Piezoelectric flextensional actuator (PFA) devices are increasingly being applied in precision mechanics, such as nanotechnology equipments, electronic microscopy instruments, cell manipulation systems, and microsurgery tools. These PFAs need to be characterized by measuring the produced nanodisplacements, and optical interferometry is well established as an accurate and precise technique for this application. In this paper, a new and efficient method for optical phase detection, here named generalized J ₁ /J ₃ method, is presented. As in the J ₁ /J ₃ conventional method, the new method is based on information contained in the photodetected signal spectrum when the drive voltage is sinusoidal and has a known frequency. The dynamic range of this method is from 0.26 to 100π rad (and higher), and only a limited number of frequencies in the magnitude spectrum of the photodetected signal are used, without the need to know the phase spectrum. The method has the advantages of being simple, passive homodyne, self-consistent, and immune to fading. Using the new method, two novel PFAs prototypes, designed using topology optimization method, are tested in terms of displacement linearity (relative to applied voltage) and frequency response.

Synthetic-heterodyne demodulation is a useful technique for dynamic displacement and velocity detection in interferometric sensors, as it can provide an output signal that is immune to interferometric drift. With the advent of cost-effective, high-speed real-time signal-processing systems and software, processing of the complex signals encountered in interferometry has become more feasible. In synthetic heterodyne, to obtain the actual dynamic displacement or vibration of the object under test requires knowledge of the interferometer visibility and also the argument of two Bessel functions. In this paper, a method is described for determining the former and setting the Bessel function argument to a set value, which ensures maximum sensitivity. Conventional synthetic-heterodyne demodulation requires the use of two in-phase local oscillators; however, the relative phase of these oscillators relative to the interferometric signal is unknown. It is shown that, by using two additional quadrature local oscillators, a demodulated signal can be obtained that is independent of this phase difference. The experimental interferometer is a Michelson configuration using a visible single-mode laser, whose current is sinusoidally modulated at a frequency of 20 kHz. The detected interferometer output is acquired using a 250 kHz analog-to-digital converter and processed in real time. The system is used to measure the displacement sensitivity frequency response and linearity of a piezoelectric mirror shifter over a range of 500 Hz to 10 kHz. The experimental results show good agreement with two data-obtained independent techniques: the signal coincidence and denominated n-commuted Pernick method.

Multiactuated piezoelectric flextensional actuators (MAPFAs) is a fast-growing technology in development, with a wide range of applications in precision mechanics and nanotechnology. In turn, optical interferometry is an adequate technique to measure nano/micro-displacements and to characterize these MAPFAs. In this work, an efficient method for homodyne phase detection, based on a well-known Bessel functions recurrence relation, is developed, providing practical applications with a high dynamic range. Fading and electronic noise are taken into account in the analysis. An important advantage of the method is that, for each measurement, only a limited number of frequencies in the magnitude spectrum of the photodetected signal are used, without the need to know the phase spectrum. The dynamic range for phase demodulation is from 0.2 to $100\pi \mathrm{rad}$ (or 10 nm to 16 μm for displacement, using 632.8 nm wavelength). The upper range can be easily expanded by adapting the electronic system to the signal characteristics. By using this interferometric technique, a new XY nanopositioner MAPFA prototype is tested in terms of linearity, displacement frequency response, and coupling rate.

An efficient and cost effective optical phase detection vibrometer based on a modified closed loop homodyne Michelson interferometer is presented. Real-time phase demodulation is carried out, using an embedded platform that performs data acquisition, signal processing, PI (proportional-integral) control and the generation of signals that drive the electrooptic Pockels cell phase shifter and the piezoelectric actuator under test. Two phase quadrature signals are generated from a single interferometric output, using the interleaving action, in alternation, of a digitally generated modulating signal, and then the wellknown differential-cross-multiplication technique is applied to perform the computation of the phase shift of interest. The quadrature condition is reached using the PI loop based on an error signal obtained from a Lissajous figure derived from out-of-phase signals. The vibrometer is capable of measuring nanometric displacements, and is simple, inexpensive, accurate, immune to fading and self-consistent. The new method was used to determine the displacement frequency response curves of two prototypes of multi-actuated flextensional piezoelectric actuators. Measurements were made between 500 Hz and 15 kHz, and the results agreed with those obtained by the standard SCM-Signal Coincidence Method.

Modern smart grid designs demand reliable sensors throughout the power delivery systems, not only to monitor the quality of the electrical energy generated by different technologies (wind, solar, hydroelectric, thermoelectric, nuclear), but also as an integral part of the generation, transmission, and distribution networks control systems. Laser polarimetric interferometry is a very suitable technique for the implementation of high sensitivity measurement instruments for various physical quantities, in particular, for high-voltage sensing. However, because the polarimetric technique is extremely sensitive to small refractive indexes variations induced in electro-optic materials by the electric field or voltage to be measured, it is also sensitive to spurious environmental quantities such as temperature variations. In this work, a novel optical voltage sensor (OVS) in conjunction with an efficient real-time method for optical phase demodulation and a PI feedback control method for signal fading suppression is demonstrated. Linearity for sinusoidal voltages having amplitudes up to 8.2 kV was evaluated, with an accuracy of 0.2% in the OVS nominal operating range. The OVS bandwidth of 5 kHz is sufficient for most electrical power quality sensor applications. Nonsinusoidal signals with high harmonic content were tested resulting in a total harmonic distortion that differed by only 0.12% from that measured by an HV reference probe. Responses to transient disturbances were also determined, showing the capability of the system to detect spikes.

Optical voltage sensors are widely used for high-voltage (HV) sensing, but the measurement accuracy is often compromised by a sensitivity drift due to variations in the ambient conditions. Synthetic-heterodyne demodulation is a useful technique for dynamic displacement measurements using interferometric sensors as it can provide a detected signal that is immune to an interferometric drift. In this paper, a new synthetic-heterodyne technique, employing the Hilbert transform and gain control feedback, is applied to a polarimetric-based optical sensor system and used to measure an HV signal. The system comprises an He-Ne laser source, optical phase modulator, and HV sensor located between two polarizers followed by a photodetector and real-time electrical signal acquisition and processing. The use of a control loop results in significant improvements in the stability and accuracy of the detected HV signal. The sensor system was used to measure a 60-Hz HV signal with an amplitude range of 300 V to 7.5 kV. The sensor was also used to successfully measure the total power line harmonic distortion of a highly distorted 4 kV signal. The experimental results show very good agreement with measurements obtained by using the industry standard signal coincidence method.