in 3D, implies very long acquisition times, hardly compatible with the stability of the X-ray synchrotron source or sample. To overcome this problem, we present a method based on partial crossed intensity measurements: it consists in two irregularly spaced intensity measurements taken in two orthogonal directions. This paper demonstrates that partial crossed intensity measurements are in principle sufficient to reconstruct 2D objects using a phase retrieval algorithm. We also describe how such measurements can be achieved in practice for 3D imaging. 3D intensity measurements taken in two orthogonal directions for a 111 Bragg peak of a sub-micrometer Au grain are shown.