Iterative phase retrieval from kinematic rocking curves in CBED patterns

Towards a full retrieval of the deformation tensor F using convergent beam electron diffraction

“…each HOLZ line g has its own DS g that is determined on the reference pattern. This procedure is applied to all HOLZ lines in the transmitted beam and some (5)(6)(7)(8)(9)(10) in the diffracted beams. Firstly, a weight w g is calculated for each line g in the transmitted beam in order to give more or less power to the HOLZ lines…”

“…, and G Kin Δ ) are determined using the kinematical equations (5) and (6). Then by varying the nine components of F, the algorithm minimizes the distance between these calculated and 'experimental' variations; more precisely it is the dist(F) function that is minimized…”

“…Various methods to retrieve strain have been developed: based on the measurement of the distances between intersections of HOLZ lines [2], on the HOLZ line positions fitted using kinematical calculations including dynamical corrections [3], on the use of the Hough transform [4], or using K-line equations [5]. The broadening of HOLZ lines due to a non-uniform strain along the electron beam complicates CBED pattern analysis [6,7]. Several groups [8,9] have analyzed the line broadening using finite-element modeling.…”

Determination of a 3D Lattice Displacement Field by Iterative Phase Retrieval of Rocking Curves of HOLZ Reflections

“…This formula shows that [1]. In the present study, the z-dependence of the 3D lattice displacement field R(z) was determined by the Fourier iterative phase retrieval of rocking curve profiles of mutually independent reflections.…”

“…The Fourier iterative phase retrieval has been applied to reconstruct the phase of € φ g , and thus, phase factor € α = −2πig ⋅ R(z) with an real space constraint of A(z) [1]. In the present study, the z-dependence of the 3D lattice displacement field R(z) was determined by the Fourier iterative phase retrieval of rocking curve profiles of mutually independent reflections.…”