TY - JOUR

T1 - Real-Time Estimation of the Tip-Sample Interactions in Tapping Mode Atomic Force Microscopy With a Regularized Kalman Filter

AU - Keyvani Janbahan, Sasan

AU - van der Veen, Gijs

AU - Tamer, Selman

AU - Sadeghian, Hamed

AU - Goosen, Hans

AU - van Keulen, Fred

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Unknown input estimation

KW - tip-sample interactions

KW - multi-harmonic AFM

KW - kalman filter

KW - regularization

UR - http://www.scopus.com/inward/record.url?scp=85083035356&partnerID=8YFLogxK

U2 - 10.1109/TNANO.2020.2974177

DO - 10.1109/TNANO.2020.2974177

M3 - Article

VL - 19

SP - 274

EP - 283

JO - IEEE Transactions on Nanotechnology

JF - IEEE Transactions on Nanotechnology

SN - 1536-125X

ER -