Phase retrieval of diffraction from highly strained crystals

Newton, Marcus C., Harder, Ross, Huang, Xiaojing, Xiong, Gang and Robinson, Ian K. (2010) Phase retrieval of diffraction from highly strained crystals. Physical Review B, 82 (16), 165436. (doi:10.1103/PhysRevB.82.165436).

Abstract

An important application of phase retrieval methods is to invert coherent x-ray diffraction measurements to obtain real-space images of nanoscale crystals. The phase information is currently recovered from reciprocal-space amplitude measurements by the application of iterative projective algorithms that solve the nonlinear and nonconvex optimization problem. Various algorithms have been developed each of which apply constraints in real and reciprocal space on the reconstructed object. In general, these methods rely on experimental data that is oversampled above the Nyquist frequency. To date, support-based methods have worked well, but are less successful for highly strained structures, defined as those which contain (real-space) phase information outside the range of ±?/2. As a direct result the acquired experimental data is, in general, inadvertently subsampled below the Nyquist frequency. In recent years, a new theory of “compressive sensing” has emerged, which dictates that an appropriately subsampled (or compressed) signal can be recovered exactly through iterative reconstruction and various routes to minimizing the ?1 norm or total variation in that signal. This has proven effective in solving several classes of convex optimization problems. Here we report on a “density-modification” phase reconstruction algorithm that applies the principles of compressive sensing to solve the nonconvex phase retrieval problem for highly strained crystalline materials. The application of a nonlinear operator in real-space minimizes the ?1 norm of the amplitude by a promotion-penalization (or “propenal”) operation that confines the density bandwidth. This was found to significantly aid in the reconstruction of highly strained nanocrystals. We show how this method is able to successfully reconstruct phase information that otherwise could not be recovered

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Contributors

Author: Marcus C. Newton

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