New improved version of J1…J4 interferometry method and its application to nanometric vibration measurements

Piezoelectric ceramics, such as PZT, can generate subnanometric displacements, but in order to generate multi-micrometric displacements, they should be either driven by high electric voltages (hundreds of volts), or operate at a mechanical resonant frequency (in narrow band), or have large dimensions (tens of centimeters). A piezoelectric flextensional actuator (PFA) is a device with small dimensions that can be driven by reduced voltages and can operate in the nano- and micro scales. Interferometric techniques are very adequate for the characterization of these devices, because there is no mechanical contact in the measurement process, and it has high sensitivity, bandwidth and dynamic range. A low cost open-loop homodyne Michelson interferometer is utilized in this work to experimentally detect the nanovibrations of PFAs, based on the spectral analysis of the interferometric signal. By employing the well known J1...J4 phase demodulation method, a new and improved version is proposed, which presents the following characteristics: is direct, self-consistent, is immune to fading, and does not present phase ambiguity problems. The proposed method has resolution that is similar to the modified J1...J4 method (0.18 rad); however, differently from the former, its dynamic range is 20% larger, does not demand Bessel functions algebraic sign correction algorithms and there are no singularities when the static phase shift between the interferometer arms is equal to an integer multiple of π/2 rad. Electronic noise and random phase drifts due to ambient perturbations are taken into account in the analysis of the method. The PFA nanopositioner characterization was based on the analysis of linearity between the applied voltage and the resulting displacement, on the displacement frequency response and determination of main resonance frequencies.