Noise reduction by signal combination in Fourier space applied to drift correction in optical tweezers
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(a) Characterization of noise in the optical tweezers setup. is the noise distribution of position B measured by method A. The subscript “trap” refers to the bead trapped in the laser focus, “stage” refers to the bead on the micropipette (which is connected to the stage). Bead positions can be measured by the QPD or the CCD camera and can be set by the piezo. Measured noise distributions and the resulting function are plotted against frequency. is close to one (or zero) at frequencies where is much bigger (or smaller) than . (b) Characterization of the QPD method. Piezo-induced displacements of the bead on the micropipette () are measured with the laser beam focused on the bead, whose deflection is measured with the QPD ().2,3 The linear relationship indicates that can accurately measure bead positions. Also displayed is as a function of time in the absence of piezo steering to the scale of the y axis. It shows that drift in this signal stays in the linear regime within the timescale of our experiments.
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Force-extension data on a single DNA molecule held between the beads as measured by optical tweezers. (a) Force applied on the DNA molecule is plotted against . The multiple stretching curves do not overlap due to stage drift at long time scales (orange box in the inset). The blue arrows indicate the timeline of one stretching-relaxation cycle. (b) The force is plotted against . The stretching curves do overlap (orange box in the inset), but the fast movements of the bead in the trap during the hysteretic transitions are not well resolved. (c) The force is plotted against , the stretching curves overlap and fast movements during the hysteretic transitions are retained.
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