Piezoelectric mirror shifter transfer function measurement, modelling, and analysis using feedback based synthetic-heterodyne Michelson interferometry

Laser vibrometry has many applications in non-contact dynamic displacement and vibration measurement. A test beam reflected from a target and a reference beam are combined and detected by a photodiode; the photodetected signal is then processed to determine the target displacement and vibration. This paper describes the use of a 9 kHz measurement bandwidth system, consisting of a Michelson interferometer and self-correcting feedback synthetic-heterodyne signal processing technique, to measure the displacement impulse response of a commercial piezoelectric mirror shifter (PMS), consisting of a mirror mounted on a Piezoelectric transducer and a connecting 50 Ω electrical coaxial cable. The actual non-ideal applied impulse and measured impulse response data were used in conjunction with the instrument variable method to determine a Laplace domain linear transfer function approximation to the actual PMS transfer function. The best transfer function fitting, having a 84% normalized root mean square goodness of fit, was obtained using a 5-th order transfer function having two complex conjugate pole pairs, with associated natural frequencies of 6.29 and 6.79 kHz, and a single real pole. The transfer function zeros consisted of a single complex conjugate zero pair, having an antiresonance frequency of 6.38 kHz and a single real zero. Knowing the analytic transfer function of PMS based nanopositioners is useful for example in the design of closed-loop phase-locked interferometers for wideband sensing.