Interferometric Displacement Sensor Research Articles

Accurate vertical nanoelectromechanical measurements

Piezoresponse Force Microscopy (PFM) is capable of detecting strains in piezoelectric materials down to the picometer range. Driven by diverse application areas, numerous weaker electromechanical materials have emerged. The smaller signals associated with them have uncovered ubiquitous crosstalk challenges that limit the accuracy of measurements and that can even mask them entirely. Previously, using an interferometric displacement sensor (IDS), we demonstrated the existence of a special spot position immediately above the tip of the cantilever, where the signal due to body-electrostatic (BES) forces is nullified. Placing the IDS detection spot at this location allows sensitive and BES artifact-free electromechanical measurements. We denote this position as xIDS/L=1, where xIDS is the spot position along the cantilever and L is the distance between the base and tip. Recently, a similar approach has been proposed for BES nullification for the more commonly used optical beam deflection (OBD) technique, with a different null position at xOBD/L≈0.6. In the present study, a large number of automated, sub-resonance spot position dependent measurements were conducted on periodically poled lithium niobate. In this work, both IDS and OBD responses were measured simultaneously, allowing direct comparisons of the two approaches. In these extensive measurements, for the IDS, we routinely observed xIDS/L≈1. In contrast, the OBD null position ranged over a significant fraction of the cantilever length. Worryingly, the magnitudes of the amplitudes measured at the respective null positions were typically different, often by as much as 100%. Theoretically, we explain these results by invoking the presence of both BES and in-plane forces electromechanical forces acting on the tip using an Euler–Bernoulli cantilever beam model. Notably, the IDS measurements support the electromechanical response of lithium niobate predicted with a rigorous electro-elastic model of a sharp PFM tip in the strong indentation contact limit [deff≈12pm/V, Kalinin et al., Phys. Rev. B 70, 184101 (2004)].

Superconducting gravimeters based on advanced nanomaterials and quantum neural network

The paper is focused on a new concept of a cryogenic-optical sensor intended for use in the space industry, geodynamics, and fundamental experiments. The basis of the sensor is a magnetic suspension with a levitating test body, a high-precision optical recorder of mechanical coordinates of the levitating body, and a signal-processing system. A Michelson-type interferometer with a laser diode and a single-mode optical fiber was used to measure the test body's displacements. The coordination of the laser diode coherence length and the difference in the interferometer optical lengths of the arms made it possible to eliminate coherent noise caused by interference from spurious reflections. The minimum recorded shift of the test body was 0.1 nm. The design of the sensor and the mathematical model of the superconducting suspension dynamics are presented. The results of experimental studies of a magnetic suspension together with an optical interferometric displacement sensor having a subnanometer sensitivity are shown.

A displacement sensor based on balloon-like optical fiber structure

A modal interferometric fiber-optic displacement sensor based on the balloon-like structure is investigated experimentally. When the bending radius of the balloon-like structure is reduced to 3.0 mm, the displacement sensitivity could reach up to 71.49 nm/mm. Moreover, the evolution process of the transmission spectra in a wide dynamic displacement range exceeding 22 mm is analyzed, which can provide guiding significance for sensor designing. The proposed displacement sensor is extremely low-cost, robust, and compact.

Anisotropic epitaxial stabilization of a low-symmetry ferroelectric with enhanced electromechanical response.

Piezoelectrics interconvert mechanical energy and electric charge and are widely used in actuators and sensors. The best performing materials are ferroelectrics at a morphotropic phase boundary, where several phases coexist. Switching between these phases by electric field produces a large electromechanical response. In ferroelectric BiFeO3, strain can create a morphotropic-phase-boundary-like phase mixture and thus generate large electric-field-dependent strains. However, this enhanced response occurs at localized, randomly positioned regions of the film. Here, we use epitaxial strain and orientation engineering in tandem-anisotropic epitaxy-to craft a low-symmetry phase of BiFeO3 that acts as a structural bridge between the rhombohedral-like and tetragonal-like polymorphs. Interferometric displacement sensor measurements reveal that this phase has an enhanced piezoelectric coefficient of ×2.4 compared with typical rhombohedral-like BiFeO3. Band-excitation frequency response measurements and first-principles calculations provide evidence that this phase undergoes a transition to the tetragonal-like polymorph under electric field, generating an enhanced piezoelectric response throughout the film and associated field-induced reversible strains. These results offer a route to engineer thin-film piezoelectrics with improved functionalities, with broader perspectives for other functional oxides.

