Arturo Tejada

Towards STEM control: Modeling framework and development of a sensor for defocus control

Scanning transmission electron microscopes are indispensable tools for material science research, since they can reveal the internal structure of a wide range of specimens. Thus, it is of scientific and industrial interest to transform these microscopes into flexible, high-throughput, unsupervised, nanomeasuring tools. To do so, processes that are currently executed manually based on visual feedback (e.g., alignment or particle measurement) should be automated, taking into consideration their time dependencies. That is, these microscopes should be studied from the systems and control perspective. To the best of our knowledge, such perspective is lacking in the literature. Thus, it is provided here through a new modeling framework that facilitates the future development of control strategies based on image analysis. The progress made towards developing an image-based sensor for defocus control is also reported. Finally, the paper also aims to introduce scanning transmission electron microscopy as an important and untapped application area for control engineers.

Introducing measure-by-wire, the systematic use of systems and control theory in transmission electron microscopy

Transmission electron microscopes (TEMs) are the tools of choice for academic and industrial research at the nano-scale. Due to their increasing use for routine, repetitive measurement tasks (e.g., quality control in production lines) there is a clear need for a new generation of high-throughput microscopes designed to autonomously extract information from specimens (e.g., particle size distribution, chemical composition, structural information, etc.). To aid in their development, a new engineering perspective on TEM design, based on principles from systems and control theory, is proposed here: measure-by-wire (not to be confused with remote microscopy). Under this perspective, the TEM operator yields the direct control of the microscopes internal processes to a hierarchy of feedback controllers and high-level supervisors. These make use of dynamical models of the main TEM components together with currently available measurement techniques to automate processes such as defocus correction or specimen displacement. Measure-by-wire is discussed in depth, and its methodology is illustrated through a detailed example: the design of a defocus regulator, a type of feedback controller that is akin to existing autofocus procedures.

Stability Analysis of Stochastic Hybrid Jump Linear Systems Using a Markov Kernel Approach

In this paper, the state dynamics of a supervisor implemented with a digital sequential system are represented with a finite state machine (FSM). The supervisor monitors a symbol sequence derived from a linear closed-loop systems performance and generates a switching signal for the closed-loop system. The effect of random events on the performance of the closed-loop system is analyzed by adding an exogenous Markov process input to the FSM, and by appropriately augmenting a switched system representation of the supervisor and the closed-loop system. For this class of hybrid jump linear systems, the switching signal is, in general, a non-Markovian process, making it hard to analyze its stability properties. This is ameliorated by introducing a sufficient mean square stability test that uses only upper bounds on the one-step transition probabilities of the switching signal. These bounds are explicitly derived from a Markov kernel associated with the hybrid system model. This stability test becomes necessary and sufficient when the switching signal is Markovian. To determine tighter stability bounds, procedures to determine the upper-bound transition probability matrices when the FSM has a Moore or a Mealy type output map are presented. Two examples illustrate the applicability of the presented results.

The role of Poisson's binomial distribution in the analysis of TEM images☆

Franks observation that a TEM bright-field image acquired under non-stationary conditions can be modeled by the time integral of the standard TEM image model [J. Frank, Nachweis von objektbewegungen im lichtoptis- chen diffraktogramm von elektronenmikroskopischen auf- nahmen, Optik 30 (2) (1969) 171-180.] is re-derived here using counting statistics based on Poissons binomial distribution. The approach yields a statistical image model that is suitable for image analysis and simulation.

On nonlinear discrete-time systems driven by Markov chains

Abstract The behavior of a class of hybrid systems in discrete-time can be represented by nonlinear difference equations with a Markov input. The analysis of such a system usually starts by establishing the Markov property of the joint process formed by combining the systems state and input. There are, however, no complete proofs of this property. This paper aims to address this problem by presenting a complete and explicit proof that uses only fundamental measure-theoretical concepts.

On the Markov property for nonlinear discrete-time systems with Markovian inputs

The behavior of a general hybrid system in discrete-time can be represented by a nonlinear difference equation x(k + 1) = Fk(x(k),thetas(k)), where thetas(k) is assumed to be a finite-state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k),thetas(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only fundamental measure-theoretical concepts

Stability analysis of upset recovery methods for electromagnetic interference

Presents a tool to analyze the effect of error recovery systems on closed-loop flight control systems. In particular, the paper develops closed-loop models and analyzes the mean-square stability effect of error recovery rollback, reset, and cold restart systems in digital control systems. The error recovery mechanisms are triggered by transient or intermittent faults which could be caused, for example, by high intensity electromagnetic radiation. The tool is illustrated by analyzing a stabilizing controller for the longitudinal dynamics of the AFTI/F-16 aircraft. This example compares different recovery methodologies by determining the minimum interarrival spacing between upsets which maintains closed-loop mean-square stability.

Towards an adaptive minimum variance control scheme for specimen drift compensation in transmission electron microscopes

Transmission electron microscopes are the tools of choice in materials science, semiconductor, and biological research and it is expected that they will be increasingly used to autonomously perform high-volume, repetitive, nano-measurements in the near future. Thus, there is a clear need to develop automation strategies for these microscopes. This paper introduces an adaptive minimum variance control scheme to compensate specimen drift, a common cause of image blurring in long-exposure images. The controller, which is new in the electron microscope literature, makes use of ARMASA, a statistical toolbox designed to identify linear models from finite-length data sets, to generate ARMA models of the drift process ‘on-the-fly’. These models are then used as part of a controller designed to reduce the drift variance. The benefits of the proposed scheme, which can be quite substantial, are illustrated through a set of simulations that use a model of the drift present in a sequence of experimental images.

POEM: A fast defocus estimation method for scanning transmission electron microscopy

The defocus polar rose estimation method (POEM) is introduced here as an alternative method for defocus estimation in scanning transmission electron microscopy. Its principle of operation is discussed in detail along with the results of initial simulation-based performance tests. The results show that POEM can attain a precision similar to that of equivalent methods in the literature but using significantly less data, thus increasing the defocus estimation speed significantly.

Towards automatic control of scanning transmission electron microscopes

Scanning transmission electron microscopes are the tools of choice for material science research, since they provide information on the internal structure of a wide range of specimens. These sophisticated machines are operated manually by skilled technicians, who execute complex and repetitive procedures, such as measuring nano-particles, using mainly visual feedback. Hence, there is a need for new global control strategies to automate these procedures. These strategies, however, must be based on a firm understanding of the microscopes from the system theoretical perspective. To the best of our knowledge, such perspective is lacking in the literature. Thus, it is provided here through a new modeling framework that facilitates the future development of global control strategies. The paper also aims to introduce scanning transmission electron microscopy as an important and untapped area of application for control engineers.