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Image processing for resonance frequency mapping in atomic force modulation microscopy
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Image of FIG. 1.
FIG. 1.

Spring-mass approximation for the cantilever-tip-sample system. is the effective mass of both cantilever and tip, is the cantilever stiffness, and is the sample stiffness.

Image of FIG. 2.
FIG. 2.

Typical cantilever’s resonance spectra in contact with PS and PB. A Lorentzian fit allows the estimation of the constant relative to the equivalent linear oscillator model for the cantilever.

Image of FIG. 3.
FIG. 3.

(a) Experimental and theoretical points describing a circle. Far from resonance, the points tend toward the never reached point (0,0). Near resonance, is always diametrically opposed to (0,0). (b) Experimental points are correctly fitted by the theoretical circle after a rotation from an angle . Such a correction is necessary to take into account the electronics’ transfer function of the system.

Image of FIG. 4.
FIG. 4.

Images of real part and imaginary part of the cantilever’s vibration at frequency .

Image of FIG. 5.
FIG. 5.

Resonance frequency and half-width at half-height images obtained by processing of the real and imaginary part images.

Image of FIG. 6.
FIG. 6.

The contact modulation seen as a small variation of indentation around a mean value . The contact force, represented according to Hertz theory, is the sum of static component and a dynamical component .


Generic image for table
Table I.

Experimental values for resonance frequency and half-width of resonance curve, calculated complex contact stiffness, and viscoelastic modulus for PS and PB.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Image processing for resonance frequency mapping in atomic force modulation microscopy