Retrieving the displacement of strained nanoobjects: the impact of bounds for the scattering magnitude in direct space

Abstract

Coherent X-ray diffraction imaging (CXDI) of the displacement field and strain distribution of nanostructures in kinematic far-field conditions requires solving a set of non-linear and non-local equations. One approach to solving these equations, which utilizes only the object's geometry and the intensity distribution in the vicinity of a Bragg peak as a priori knowledge, is the HIO+ER-algorithm. Despite its success for a number of applications, reconstruction in the case of highly strained nanostructures is likely to fail. To overcome the algorithm's current limitations, we propose the HIO M O R +ER M -algorithm which allows taking advantage of additional a priori knowledge of the local scattering magnitude and remedies HIO+ER's stagnation by incorporation of randomized overrelaxation at the same time. This approach achieves significant improvements in CXDI data analysis at high strains and greatly reduces sensitivity to the reconstruction's initial guess. These benefits are demonstrated in a systematic numerical study for a periodic array of strained silicon nanowires. Finally, appropriate treatment of reciprocal space points below noise level is investigated.

Bragg–Laue X-ray dynamical diffraction on perfect and deformed lateral crystalline structures

“…Lateral structures are also often the objects of interest (see e.g. Cha et al, 2010;Kö hl et al, 2013;Yang et al, 2013) in applications of coherent diffraction imaging (CDI) [see a recent review of Bragg CDI by Vartanyants & Yefanov (2015) and references therein].…”

Perspectives and limitations of symmetric X-ray Bragg reflections for inspecting polytypism in nanowires

“…We do neither discuss the separation of the scattering from the nanowires and parasitic growth (Kö hl et al, 2015) nor data evaluation of single-nanowire X-ray measurements (Biermanns et al, 2009;Biermanns, 2012;Kö hl et al, 2012Kö hl et al, , 2013Minkevich et al, 2014;Rodriguez et al, 2013;Marchesini, 2007a,b;Adams et al, 2012;Chushkin & Zontone, 2013;Trahan & Hyland, 2013) in this manuscript.…”

Identifying Defects with Guided Algorithms in Bragg Coherent Diffractive Imaging

“…This procedure was improved upon recently by the utilization of guided algorithms 33 , 34 in which phase retrieval is performed a number of times and the results are combined before being used as the initial start for another set of iterations. Note that some past approaches have focused on modifying the algorithms themselves 35 , 36 while in guided algorithms the algorithm starting point is influenced but the algorithms are unmodified. Guided phase retrieval algorithms have produced consistent experimental results for dislocation imaging 17 , 19 , 26 , 27 .…”

“…The Sharp and Sharp norm promote anti-sparsity indirectly through amplitude uniformity. Finally, we note that the fitness metrics are only used to influence the initial starting point of the reconstruction algorithms and not the algorithms themselves, as in previous approaches 35 , 36 .…”