Abstract
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.
Highlights
Laser interferometry has many applications in the measurement of dynamic displacement and velocity of vibrating objects [1,2,3,4]
In this paper we describe the application of the latter system, having a measurement bandwidth extending from approximately 200 Hz to 9 kHz, to measure the impulse response of a Piezoelectric Mirror Shifter (PMS)
The experimental applied impulse was not an ideal impulse and as such its amplitude spectrum monotonically decreases with frequency; thereby the PMS transfer function cannot be determined by taking the inverse Laplace transform of the measured impulse response
Summary
Laser interferometry has many applications in the measurement of dynamic displacement and velocity of vibrating objects [1,2,3,4]. Many different signal processing methods have been investigated to recover the dynamic phase shift; the detection sensitivity can be adversely affected by environmentally induced optical path variations. Synthetic-heterodyne (SH) processing is useful as it eliminates slowly varying changes in sensitivity due to environmentally induced optical path variations such as those caused by temperature fluctuation induced refractive index changes [5,6]. The resulting photodetected signal is a frequency modulated type signal, the phase of which is the sum of two components: a slowly varying component due to environmental fluctuations and a component proportional to the vibration signal. Knowing the transfer function of PMS based nanopositioners is required for example in the design of closed-loop phase-locked interferometers for wideband sensing [9]
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