Dual-heterodyne Kelvin probe force microscopy

• Benjamin Grévin,
• Fatima Husainy,
• Dmitry Aldakov and
• Cyril Aumaître

Beilstein J. Nanotechnol. 2023, 14, 1068–1084, doi:10.3762/bjnano.14.88

• signal for that purpose. Unfortunately, contrary to the case of measurements performed in data-cube spectroscopy (shown hereafter), it is here not possible to determine the phase reference level (Φ0). It is still possible, however, to draw a partial conclusion from the examination of the phase data

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

• Berkin Uluutku and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 453–465, doi:10.3762/bjnano.11.37

• lowest value of the current occurs when the cosine reaches its maximum value. Since the oscillation phase reference is arbitrary, it is convenient to replace the time variable as follows: Note that the left-hand side of Equation 4 depends on the variable τ, whereas the right-hand side depends on t

Correction to "Energy dissipation in multifrequency atomic force microscopy"

• Valentina Pukhova,
• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2014, 5, 667–667, doi:10.3762/bjnano.5.78

• /bjnano.5.78 Keywords: band excitation; multifrequency atomic force microscopy (AFM); phase reference; wavelet transforms; In the section "Energy dissipation" of the above manuscript, there is a typesetting error in the mathematical expressions after Equation 5. The correct form must be: The energy

Energy dissipation in multifrequency atomic force microscopy

• Valentina Pukhova,
• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2014, 5, 494–500, doi:10.3762/bjnano.5.57

• evolution is studied by wavelet analysis techniques that have general relevance for multi-mode atomic force microscopy, in a regime where few cantilever oscillation cycles characterize the tip–sample interaction. Keywords: band excitation; multifrequency atomic force microscopy (AFM); phase reference

• usefulness of the sinc function as a phase reference, consider the following identities: where ω = 2π/T. These identities show that as the shaping factor a tends to zero, the sinc function tends to a Dirac delta function that can be expressed as an infinite sum of cosines of increasing frequencies all with

• sinc function allows to obtain a phase reference for every oscillation frequency that composes the signal in the neighborhood of the sinc peak. Note that the XWT rapidly tends to zero off the peak of the sinc function because its amplitude decreases rapidly. WT and XWT are particularly useful in