Correction method for dynamic measurement with an optical lever AFM (Effects of ambient fluid and surface force)

Cantilever vibration in an optical lever AFM is theoretically analyzed considering the effect of surface force and ambient fluid. The surface force between the tip and the sample is modeled using a cantilever with a spring and damping added to the tip, and the effect of ambient fluid on the cantilever vibration is analyzed using the bead model. The amplitude ratios of the forced vibration were derived by solving the equation of motion. There are discrepancies between the amplitude ratio derived from bending vibration theory and that obtained through the optical lever method. The amplitude ratio from bending vibration theory reveals that the effect of surface force dominates primarily below the second resonant frequency. The tip-added spring affects the resonant frequency shift and amplitude ratio, while the tip-added damping mainly affects the amplitude ratio at the resonant frequency. In contrast, the amplitude ratio considering the optical lever method reveals that anti-resonance occurs when the tip-added spring constant is positive, which is not observed in bending vibration theory. The amplitude ratio of the cantilever is modified by introducing a correction factor. The correction factor decreases with excitation frequency except for the frequency where the anti-resonance occurs. The correction factor becomes small when the ambient fluid has high density and viscosity.