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Real-time Topography and Hamaker Constant Estimation in Atomic Force Microscopy Based on Adaptive Fading Extended Kalman Filter

  • Control Theory and Applications
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Abstract

In this study, a novel technique based on adaptive fading extended Kalman filter for atomic force microscopy is proposed to directly estimate the topography of a sample surface without needing any control system. While in conventional imaging techniques, the scanning speed or the bandwidth is limited due to a relatively large settling time, the method proposed in this research is able to address this issue and estimate the topography throughout transient oscillation of the microcantilever. With this aim, an estimation process using an adaptive fading extended Kalman filter (augmented with forgetting factor) as the system observer is designed and coupled with the system dynamics to obtain sample topography. Obtained results demonstrate that the sample height is estimated by this algorithm with high accuracy and a relatively high scanning speed. Moreover, the observer is able to identify the topography and Hamaker constant simultaneously. Therefore, the presented approach can compensate for the low scanning speed of the classical imaging method as well as eliminate the need for a closed-loop controller.

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References

  1. G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Physical Review Letters, vol. 56, no. 9, pp. 930–933, 1986.

    Article  Google Scholar 

  2. O. H. Willemsen, M. M. E. Snel, A. Cambi, J. Greve, B. G. de Grooth, and C. G. Figdor, “Biomolecular interactions measured by atomic force microscopy,” Biophysical Journal, vol. 79, no. 6, pp. 3267–3281, 2000.

    Article  Google Scholar 

  3. M. Guthold, G. Matthew, A. Negishi, R. M. Taylor II, D. Erie, F. P. Brooks Jr., and R. Superfine, “Quantitative manipulation of DNA and viruses with the nanomanipulator scanning force microscope,” Surface and Interface Analysis, vol. 27, no. 5, pp. 437–443, 1999.

    Article  Google Scholar 

  4. G. R. Jayanth and C. Menq, “Modeling and design of a magnetically actuated two-axis compliant micromanipulator for nanomanipulation,” IEEE/ASME Transactions on Mechatronics, vol. 15, no. 3, pp. 360–370, 2010.

    Article  Google Scholar 

  5. H. G. Hansma, “Surface biology of DNA by atomic force microscopy,” Annual Review of Physical Chemistry, vol. 52, no. 1, pp. 71–92, 2001.

    Article  Google Scholar 

  6. Y. Huang, P. Cheng, and C. H. Menq, “Dynamic force sensing using an optically trapped probing system,” IEEE/ASME Transactions on Mechatronics, vol. 16, no. 6, pp. 1145–1154, 2011.

    Article  Google Scholar 

  7. M. A. Mabrok, A. G. Kallapur, I. R. Petersen, and A. Lanzon, “Spectral conditions for negative imaginary systems with applications to nanopositioning,” IEEE/ASME Transactions on Mechatronics, vol. 19, no. 3, pp. 895–903, 2014.

    Article  Google Scholar 

  8. N. Jalili and K. Laxminarayana, “A review of atomic force microscopy imaging systems: Application to molecular metrology and biological sciences,” Mechatronics, vol. 14, no. 8, pp. 907–945, 2004.

    Article  Google Scholar 

  9. R. García and R. Pérez, “Dynamic atomic force microscopy methods,” Surface Science Reports, vol. 47, no. 6, pp. 197–301, 2002.

    Article  Google Scholar 

  10. M. S. Rana, H. R. Pota, and I. R. Petersen, “Performance of sinusoidal scanning with MPC in AFM imaging,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 1, pp. 73–83, 2015.

    Article  Google Scholar 

  11. O. M. El Rifai and K. Youcef-Toumi, “Coupling in piezoelectric tube scanners used in scanning probe microscopes,” Proceedings of the American Control Conference. (Cat. No. 01CH37148), vol. 4, pp. 3251–3255, 2001.

    Article  Google Scholar 

  12. S. K. Das, H. R. Pota, and I. R. Petersen, “Damping controller design for nanopositioners: A mixed passivity, negative-imaginary, and small-gain approach,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 1, pp. 416–426, 2015.

    Article  Google Scholar 

  13. M. S. Rana, H. R. Pota, and I. R. Petersen, “High-speed AFM image scanning using observer-based MPC-notch control,” IEEE Transactions on Nanotechnology, vol. 12, no. 2, pp. 246–254, 2013.

    Article  Google Scholar 

  14. T. Sulchek, R. Hsieh, J. D. Adams, G. G. Yaralioglu, S. C. Minne, and C. F. Quate, “High-speed tapping mode imaging with active Q control for atomic force microscopy,” Applied Physics Letters, vol. 76, no. 11, pp. 1473–1475, 2000.

