arXiv subjects

Christoph T. Koch

Publications and source records attributed to Christoph T. Koch.

22 records · Page 2Linked to original sources

arXiv2019

Various Compressed Sensing Set-Ups Evaluated Against Shannon Sampling Under Constraint of Constant Illumination

Under the constraint of constant illumination, an information criterion is formulated for the Fisher information that compressed sensing measurements in optical and transmission electron microscopy contain about the underlying parameters. Since this approach requires prior knowledge of the signal's support in the sparse basis, we develop a heuristic quantity, the detective quantum efficiency (DQE), that tracks this information criterion well without this knowledge. It is shown that for the investigated choice of sensing matrices, and in the absence of read-out noise, i.e. with only Poisson noise present, compressed sensing does not raise the amount of Fisher information in the recordings above that of Shannon sampling. Furthermore, enabled by the DQE's analytical tractability, the experimental designs are optimized by finding out the optimal fraction of on-pixels as a function of dose and read-out noise. Finally, we introduce a regularization and demonstrate, through simulations and experiment, that it yields reconstructions attaining minimum mean squared error at experimental settings predicted by the DQE as optimal.

physics.ins-det↗

arXiv2018

Design and Application of a Relativistic Kramers-Kronig Analysis Algorithm

Low-loss electron energy loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM) probes the valence electron density and relevant optoelectronic properties such as band gap energies and other band structure transitions. The measured spectra can be formulated in a dielectric theory framework, comparable to optical spectroscopies and ab-initio simulations. Moreover, Kramers-Kronig analysis (KKA), an inverse algorithm based on the homonym relations, can be employed for the retrieval of the complex dielectric function (CDF). However, spurious contributions traditionally not considered in this framework typically impact low-loss EELS modifying the spectral shapes and precluding the correct measurement and retrieval of the dielectric information. A relativistic KKA algorithm is able to account for the bulk and surface radiative-loss contributions to low-loss EELS, revealing the correct dielectric properties. Using a synthetic low-loss EELS model, we propose some modifications on the naive implementation of this algorithm that broadens its range of application. The robustness of the algorithm is improved by regularization, appliying previous knowledge about the shape and smoothness of the correction term. Additionally, our efficient numerical integration methodology allows processing hyperspectral datasets in a reasonable amount of time. Harnessing these abilities, we show how simultaneous relativistic KKA processing of several spectra can share information to produce an improved result.

cond-mat.mtrl-sci↗

arXiv2012

Breaking the Mode Degeneracy of Surface-Plasmon Resonances in a Triangular System

In this paper, we present a systematic investigation of symmetry-breaking in the plasmonic modes of triangular gold nanoprisms. Their geometrical C3 symmetry is one of the simplest possible that allows degeneracy in the particle's mode spectrum. It is reduced to the non-degenerate symmetries Cv or E by positioning additional, smaller gold nanoprisms in close proximity, either in a lateral or a vertical configuration. Corresponding to the lower symmetry of the system, its eigenmodes also feature lower symmetries (Cv), or preserve only the identity (E) as symmetry. We discuss how breaking the symmetry of the plasmonic system not only breaks the degeneracy of some lower order modes, but also how it alters the damping and eigenenergies of the observed Fano-type resonances.

physics.chem-ph↗

arXiv2008

Using dynamically scattered electrons for 3-dimensional potential reconstruction

Three-dimensional charge density maps computed by first-principles methods provide information about atom positions and the bonds between them, data which is particularly valuable when trying to understand the properties of point defects, dislocations, and interfaces. This letter presents a method by which 3-dimensional maps of the electrostatic potential, related to the charge density map by the Poisson equation, can be obtained experimentally at 0.1 nm resolution or better. This method requires data acquired by holographic transmission electron microscopy (TEM) methods such as off-axis electron holography or focal series reconstruction for different directions of the incident electron beam. The reconstruction of the 3-dimensional electrostatic (and absorptive) potential is achieved by making use of changes in the dynamical scattering within the sample as the direction of the incident beam varies.

cond-mat.mtrl-sci↗