A comparison between minimum variance control and other online compensation methods for specimen drift in transmission electron microscopy

Transmission electron microscopes (TEMs) 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. In particular, an important feature in need of automation is specimen drift compensation, which is a common cause of image blurring in long-exposure TEM images, especially at high magnifications. In this paper, a systematic online approach to specimen drift compensation, called adaptive minimum variance control, is discussed in detail. The method makes use of an identified drift model, continuously updated from online drift measurements, to predict and ameliorate future drift values, significantly reducing their variance. The method’s performance, measured in terms of drift variance reduction, is illustrated using both experimental and simulated data, and it is then compared with the performance of two pragmatic model-free methods: last data point prediction and linear extrapolation prediction.

[1]  P. Phillips,et al.  Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? , 1992 .

[2]  Arturo Tejada,et al.  Defocus Polar rOse Estimation Method (POEM): A Fast Defocus Estimation Method for STEM , 2012, IEEE Transactions on Instrumentation and Measurement.

[3]  D. B. Preston Spectral Analysis and Time Series , 1983 .

[4]  Jan Flusser,et al.  Image registration methods: a survey , 2003, Image Vis. Comput..

[5]  Björn Wittenmark,et al.  On Self Tuning Regulators , 1973 .

[6]  Michael T Snella Drift correction for scanning-electron microscopy , 2010 .

[7]  J. Spence High-Resolution Electron Microscopy , 2003 .

[8]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[9]  Bernhard Pfaff,et al.  Analysis of Integrated and Cointegrated Time Series with R , 2005 .

[10]  M Maarten Steinbuch,et al.  Model-Based Drift Control for Electron Microscopes , 2011 .

[11]  J. Plitzko,et al.  Quantitative thin film analysis by energy filtering transmission electron microscopy , 1999 .

[12]  Arturo Tejada,et al.  Towards STEM control: Modeling framework and development of a sensor for defocus control , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[13]  Piet M. T. Broersen,et al.  Automatic Autocorrelation and Spectral Analysis , 2006 .

[14]  Arturo Tejada,et al.  Towards automatic control of scanning transmission electron microscopes , 2009, 2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC).

[15]  James D. Hamilton Time Series Analysis , 1994 .

[16]  Arturo Tejada,et al.  POEM: A fast defocus estimation method for scanning transmission electron microscopy , 2011, 2011 IEEE International Instrumentation and Measurement Technology Conference.

[17]  David B. Williams,et al.  Transmission Electron Microscopy , 1996 .

[18]  Marc De Graef,et al.  Introduction to Conventional Transmission Electron Microscopy: Defects in crystals , 2003 .

[19]  Arturo Tejada,et al.  Towards an adaptive minimum variance control scheme for specimen drift compensation in transmission electron microscopes , 2011, The 2011 International Workshop on Multidimensional (nD) Systems.

[20]  U. Eigenthaler,et al.  Plasmon energy mapping in energy-filtering transmission electron microscopy. , 2003, Ultramicroscopy.

[21]  Arturo Tejada,et al.  Identification of Time Series Models From Segments—Application to Scanning Transmission Electron Microscopy Images , 2013, IEEE Transactions on Instrumentation and Measurement.

[22]  Maarten Steinbuch,et al.  Hierarchical control for drift correction in transmission electron microscopes , 2011, 2011 IEEE International Conference on Control Applications (CCA).

[23]  M. Graef Introduction to Conventional Transmission Electron Microscopy: List of symbols , 2003 .

[24]  J Pulokas,et al.  Improving the positional accuracy of the goniometer on the Philips CM series TEM. , 1999, Journal of structural biology.

[25]  Dirk Eddelbuettel,et al.  Analysis of Integrated and Cointegrated Time Series with R (2nd Edition) , 2009 .

[26]  K. Åström Introduction to Stochastic Control Theory , 1970 .

[27]  David B. Williams,et al.  Transmission Electron Microscopy: A Textbook for Materials Science , 1996 .

[28]  Hirotugu Akaike,et al.  A fundamental relation between predictor identification and power spectrum estimation , 1970 .

[29]  Arturo Tejada,et al.  Introducing measure-by-wire, the systematic use of systems and control theory in transmission electron microscopy. , 2011, Ultramicroscopy.

[30]  Piet M. T. Broersen,et al.  Automatic spectral analysis with time series models , 2002, IEEE Trans. Instrum. Meas..

[31]  B. Pasik-Duncan,et al.  Adaptive Control , 1996, IEEE Control Systems.

[32]  M. Koguchi,et al.  A specimen-drift-free EDX mapping system in a STEM for observing two-dimensional profiles of low dose elements in fine semiconductor devices. , 2002, Journal of electron microscopy.

[33]  P. Phillips Testing for a Unit Root in Time Series Regression , 1988 .

[34]  Robin J. Evans,et al.  Minimum-variance control of linear time-varying systems , 1997, Autom..

[35]  Weicun Zhang,et al.  On the stability and convergence of self-tuning control–virtual equivalent system approach , 2010, Int. J. Control.

[36]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[37]  E. Hannan Rational Transfer Function Approximation , 1987 .

[38]  Karl Johan Åström,et al.  Computer control of a paper machine: an application of linear stochastic control theory , 1967 .

[39]  Hiroshi Kakibayashi,et al.  Chapter 4 – Hitachi's Development of Cold-Field Emission Scanning Transmission Electron Microscopes , 2009 .

[40]  Peter Bloomfield,et al.  On the error of prediction of a time series , 1972 .

[41]  Prabahan Basu,et al.  A nonparametric test for stationarity based on local Fourier analysis , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[42]  James Durbin,et al.  The fitting of time series models , 1960 .

[43]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[44]  Jiaya Jia,et al.  High-quality motion deblurring from a single image , 2008, SIGGRAPH 2008.