Calibrating oscillation response of a piezo-stage using optical tweezers

In optical tweezers, a piezo-stage (PZT) is widely used to precisely position samples for force clamp, calibrating optical trap and stretching DNA. For a trapped bead in solution, the oscillation response of PZT is vital for all kinds of applications. A coupling ratio, actual amplitude to nominal amplitude, can be calibrated by power spectral density during sinusoidal oscillations. With oscillation frequency increasing, coupling ratio decreases in both x- and y-directions, which is also confirmed by the calibration with light scattering of scanning two aligned beads on slide. Those oscillation responses are related with deformability of chamber and the intrinsic characteristics of PZT. If we take nominal amplitude as actual amplitude for sinusoidal oscillations at 50 Hz, the amplitude is overestimated ~2 times in x-direction and ~3 times in y-direction. That will lead to huge errors for subsequent calibrations.