Principle of the measurement sensitivity calibration based on contact detection method, illustrated using a sequential two-experiment example with distinct initial oscillation amplitudes: (a) oscillation amplitude A m and (b) oscillation amplitude A n . Principle of the contact detection mechanism is illustrated in (c), wherein three consecutive cycles with distinct tip-sample interactions: no contact, exact contact and after contact are shown.
(a) Schematic of signal processing and control modules implemented in FPGA along with the hardware integration. (b) Hardware environment for implementation of the proposed measurement sensitivity calibration algorithm, including the Cyclone IV FPGA board, the ADC (ADS5424, TI, sampling rate 50 MHz) and the DAC (DAC8811, TI, update rate 2 MHz). (c) Side-view SEM image of the magnetic particle (10 μm diameter) attached onto the backside of the cantilever above the tip location.
Bottom-view SEM images of (a) Cantilever A, PPP-CONTAuD from Nanosensors, (b) Cantilever B, lever 2 of TR800PSA from Olympus, (c) Cantilever C, HYDRA2R-100NG from AppNano. All three cantilevers were imaged with 200× magnification. The dotted circles on the cantilever body indicate the laser spot locations on the backside of the cantilevers where measurement sensitivities were calibrated.
Calibration of the measurement sensitivities of (a) the first dynamic mode and (b) the second dynamic mode of Cantilever A using the method based on contact detection. In each figure, squares represent seven sets of recorded contact point data corresponding to distinct initial oscillation amplitudes and the solid line is the least-square fitting result, wherein the slope of the fitted line represents the measurement sensitivity of the specific dynamic mode.
(a) Comparison of the measurement sensitivity ratios between the second and first dynamic modes of Cantilever A from the experimental calibration (square) and the analytical calculation (solid line). (b) Reconstructed mode shapes of the first (solid line) and the second (dotted line) dynamic modes using identified mode wavelength α i and Eq. (6) . Mode shapes were normalized so that Φ i (1) = −1.
(a) Determination of the sample surface position with the cantilever excited at the first dynamic mode and gently tapping the sample surface. The solid horizontal line, formed by the lowest points of the reconstructed tip position in each cycle, shows the vertical position of the sample surface. (b) Tip position reconstruction with the calibrated measurement sensitivities of the first (dotted line) and the second (solid line) dynamic modes, respectively, when the cantilever was excited at the second dynamic mode and gently tapped the sample surface. To find the case of gentle tapping shown in (b), a series of deflection signals, corresponding to monotonously increased oscillation amplitudes of the cantilever excited at the second dynamic mode, were measured. Three of them associated with distinct tip-sample interactions: (c) without tapping, (d) gentle tapping, and (e) hard tapping are shown.
Calibration results of the measurement sensitivities of the first and second dynamic modes for Cantilevers A–C. S 1 and S 2 are the calibrated measurement sensitivities of the first and second dynamic modes, respectively, with the standard deviation of the results of five calibration experiments listed as error. The static measurement sensitivity S 0 calibrated from the deflection-distance curve is listed and compared with the calibrated S 1, with the percentage relative difference shown in parenthesis. Furthermore, the converted S 1 calculated from S 0 using correction factor χ is also listed and compared with the calibrated S 1. The resonance frequencies of the first and second dynamic modes of all three cantilevers used in water are listed as follows: Cantilever A, f 1 = 3.2 kHz, f 2 = 26 kHz; Cantilever B, f 1 = 3.9 kHz, f 2 = 30 kHz; Cantilever C, f 1 = 0.8 kHz, f 2 = 20 kHz.
Calibration results of the measurement sensitivities of the first and second dynamic modes for Cantilever A (PPP-CONTAuD) at seven distinct laser spot locations along the cantilever longitudinal axis. The laser spot location is denoted as l b /L, i.e., the relative laser spot location compared to the total length of the cantilever.
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