Real-Time Estimation of the Tip-Sample Interactions in Tapping Mode Atomic Force Microscopy With a Regularized Kalman Filter

Sasan Keyvani Janbahan, Gijs van der Veen, Selman Tamer, Hamed Sadeghian, Hans Goosen, Fred van Keulen

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


The real-time and accurate measurement of tip-sample interaction forces in Tapping Mode Atomic Force Microscopy (TM-AFM) is a remaining challenge. This obstruction fundamentally stems from the causality of the physical systems. Since i) the input of the dynamic systems propagates to the output with some delay, and ii) , multiple different inputs can generate the same output, there exist no measurement or estimation technique that can estimate the force input of the systems in real-time without phase and amplitude distortion. However, an approximate and delayed estimation can still be possible. This article presents a general-purpose algorithm which aims to estimate an approximation of the force input of TM-AFM with minimum delay and error. For this reason, first, the input estimation problem is converted to an ill-posed state observation problem. Then, a Tikhonov-like regularization technique is applied to eliminate the ill-conditioning and estimate the force input using a linear Kalman filter. The proposed input observer is remarkably robust, real-time in the order of the sampling frequency, and applicable for any Linear Time Invariant (LTI) system with a (semi-) periodic process. Simulation and experimental results show that using the proposed algorithm with a wide-band AFM probe; one can determine the tip-sample forces with only a few percent error and a delay in the order of sampling time. Unlike the existing force estimation techniques for AFM, this algorithm does not require any prior knowledge of the force-distance relationship which can be very beneficial for the closed-loop control of AFM.
Original languageEnglish
Pages (from-to)274-283
JournalIEEE Transactions on Nanotechnology
Publication statusPublished - 2020


  • Unknown input estimation
  • tip-sample interactions
  • multi-harmonic AFM
  • kalman filter
  • regularization


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