Correlating Crystallographic Orientation and Ferroic Properties of Twin Domains in Metal Halide Perovskites.

Metal halide perovskite (MHP) solar cells have attracted worldwide research interest. Although it has been well established that grain, grain boundary, and grain facet affect MHPs optoelectronic properties, less is known about subgrain structures. Recently, MHP twin stripes, a subgrain feature, have stimulated extensive discussion due to the potential for both beneficial and detrimental effects of ferroelectricity on optoelectronic properties. Connecting the ferroic behavior of twin stripes in MHPs with crystal orientation will be a vital step to understand the ferroic nature and the effects of twin stripes. In this work, we studied the crystallographic orientation and ferroic properties of CH3NH3PbI3 twin stripes, using electron backscatter diffraction (EBSD) and advanced piezoresponse force microscopy (PFM), respectively. Using EBSD, we discovered that the orientation relationship across the twin walls in CH3NH3PbI3 is a 90° rotation about ⟨1̅1̅0⟩, with the ⟨030⟩ and ⟨111⟩ directions parallel to the direction normal to the surface. By careful inspection of CH3NH3PbI3 PFM results including in-plane and out-of-plane PFM measurements, we demonstrate some nonferroelectric contributions to the PFM responses of this CH3NH3PbI3 sample, suggesting that the PFM signal in this CH3NH3PbI3 sample is affected by nonferroelectric and nonpiezoelectric forces. If there is piezoelectric response, it is below the detection sensitivity of our interferometric displacement sensor PFM (<0.615 pm/V). Overall, this work offers an integrated picture describing the crystallographic orientations and the origin of PFM signal of MHPs twin stripes, which is critical to understanding the ferroicity in MHPs.

Multimodal fringe detection for a self-mixing interferometry-based vibration sensor.

Robust detection of interferometric fringes is critical for accurate sensing by self-mixing interferometric (SMI) displacement sensors. Mode-hopping of a laser diode (LD) can potentially diversify SMI fringes, transforming them from mono-modal to multimodal. Thus, fringe detection of a multimodal SMI signal becomes a bigger challenge as the relative strength of each mode may be different, leading to further diversity in the fringes belonging to each regime. Also the SMI signals from each mode are incoherently added, so the composite multimodal SMI signal is of complex nature. In this paper, a robust method is proposed for the detection of multimodal fringes, which is also able to detect traditionally encountered mono-modal fringes. Since fringes are actually peaks of SMI signals, the proposed method detects all of these peaks and separates the genuine peaks that correspond to true fringes from the falsely detected peaks, corresponding to false fringes. An experimental dataset of 60 SMI signals was acquired by using two different LDs to validate our proposed method. The proposed method has correctly detected the SMI fringes with an accuracy of 99.6%. However, at the same time, 0.7% false fringes were also detected while 0.3% true fringes were undetected by the proposed method.

