Histogram of the quality factor, Q, obtained from fits to synthetic data of a noisy Lorentzian; ε = 0.001, A 0 = 1, f 0 = 1, Q 0 = 100 ≫ 1, and β = 5. Similar results are obtained for all other fit parameters, and for a narrower fit range of β = 2 (not shown). Fit to Gaussian distribution (solid line).
Histograms of the resonant frequencies, f R , and quality factors, Q, obtained from fits to measurements of cantilever PSD. Measured means: f 0 = 31.15 kHz, Q 0 = 43.41. Amplitude histograms affected by thermal drift (not shown). Fits to Gaussian distributions (solid lines).
Averaged periodograms (N ave = 50) of the cantilever, with Lorentzian fits (solid lines), for minimum and maximum fitted quality factors: (a) Q = 36.10, and (b) Q = 53.49. Mean quality factor for the entire sample set is Q 0 = 43.41.
Comparison of relative standard deviations of simulation data (Fig. 1) and Eq. (12), for all fit parameters, for β = 5 (similar agreement found for β = 2). Variable X represents specified fit parameters and ε = 0.001 has been normalized from the results.
Comparison of relative standard deviations for resonant frequency, f R , and quality factor, Q, of cantilever measurements (Fig. 2) and Eq. (17). Variable X represents specified fit parameters.
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