A comparison between minimum variance control and other online compensation methods for specimen drift in transmission electron microscopy. (English) Zbl 1305.93102

Summary: 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.


93C40 Adaptive control/observation systems
93C95 Application models in control theory


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[1] Akaike, H. (1970). A fundamental relation between predictor identification and power spectrum estimation. Annals of the Institute of Statistical Mathematics, 22(1), 219-223. · Zbl 0259.62077
[2] Åström, K. J. (1967). Computer control of a paper machine: An application of linear stochastic control theory. IBM Journal of Research and Development, 11(4), 389-405.
[3] Åström, K. J. (1970). Introduction to stochastic control theory. New York, NY: Academic Press. · Zbl 0226.93027
[4] Åström, K. J., & Wittenmark, B. (1973). On self tuning regulators. Automatica, 9(2), 185-199. · Zbl 0249.93049
[5] Åström, K. J., & Wittenmark, B. (1995). Adaptive control reading. Massachusetts: Addison-Wesley.
[6] Basu, P., Rudoy, D., & Wolfe, P. J. (2009). A nonparametric test for stationarity based on local Fourier analysis. In Proceedings of the 2009 IEEE international conference on acoustics, speech and signal processing (pp. 3005-3008). Taipei, Taiwan.
[7] Bloomfield, P. (1972). On the error of prediction of a time series. Biometrika, 59(3), 501-507. · Zbl 0263.62053
[8] Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time series analysis: Forecasting and control. Oakland, CA: Holden-Day. · Zbl 0363.62069
[9] Broersen, P. M. T. (2002). Automatic spectral analysis with time series models. IEEE Transactions on Instrumentation and Measurement, 51(2), 211-216.
[10] Broersen, P. M. T. (2006). Automatic autocorrelation and spectral analysis. London: Springer.
[11] Broersen, P. M. T. (2009). ARMASA toolbox for Matlab. http://goo.gl/jMNWK.
[12] De Graef, M. (2003). Introduction to conventional transmission electron microscopy. Cambridge: Cambridge University Press.
[13] Durbin, J. (1960). The fitting of time series models. Revue de l’Institut International de Statistique, 28(3), 233-243. · Zbl 0101.35604
[14] Erkelens, J. S., Tejada, A., & den Dekker, A. J. (2013). Identification of time series models from segments: Application to scanning transmission electron microscopy images. IEEE Transactions on Instrumentation and Measurement, 62, to appear.
[15] Franklin, G. F., Powell, J. D., & Workman, M. L. (1998). Digital control of dynamical systems (3rd ed.). Menlo Park, CA: Addison-Wesley. · Zbl 0697.93002
[16] Hamilton, J. D. (1994). Time series analysis. Princeton, NJ: Princeton University Press. · Zbl 0831.62061
[17] Hannan, E. J. (1987). Rational transfer function approximation. Statistical Science, 2(2), 135-151. · Zbl 0955.93518
[18] Howe, JM; Banhart, F. (ed.), In-situ HRTEM studies of interface dynamics during solid-solid phase transformations in metal alloys, 167-186 (2008), Singapore
[19] Inada, H.; Kakibayashi, H.; Isakozawa, S.; Hashimoto, T.; Yaguchi, T.; Nakamura, K.; Hawkes, PW (ed.), Hitachi’s development of cold-field emission scanning transmission electron microscopes, No. 159, 123-186 (2009), London
[20] Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1-3), 159-178. · Zbl 0871.62100
[21] Li, Z., & Evans, R. (1997). Minimum-variance control of linear time-varying systems. Automatica, 33(8), 1531-1537. · Zbl 0885.93056
[22] Liu, Z., & Gu, W. (2004). High-speed and high-precision deflectors applied in electron beam lithography system based on scanning electron microscopy. Journal of Vacuum Science and Technology. B: Microelectronics and Nanometer Structures, 22(6), 3557-3559.
[23] Pfaff, B. (2008). Analysis of integrated and cointegrated time series with R (2nd ed.). New York, NY: Springer. · Zbl 1165.62068
[24] Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biomètrika, 75(2), 335-346. · Zbl 0644.62094
[25] Plitzko, J. M., & Mayer, J. (1999). Quantitative thin film analysis by energy filtering transmission electron microscopy. Ultramicroscopy, 78(1-4), 207-219.
[26] Priestley, M. B. (1981a). Spectral analysis and time series (Vol. 1). New York, NY: Academic Press. · Zbl 0537.62075
[27] Priestley, M. B. (1981b). Spectral analysis and time series (Vol. 2). New York, NY: Academic Press. · Zbl 0537.62075