Sub-7-nm textured ZrO2 with giant ferroelectricity

An ~6.5 nm pure ZrO2 thin film with a giant ferroelectric remanent polarization (Pr) of ~50 μCcm−2 and an effective piezoelectric coefficient (d33) of 7−9 pm/V is reported. The film was prepared on a (111)-oriented Pt electrode using plasma-enhanced atomic layer deposition at 300 °C, followed by annealing at 400 °C, and exhibited a preferred orientation of the orthorhombic (111) planes in the in-plane direction. The Pr value of ~50 μCcm−2 is the largest reported to date for both perovskite and fluorite nanoscale ferroelectric thin films (< 120 nm) on a Pt electrode. Furthermore, the processing temperature of 300−400 °C is the lowest reported to date to produce a Pr of ~50 μCcm−2 in nanoscale ferroelectrics on a Pt electrode. The giant Pr, ascribed to the preferred crystal orientation, was confirmed by the positive-up negative-down (PUND) polarization measurement with a long delay time to allow the relaxation of polarization. The effective d33 was obtained using piezoresponse force microscopy with an interferometric displacement sensor to minimize the frequency-dependent artifacts and the effects of cantilever dynamics. The low-temperature preparation of the textured ZrO2 ultrathin film with a giant Pr is extremely advantageous for device scaling and process integration in advanced nanoelectronics.

Thickness and strain dependence of piezoelectric coefficient in BaTiO3 thin films

We explore the thickness dependence of the converse piezoelectric coefficient (${d}_{33}$) in epitaxial thin films of ${\mathrm{BaTiO}}_{3}$ (BTO) grown on (001) ${\mathrm{SrTiO}}_{3}$ substrates. Piezoresponse force microscope was performed using an atomic force microscope equipped with an interferometric displacement sensor allowing direct quantification of electromechanical coupling coefficients in BTO free from unwanted background contributions. We find that 80-nm-thick films exhibit a ${d}_{33}$ of $\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}20.5\phantom{\rule{0.16em}{0ex}}\mathrm{pm}/\mathrm{V}$, but as the thickness is reduced, the ${d}_{33}$ reduces to less than 2 pm/V for a 10 nm film. To explain the atomistic origin of the effect, we performed molecular dynamics simulations with a recently developed ab initio-derived reactive force field, constructed using the ReaxFF framework. Simulations predict that under applied electric fields thin films of ${\mathrm{BaTiO}}_{3}$ show an increasing thickness, with compressive strain, of the region screening the depolarization-field. This study confirms quantitatively the drop in piezoelectric performance in BTO ultrathin films and again highlights the importance of the screening mechanisms when films approach the ultrathin limits in dictating the functional behaviors.

A novel digital phase detection method for frequency-modulated continuous-wave interferometric fiber-optic displacement sensor

A novel digital phase detection method is proposed for the high accuracy and large dynamic range interrogation of frequency-modulated continuous-wave (FMCW) interferometric fiber-optic displacement sensors. Firstly, a peak of beat signal is found coarsely, and the range of the peak is obtained. Then golden section is used to find the peak accurately, in which cross-correlation filtering is used to calculate the value of golden section points. The simulation in the MATLAB environment show that the phase discrimination error is 0.073 rad, and displacement error is 9 nm, when the signal-to-noise ratio is 20 dB. In the real-time interrogation of a FMCW fiber-optic displacement sensor, we realized a repeatability error of 3.5 nm, a standard error of 4.5 nm and a linearity of 0.9999. The experimental results show that the method can achieve real-time displacement measurement with high accuracy and large dynamic range.

An Optical Interferometric Triaxial Displacement Sensor for Structural Health Monitoring: Characterization of Sliding and Debonding for a Delamination Process.

This paper presents an extrinsic Fabry–Perot interferometer-based optical fiber sensor (EFPI) for measuring three-dimensional (3D) displacements, including interfacial sliding and debonding during delamination. The idea employs three spatially arranged EFPIs as the sensing elements. In our sensor, the three EFPIs are formed by three endfaces of three optical fibers and their corresponding inclined mirrors. Two coincident roof-like metallic structures are used to support the three fibers and the three mirrors, respectively. Our sensor was calibrated and then used to monitor interfacial sliding and debonding between a long square brick of mortar and its support structure (i.e., a steel base plate) during the drying/curing process. This robust and easy-to-manufacture triaxial EFPI-based 3D displacement sensor has great potential in structural health monitoring, the construction industry, oil well monitoring, and geotechnology.

