Fitting of Atomic Force Microscopy Force Curves with a Sparse Representation Model

Qing Wang,Junbo Duan,Nan Hu

doi:10.1155/2021/1951456

Abstract

Atomic force microscopy (AFM) is a high-resolution scanning technology, and the measured data are a set of force curves, which can be fitted with a piecewise curve model and be analyzed further. Most methods usually follow a two-step strategy: first, the discontinuities (or breakpoints) are detected as the boundaries of two consecutive pieces; second, each piece separated by the discontinuities is fitted with a parametric model, such as the well-known worm-like chain (WLC) model. The disadvantage of this method is that the fitting (the second step) accuracy depends largely on the discontinuity detection (the first step) accuracy. In this study, a sparse representation model is proposed to jointly detect discontinuities and fit curves. The proposed model fits the curve with a linear combination of parametric functions, and the estimation of the parameters in the model can be formulated as an optimization problem with ℓ 0 -norm constraint. The performance of the proposed model is demonstrated by the fitting of AFM retraction force curves with the WLC model. Results shows that the proposed method can segment the force curve and estimate the parameter jointly with better accuracy, and hence, it is promising for automatic AFM force curve processing.

Highlights

Atomic force microscopy (AFM) is a high-resolution scanning technology, and the measured data are a set of force curves, which can be fitted with a piecewise curve model and be analyzed further
A sparse representation model is proposed to jointly detect discontinuities and fit curves. e proposed model fits the curve with a linear combination of parametric functions, and the estimation of the parameters in the model can be formulated as an optimization problem with l0-norm constraint. e performance of the proposed model is demonstrated by the fitting of AFM retraction force curves with the worm-like chain (WLC) model
A typical AFM instrument consists of five components: laser generator, probe, cantilever, piezoelectric scanner, and photodiode detector. e testing sample is mounted above the piezoelectric scanner, which can move in an approaching manner toward the probe or a retracting manner away from the probe

Summary

Research Article

Fitting of Atomic Force Microscopy Force Curves with a Sparse Representation Model. Atomic force microscopy (AFM) is a high-resolution scanning technology, and the measured data are a set of force curves, which can be fitted with a piecewise curve model and be analyzed further. A sparse representation model is proposed to jointly detect discontinuities and fit curves. A set of functions consisting of piecewise polynomials were used to fit the force curve. The noisy curve was segmented into pieces by the detected discontinuities, and each piece was fitted with a parametric model by nonlinear optimization. Another way of parameter estimation is clustering in the space of model parameters directly, and curve fitting can be avoided.

Methodology

WLC FJC