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Estimating the transfer function of the cantilever in atomic force microscopy: A system identification approach
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Image of FIG. 1.
FIG. 1.

(Color online) (a) Scheme of an AFM and (b) the description by a dynamic system. The cantilever is modeled as the linear time-invariant system . The forces acting on the tip (input 2) and the external driving (input 1) are system inputs, whereas the tip deflection and the photodiode signal are system outputs. The nonlinear tip-sample forces are treated as a nonlinear output feedback. The photodiode electronics is included as a separate system . The data acquisition can also lead to a time delay . In addition, process noise and measurement noise may be present.

Image of FIG. 2.
FIG. 2.

(Color online) Experimental data. (a) The entire force curve. Details: (b) Oscillations induced by the snap-to-contact event. (c) Oscillations of the free cantilever after snapping off the surface. (d) The averaged oscillations after snap-off (thin line) and the estimate for the tip force (thick line); .

Image of FIG. 3.
FIG. 3.

(Color online) Comparison between ETFE (red), smoothed ETFE (blue, dashed) and an 11th-order parametric estimate (black) of the free cantilever. The response of the smoothed ETFE and the parametric estimate coincides over a wide range of frequencies.

Image of FIG. 4.
FIG. 4.

Bode plot of the empirical transfer function estimate (ETFE) for the surface-coupled cantilever as obtained from the jump-to-contact response. The transmission zeros are at the same frequencies as for the free cantilever. The resonances are shifted to higher frequencies as compared to the free cantilever in Fig. 3.

Image of FIG. 5.
FIG. 5.

(Color online) Pole-zero map of the parametric estimate with a sampling rate of . The weakly damped poles and zeros close to the unit circle correspond to the mechanical characteristics of the cantilever.


Generic image for table
Table I.

Summary of the resonant frequencies and . The values were obtained by sweeping the driving frequency and the parameter estimation procedure, respectively. The corresponding modal quality factors are also given.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Estimating the transfer function of the cantilever in atomic force microscopy: A system identification approach