Noise compensation in a Fabry-Perot-based displacement sensor operating at picometer-level resolution

An approach for compensating the influence of the interrogator noises on the readings of the extrinsic Fabry-Perot interferometric displacement sensor is proposed. With the use of a reference interferometer and special processing, the sensor resolution was about twofold improved and comprised 12-25 pm instead of 15-46 pm for a wide range of EFPI baselines.

A simple pendulum borehole tiltmeter based on a triaxial optical-fibre displacement sensor

Sensitive instruments like strainmeters and tiltmeters are necessary for measuring slowly varying low amplitude Earth deformations. Nonetheless, laser and fibre interferometers are particularly suitable for interrogating such instruments due to their extreme precision and accuracy. In this paper, a practical design of a simple pendulum borehole tiltmeter based on laser fibre interferometric displacement sensors is presented. A prototype instrument has been constructed using welded borosilicate with a pendulum length of 0.85 m resulting in a main resonance frequency of 0.6 Hz. By implementing three coplanar extrinsic fibre Fabry-Perot in-terferometric probes and appropriate signal filtering, our instrument provides tilt measurements that are insensitive to parasitic deformations caused by temperature and pressure variations. This prototype has been installed in an underground facility (Rustrel, France) where results show accurate measurements of Earth strains derived from Earth and ocean tides, local hydro-logic effects, as well as local and remote earthquakes. The large dynamic range and the high sensitivity of this tiltmeter render it an invaluable tool for numerous geophysical applications such as transient fault motion, volcanic strain and reservoir monitoring.

Sensitivity enhancement beyond the wavelength limit in a novel sub-micron displacement sensor.

We propose and demonstrate sub-micron displacement sensing and sensitivity enhancement using a two-frequency interferometer and a Kerr phase-interrogator. Displacement induces phase variation on a sinusoidally modulated optical signal by changing the length of the path that either of the signal's two spectral components propagates through. A Kerr phase-interrogator converts the resulting phase variation into power variation allowing for sub-micron displacement sensing. The sensitivity of this novel displacement sensor is enhanced beyond the wavelength-limited sensitivity of the widely used Michelson interferometric displacement sensor. The proposed approach for sensitivity enhancement creates a whole new class of sensors with ultra-high sensitivity.

Fiber-based distance sensing interferometry.

We present an interferometric displacement sensor based on a folded low-finesse Fabry-Perot cavity. The fiber-optic sensor uses a quadrature detection scheme based on the wavelength modulation of a DFB laser. This enables measuring position changes over a range of 1 m for velocities up to 2 m/s. The sensor is well suited to work in extreme environments such as ultrahigh vacuum, cryogenic temperatures, or high magnetic fields and supports multichannel applications. The interferometer achieves a repeatability of 0.44 nm(3σ) at a working distance of 20 mm, a resolution of 1 pm, and an accuracy of 1 nm.

Direct measurements of irradiation-induced creep in micropillars of amorphous Cu56Ti38Ag6, Zr52Ni48, Si, and SiO2

We report in situ measurements of irradiation-induced creep on amorphous (a-) Cu56Ti38Ag6, Zr52Ni48, Si, and SiO2. Micropillars 1 μm in diameter and 2 μm in height were irradiated with ∼2 MeV heavy ions during uniaxial compression at room temperature. The creep measurements were performed using a custom mechanical testing apparatus utilizing a nanopositioner, a silicon beam transducer, and an interferometric laser displacement sensor. We observed Newtonian flow in all tested materials. For a-Cu56Ti38Ag6, a-Zr52Ni48, a-Si, and Kr+ irradiated a-SiO2 irradiation-induced fluidities were found to be nearly the same, ≈3 GPa−1 dpa−1, whereas for Ne+ irradiated a-SiO2 the fluidity was much higher, 83 GPa−1 dpa−1. A fluidity of 3 GPa−1 dpa−1 can be explained by point-defect mediated plastic flow induced by nuclear collisions. The fluidity of a-SiO2 can also be explained by this model when nuclear stopping dominates the energy loss, but when the electronic stopping exceeds 1 keV/nm, stress relaxation in thermal spikes also contributes to the fluidity.

