Accurate, rapid identification of dislocation lines in coherent diffractive imaging via a min-max optimization formulation

Defects such as dislocations impact materials properties and their response during external stimuli. Defect engineering has emerged as a possible route to improving the performance of materials over a wide range of applications, including batteries, solar cells, and semiconductors. Imaging these defects in their native operating conditions to establish the structure-function relationship and, ultimately, to improve performance has remained a considerable challenge for both electron-based and x-ray-based imaging techniques. However, the advent of Bragg coherent x-ray diffractive imaging (BCDI) has made possible the 3D imaging of multiple dislocations in nanoparticles ranging in size from 100 nm to1000 nm. While the imaging process succeeds in many cases, nuances in identifying the dislocations has left manual identification as the preferred method. Derivative-based methods are also used, but they can be inaccurate and are computationally inefficient. Here we demonstrate a derivative-free method that is both more accurate and more computationally efficient than either derivative- or human-based methods for identifying 3D dislocation lines in nanocrystal images produced by BCDI. We formulate the problem as a min-max optimization problem and show exceptional accuracy for experimental images. We demonstrate a 260x speedup for a typical experimental dataset with higher accuracy over current methods. We discuss the possibility of using this algorithm as part of a sparsity-based phase retrieval process. We also provide the MATLAB code for use by other researchers

Localization, Stability, and Resolution of Topological Derivative Based Imaging Functionals in Elasticity

The focus of this work is on rigorous mathematical analysis of the topological derivative based detection algorithms for the localization of an elastic inclusion of vanishing characteristic size. A filtered quadratic misfit is considered and the performance of the topological derivative imaging functional resulting therefrom is analyzed. Our analysis reveals that the imaging functional may not attain its maximum at the location of the inclusion. Moreover, the resolution of the image is below the diffraction limit. Both phenomena are due to the coupling of pressure and shear waves propagating with different wave speeds and polarization directions. A novel imaging functional based on the weighted Helmholtz decomposition of the topological derivative is, therefore, introduced. It is thereby substantiated that the maximum of the imaging functional is attained at the location of the inclusion and the resolution is enhanced and it proves to be the diffraction limit. Finally, we investigate the stability of the proposed imaging functionals with respect to measurement and medium noises.Comment: 38 pages. A new subsection 6.4 is added where we consider the case of random Lam\'e coefficients. We thought this would corrupt the statistical stability of the imaging functional but our calculus shows that this is not the case as long as the random fluctuation is weak so that Born approximation is vali

Fast shape reconstruction of perfectly conducting cracks by using a multi-frequency topological derivative strategy

This paper concerns a fast, one-step iterative technique of imaging extended perfectly conducting cracks with Dirichlet boundary condition. In order to reconstruct the shape of cracks from scattered field data measured at the boundary, we introduce a topological derivative-based electromagnetic imaging function operated at several nonzero frequencies. The properties of the imaging function are carefully analyzed for the configurations of both symmetric and non-symmetric incident field directions. This analysis explains why the application of incident fields with symmetric direction operated at multiple frequencies guarantees a successful reconstruction. Various numerical simulations with noise-corrupted data are conducted to assess the performance, effectiveness, robustness, and limitations of the proposed technique.Comment: 17 pages, 27 figure

Dual-modal SERS/fluorescence AuNP probe for mitochondrial imaging

A novel SERS/fluorescent multimodal imaging probe for mitochondria has been synthesised using 12 nm diameter gold nanoparticles (AuNP) surface functionalised with a rhodamine thiol derivative ligand. The normal pH dependant acidic fluorescence of the rhodamine based ligand is inversed when conjugated with the AuNP and higher emission intensity is observed at basic pH. This switch correlates to a pKa at pH 6.62, which makes it an ideal candidate for a pH sensitive imaging probe in the biological range (6.5-7.4). The observed pH sensitivity when attached to the AuNP is thought to be due to the formation of a spirolactam ring on the ligand, going from positively charged (+18 mV) to negatively charged (-60 mV) as the pH is changed from acidic to basic. Additionally, conjugation of the ligand to the AuNP serves to enhance the Raman signal of the rhodamine ligand through Surface Enhanced Raman Scattering (SERS). Confocal microscopy has shown that the probe enters HEK293 (kidney), A2780 (ovarian cancer) and Min6 (pancreatic beta) cells within an hour and a half incubation time. The probe was shown to localise in the mitochondria, thus providing a novel pH dependent SERS/fluorescent multimodal imaging probe for mitochondria

Topological Derivative for Imaging of Thin Electromagnetic Inhomogeneity: Least Condition of Incident Directions

It is well-known that using topological derivative is an effective noniterative technique for imaging of crack-like electromagnetic inhomogeneity with small thickness when small number of incident directions are applied. However, there is no theoretical investigation about the configuration of the range of incident directions. In this paper, we carefully explore the mathematical structure of topological derivative imaging functional by establishing a relationship with an infinite series of Bessel functions of integer order of the first kind. Based on this, we identify the condition of the range of incident directions and it is highly depending on the shape of unknown defect. Results of numerical simulations with noisy data support our identification