    Article  Google Scholar 

  15. T. Sulchek, G. G. Yaralioglu, C. F. Quate, and S. C. Minne, “Characterization and optimization of scan speed for tapping-mode atomic force microscopy,” Review of Scientific Instruments, vol. 73, no. 8, pp. 2928–2936, 2002.

    Article  Google Scholar 

  16. M. Balantekin and F. L. Değertekin, “Optimizing the driving scheme of a self-actuated atomic force microscope probe for high-speed applications,” Ultramicroscopy, vol. 111, no. 8, pp. 1388–1394, 2011.

    Article  Google Scholar 

  17. D. R. Sahoo, A. Sebastian, and M. V. Salapaka, “Transient-signal-based sample-detection in atomic force microscopy,” Applied Physics Letters, vol. 83, no. 26, pp. 5521–5523, 2003.

    Article  Google Scholar 

  18. D. R. Sahoo, A. Sebastian, and M. V. Salapaka, “An ultra-fast scheme for sample-detection in dynamic-mode atomic force microscopy,” Proc. of NSTI Nanotechnology Conference and Trade Show-NSTI Nanotech, vol. 3, pp. 11–14, 2004.

    Google Scholar 

  19. K. S. Karvinen, M. G. Ruppert, K. Mahata, and S. O. R. Moheimani, “Direct tip-sample force estimation for high-speed dynamic mode atomic force microscopy,” IEEE Transactions on Nanotechnology, vol. 13, no. 6, pp. 1257–1265, 2014.

    Article  Google Scholar 

  20. M. R. Javazm and H. N. Pishkenari, “Observer design for topography estimation in atomic force microscopy using neural and fuzzy networks,” Ultramicroscopy, vol. 214, p. 113008, 2020.

    Article  Google Scholar 

  21. M. G. Ruppert and S. O. R. Moheimani, “Multimode Q control in tapping-mode afm: enabling imaging on higher flexural eigenmodes,” IEEE Transactions on Control Systems Technology, vol. 24, no. 4, pp. 1149–1159, 2016.

    Article  Google Scholar 

  22. I. S. Bozchalooi and K. Youcef-Toumi, “Multi-actuation and PI control: A simple recipe for high-speed and large-range atomic force microscopy,” Ultramicroscopy, vol. 146, pp. 117–124, 2014.

    Article  Google Scholar 

  23. H. N. Pishkenari, N. Jalili, and A. Meghdari, “Acquisition of high-precision images for non-contact atomic force microscopy,” Mechatronics, vol. 16, no. 10, pp. 655–664, 2006.

    Article  Google Scholar 

  24. S. Necipoglu, S. A. Cebeci, Y. E. Has, L. Guvenc, and C. Basdogan, “Robust repetitive controller for fast AFM imaging,” IEEE Transactions on Nanotechnology, vol. 10, no. 5, pp. 1074–1082, 2011.

    Article  Google Scholar 

  25. H.-T. Seo, S. Kim, and K.-S. Kim, “An H∞ design of disturbance observer for a class of linear time-invariant single-input/single-output systems,” International Journal of Control, Automation and Systems, vol. 18, no. 7, pp. 1662–1670, 2020.

    Article  Google Scholar 

  26. L. Xu, K. Ma, and H. Fan, “Unscented Kalman filtering for nonlinear state estimation with correlated noises and missing measurements,” International Journal of Control, Automation and Systems, vol. 16, no. 3, pp. 1011–1020, 2018.

    Article  Google Scholar 

  27. H. Yan, J. Sun, H. Zhang, X. Zhan, and F. Yang, “Event-triggered H∞ state estimation of 2-DoF quarter-car suspension systems with nonhomogeneous Markov switching,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, pp. 1–10, 2018.

  28. H. Zhang, Z. Wang, H. Yan, F. Yang, and X. Zhou, “Adaptive event-triggered transmission scheme and H∞ filtering co-design over a filtering network with switching topology,” IEEE Transactions on Cybernetics, vol. 49, no. 12, pp. 4296–4307, 2019.

    Article  Google Scholar 

  29. H. Zhang, X. Zhou, Z. Wang, and H. Yan, “Maneuvering target tracking with event-based mixture Kalman filter in mobile sensor networks,” IEEE Transactions on Cybernetics, pp. 1–12, 2019.

  30. H. Zhang, X. Zhou, Z. Wang, H. Yan, and J. Sun, “Adaptive consensus-based distributed target tracking with dynamic cluster in sensor networks,” IEEE Transactions on Cybernetics, vol. 49, no. 5, pp. 1580–1591, 2019.

