Related papers: Topological metrology and its application to optic…
Unprecedented atomic-scale measurement resolution has recently been demonstrated in single-shot optical localization metrology based on deep-learning analyses of diffraction patterns of topologically structured light scattered from objects.…
We present an optical metrology system for characterization of topography of micro/nano-structures on a surface or embedded in a semi-transparent material. Based on the principles of scatterometry, where the intensity of scattered light is…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…
It has been seen recently that when probing a nanoscale object to determine, for example, size or position via light scattering, significant advantage in measurement precision can be gained from exploiting phase singularities in a…
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
Traceability to the International System of Units (SI) is fundamental to measurement accuracy and reliability. In this study, we demonstrate subnanometer traceability of localization microscopy, establishing a metrological foundation for…
Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods, or explicitly designed and built lithographically. Correlated disorder, induced by a minimum…
The concepts of topology provide a powerful tool to tailor the propagation and localization of light. While electromagnetic waves have only two polarization states, engineered degeneracies of photonic modes provide novel opportunities…
Topology optimization methods for inverse design of nano-photonic systems have recently become extremely popular and are presented in various forms and under various names. Approaches comprise gradient and non-gradient based algorithms…
The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…
Topology is a powerful framework for controlling and manipulating light, minimizing detrimental perturbations on the photonic properties. Combining nanophotonics with topological concepts presents opportunities for both fundamental physics…
Concepts such as energy dependence, random deployment, dynamic topological update, self-organization, varying large number of nodes are among many factors that make WSNs a type of complex system. However, when analyzing WSNs properties…
We introduce a functor which associates to every measure preserving system (X,B,\mu,T) a topological system (C_2(\mu),\tilde{T}) defined on the space of 2-fold couplings of \mu, called the topological lens of T. We show that often the…
We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
How can we perform a metrological task if only limited control over a quantum system is given? Here, we present systematic methods for conducting nonlinear quantum metrology in scenarios lacking a common reference frame. Our approach…
Measurements of positional coordinates and dimensions - whether by human vision or optical instrumentation - are fundamental to safety, industrial productivity, manufacturing quality/accuracy, and scientific discovery. The ultimate…
Topological properties of photonic structures described by Hamiltonian matrices have been extensively studied in recent years. Photonic systems are often open systems, and their coupling with the environment is characterized by scattering…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…