[28] Pulokas, J., Green, C., Kisseberth, N., Potter, C. S., & Carragher, B. (1999). Improving the positional accuracy of the goniometer on the philips CM series TEM. Journal of Structural Biology, 128(3), 250-256.
[29] Reimer, L. (1993). Transmission electron micrsocopy. Physics of image formation and microanalysis (3rd ed.). Berlin, Heidelberg: Springer.
[30] Sachs, D., Nasiri, S., & Goehl, D. (2006). Image stabilization technology overview. http://goo.gl/YVHiN, White Paper.
[31] Saka, H.; Banhart, F. (ed.), In-situ high-resolution observation of solid-solid, solid-liquid and solid-gas reactions (2008), Singapore
[32] Shan, Q., Jia, J., & Agarwala, A. (2008). High-quality motion deblurring from a single image. ACM Transactions on Graphics (SIGGRAPH), 27(3), article 73.
[33] Sigle, W., Krämer, S., Varshney, V., Zern, A., Eigenthaler, U., & Rühle, M. (2003). Plasmon energy mapping in energy-filtering transmission electron microscopy. Ultramicroscopy, 96(3-4), 565-571.
[34] Snella, M. T. (2010). Drift correction for scanning-electron microscopy. Master’s thesis. Boston, MA: Massachusetts Institute of Technology.
[35] Spence, J. C. H. (2003). High-resolution electron microscopy (3rd ed.). New York, NY: Oxford University Press.
[36] Tarău, A. N., Nuij, P., & Steinbuch, M. (2011a). Hierarchical control for drift correction in transmission electron microscopes. In Proceedings of the 20th IEEE international conference on control applications (pp. 351-356). Denver, CO. · Zbl 0249.93049
[37] Tarău, A. N., Nuij, P., & Steinbuch, M. (2011b). Model-based drift control for electron microscopes. In Proceedings of the 18th IFAC World Congress (pp. 8583-8588). Milano, Italy. · Zbl 0259.62077
[38] Tejada, A., & den Dekker, A. J. (2011). POEM: A fast defocus estimation method for scanning transmission electron microscopy. In Proceedings of the 2011 IEEE international instrumentation and measurement technology conference (pp. 1228-1232). Hangzhou, China.
[39] Tejada, A., & den Dekker, A. J. (2012). Defocus polar rose estimation method (POEM): A fast defocus estimation method for STEM. IEEE Transactions on Instrumentation and Measurement, 61(10), 2723-2730.
[40] Tejada, A., Van Den Broek, W., van der Hoeven, S., & den Dekker, A. J. (2009a). Towards STEM control: Modeling framework and development of a sensor for defocus control. In Proceedings of 48th IEEE conference on decision and control (pp. 8310-8315). Shanghai, China.
[41] Tejada, A., van der Hoeven, S. W., den Dekker, A. J., & Van den Hof, P. M. J. (2009b). Towards automatic control of scanning transmission electron microscopes. In Proceedings of the 18th IEEE international conference on control applications (pp. 788-793). Saint Petersburg, Russia.
[42] Tejada, A., den Dekker, A. J., & Van Den Broek, W. (2011a). Introducing measure-by-wire, the systematic use of systems and control theory in transmission electron microscopy. Ultramicroscopy, 111(11), 1581-1591.
[43] Tejada, A., Vos, P., & den Dekker, A. J. (2011b). Towards an adaptive minimum variance control scheme for specimen drift compensation in transmission electron microscopes. In Proceedings of 7th international workshop on multidimensional (nD) systems. Poitiers, France. · Zbl 0249.93049
[44] Tsuneta, R., Koguchi, M., Nakamura, K., & Nishida, A. (2002). A specimen-drift-free EDX mapping system in a STEM for observing two-dimensional profiles of low dose elements in fine semiconductor devices. Journal of Electron Microscopy, 51(3), 167-171.
[45] Williams, D. B., & Carter, C. B. (2009). Transmission electron microscopy. A textbook for materials science. New York, NY: Springer.
[46] Yamamoto, T. (1975). Asymptotic mean square error of multi-step prediction from mixed autoregressive moving average model. CORE Discussion Papers No. 7521, Center for Operations Research & Econometrics, Heverlee, Belgium.
[47] Yang, Q., Jagannathan, S., & Bohannan, E. W. (2008). Automatic drift compensation using phase correlation method for nanomanipulation. IEEE Transactions on Nanotechnology, 7(2), 209-216.
[48] Zhang, W. (2010). On the stability and convergence of self-tuning controlvirtual equivalent system approach. International Journal of Control, 83(5), 879-896. · Zbl 1197.93089
[49] Zitová, B., & Flusser, J. (2003). Image registration methods: A survey. Image and Vision Computing, 21(11), 977-1000.
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