    Article  Google Scholar 

  31. L. Ozbek and M. Efe, “An adaptive extended Kalman filter with application to compartment models,” Communications in Statistics-Simulation and Computation, vol. 33, no. 1, pp. 145–158, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  32. J. N. Yang, S. Lin, H. Huang, and L. Zhou, “An adaptive extended Kalman filter for structural damage identification,” Structural Control and Health Monitoring, vol. 13, no. 4, pp. 849–867, 2006.

    Article  Google Scholar 

  33. F. Deng, H.-L. Yang, and L.-J. Wang, “Adaptive unscented Kalman filter based estimation and filtering for dynamic positioning with model uncertainties,” International Journal of Control, Automation and Systems, vol. 17, no. 3, pp. 667–678, 2019.

    Article  Google Scholar 

  34. J. J. Steckenrider and T. Furukawa, “A probabilistic model-adaptive approach for tracking of motion with heightened uncertainty,” International Journal of Control, Automation and Systems, vol. 18, no. 10, pp. 2687–2698, 2020.

    Article  Google Scholar 

  35. Q. Xia, M. Rao, Y. Ying, and X. Shen, “Adaptive fading Kalman filter with an application,” Automatica, vol. 30, no. 8, pp. 1333–1338, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  36. Z. Du and X. Li, “Strong tracking tobit Kalman filter with model uncertainties,” International Journal of Control, Automation and Systems, vol. 17, no. 2, pp. 345–355, 2019.

    Article  Google Scholar 

  37. J. Li, C. Hua, Y. Tang, and X. Guan, “A time-varying forgetting factor stochastic gradient combined with Kalman filter algorithm for parameter identification of dynamic systems,” Nonlinear Dynamics, vol. 78, no. 3, pp. 1943–1952, 2014.

    Article  Google Scholar 

  38. M. S. Haghighi, M. Sajjadi, and H. N. Pishkenari, “Modelbased topography estimation in trolling mode atomic force microscopy,” Applied Mathematical Modelling, vol. 77, pp. 1025–1040, 2020.

    Article  MathSciNet  MATH  Google Scholar 

  39. M. R. P. Ragazzon, J. T. Gravdahl, K. Y. Pettersen, and A. A. Eielsen, “Topography and force imaging in atomic force microscopy by state and parameter estimation,” Proc. of American Control Conference, ACC 2015, vol. 2015-July, pp. 3496–3502, 2015.

    Article  Google Scholar 

  40. C. Biçer, E. K. Babacan, and L. Özbek, “Stability of the adaptive fading extended Kalman filter with the matrix forgetting factor,” Turkish Journal of Electrical Engineering and Computer Sciences, vol. 20, no. 5, pp. 819–833, 2012.

    Google Scholar 

  41. R. Garcia and E. T. Herruzo, “The emergence of multifrequency force microscopy,” Nature Nanotechnology, vol. 7, no. 4, pp. 217–226, 2012.

    Article  Google Scholar 

  42. R. Garcia and R. Proksch, “Nanomechanical mapping of soft matter by bimodal force microscopy,” European Polymer Journal, vol. 49, no. 8, pp. 1897–1906, 2013.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Sharif University of Technology, Tehran, Iran

    Milad Seifnejad Haghighi

  2. Micro/Nano robotics Laboratory in the Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Hossein Nejat Pishkenari

Authors
  1. Milad Seifnejad Haghighi
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  2. Hossein Nejat Pishkenari
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Corresponding author

Correspondence to Hossein Nejat Pishkenari.

Additional information

The authors appreciate partial financial support from Iranian National Science Foundation and Research Office of Sharif University of Technology.

Milad Seifnejad Haghighi received his B.Sc. degree in mechanical engineering from Shiraz University, Shiraz, Iran, in 2016. He pursued his education at Sharif University of Technology, Tehran, Iran and graduated with a M.Sc. degree in 2019. His research interests mostly include modeling, development, and control of N/MEMS as well as robotics, control and dynamics.

Hossein Nejat Pishkenari received his B.Sc., M.Sc., and Ph.D. degrees in mechanical engineering from the Sharif University of Technology, in 2003, 2005 and 2010, respectively. Then he joined the Department of Mechanical Engineering at the Sharif University of Technology in 2012. Currently, he is directing the Micro/Nano robotics Laboratory and the corresponding ongoing research projects in this field.

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Haghighi, M.S., Pishkenari, H.N. Real-time Topography and Hamaker Constant Estimation in Atomic Force Microscopy Based on Adaptive Fading Extended Kalman Filter. Int. J. Control Autom. Syst. 19, 2455–2467 (2021). https://doi.org/10.1007/s12555-020-0076-7

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  • DOI: https://doi.org/10.1007/s12555-020-0076-7

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