Noise in combined optical microscopy and dynamic force spectroscopy: Toward in vivo hydration measurements
Deflection noise density characterization of the mechanical noise in our MFP-3D-BIO system. These curves show the power spectrum of the deflection signal of a cantilever in water in the Asylum Research closed liquid cell which is in contact with a mica surface on a 25 mm diameter no. 1.5 coverslip with the virtually zero feedback. The baseline noise is 72 pm rms. This increases to 180 pm when the 60× oil immersion objective is brought into contact with the coverslip. With the objective in contact and liquid cooled CCD running, the rms mechanical noise increases to 825 pm This can be mediated by increasing the focus tension of the optical microscope and locking the objective focus, reducing the value to 530 pm. Using smaller 12 mm diameter coverslips produces stronger mechanical coupling and 1070 pm rms.
(Color online) This plot shows the frequency shift noise density calculated using the model in Kobayashi et al. (Ref. 16) 2009 modified to include the noise due to vibration as well as the roll-off in frequency shift with increasing . The force law used in this calculation was estimated from frequency shift distance data measured in our AFM (Ref. 22). The noise density has been calculated for tip-sample separation of 1 nm and several deflection sensor noise levels (5, 10, 50, 100, 200, 500, and ). Other model parameters are as follows: an oscillation amplitude of 1 nm, a cantilever spring constant of 40 N/m, an oscillation frequency of 150 kHz, and factor of 6 in liquid. Solid black curves include vibrations, modeled with a flat frequency response, at a rms level corresponding to the baseline noise on an AFM mounted on an inverted optical microscope. Vibrations are excluded from the calculation in the dotted curves. For lower values of the deflection sensor noise the vibrations dominate the noise density and are a significant contribution at higher deflection sensor noise levels (Asylum AFM is ).
Solid curve in (a) is the frequency shift distance curve calculated using the empirical results of Higgins et al., 2006 (Ref. 8). The points represent the addition of noise appropriate to our AFM including vibrations (deflection sensor noise: and vibration noise: ). The problem is inverted in (b) where the data points are the force calculated from the frequency shift in (a) and the solid line is the empirical force law fit to the data. The parameters recovered from the fit are close to those of the original input.
Shown in (a) and (b) are sample frequency shift distance curves collected above mica in water (a) and mica in OMCTS (b). Raw data are shown as points while the lines have been filtered using a Savitzky–Golay filter for analysis using our supervised peak finding code. Hundreds of frequency shift distance curves from different experiments and tips in water and OMCTS were analyzed and molecular spacings calculated to generate the histograms shown in the insets in (a) and (b). In water, the average peak spacing was found to be 0.24 nm and in OMCTS the average peak spacing was found to be 0.75 nm in good agreement with reported values (Ref. 19). It should be noted that although the measured quantity is a frequency shift, under mechanical excitation in liquid, the measured frequency shift can be affected by parasitic resonances (Refs. 23 and 24). but peak spacings are unaffected. We also compared FM (c) and PM (d) measurements using Nanosensor PPP-FMAuD tips and found the hydration peaks to be readily observable in AM mode with very high signal-to-noise.
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