Resolution limits of extrinsic Fabry–Perot interferometric displacement sensors utilizing wavelength scanning interrogation

The factors limiting the resolution of displacement sensors based on the extrinsic Fabry-Perot interferometer were studied. An analytical model giving the dependency of extrinsic Fabry-Perot interferometric (EFPI) resolution on the parameters of an optical setup and a sensor interrogator was developed. The proposed model enables one to either estimate the limit of possible resolution achievable with a given setup, or derive the requirements for optical elements and/or a sensor interrogator necessary for attaining the desired sensor resolution. An experiment supporting the analytical derivations was performed, demonstrating a large dynamic measurement range (with cavity length from tens of microns to 5mm), a high baseline resolution (from 14pm), and good agreement with the model.

Real time self-mixing interferometric laser sensor for embedded applications

We present a Self-Mixing (SM) interferometric laser displacement sensor that is capable of providing correct target measurements in real time, even when it is subject to extraneous parasitic movements. The sensor achieves such robustness by using an embedded MEMS Solid -State Accelerometer (SSA) that has been coupled with the laser sensor. The SSA thus measures the extraneous movement acting on the laser s ensor and this information is used to provide correct sensing. The proposed SSA-SM sensing system uses Consecutive-Samples based Unwrapping (CSU) to process the SM interferometric signal while a Digital Signal Processor (DSP) takes care of band-pass filtering, double integration as well as phase and gain corrections needed for the acceleration signal. Hence, a compact, real-time, precise and self-aligned SSA-SM sensor has been designed that has a displacement measurement precision of approximately 100 nm with a parasitic movement elimination of 31dB for a laser diode emitting at 785 nm.

Design and Analysis of an Embedded Accelerometer Coupled Self-Mixing Laser Displacement Sensor

This paper presents the operating principle and signal processing needed for the design of a reliable solid-state accelerometer (SSA) coupled self-mixing (SM) interferometric laser displacement sensor for embedded applications. The influence of signal processing methods and accelerometer characteristics on the complete sensing system performance is studied, and four different SSA-SM sensing systems are examined and characterized. Through comparing their performance, the sensing system precision is limited by the noise density of the employed accelerometer as well as the used SM displacement retrieval technique, whereas the system bandwidth is mainly limited by the choice of a given accelerometer. Furthermore, this paper analyzes the phase and gain-matching properties that the SSA-SM should reach to guarantee proper extraneous vibrations correction. Finally, the proof of concept of a real-time SSA-SM sensing system indicating 30-dB correction is presented. This prototype demonstrates the possibility of using such a real-time sensing system for embedded and industrial applications in which the presence of extraneous movements would hinder traditional sensors use.

A temperature-compensated fibre optic extrinsic Fabry–Perot interferometric displacement sensor for fault measurement in geomechanics

A fibre optic extrinsic Fabry–Perot interferometric (EFPI) displacement sensor for fault measurement in geomechanics is experimentally demonstrated. By using a metal tube and metal bars the EFPI displacement sensor can demonstrate high strength and high stability, as the effects of the harsh environment are mitigated. The sensor is fixed to a long stainless steel pipe which is inserted into a drilled hole and placed across the fault zone. In this way, the sensor can be placed easily and accurately in the fault zone. In order to eliminate the influence of temperature two metal bars of different materials, and therefore with different thermal expansion coefficients, are used. Thus, the sensor itself is capable of compensating for temperature. The experimental results show that the ratio of the cavity length to the temperature reduces from 0.142 to −0.045 µm °C−1. In a continuous test, the measurement results vary over a range of 4.954 µm and the standard deviation is 1.196 µm, when the temperature is changed from 17 to 80 °C.

Theoretical analysis of a parallel-plate electroosmotic hydrogel actuation and sensing platform

Abstract This paper addresses the dynamic electrical response of a charged or uncharged hydrogel that is sandwiched between a bottom fixed plate and a top floating, parallel plate. We demonstrate how this configuration might be adopted as a novel chemical- or bio-sensing platform. It might also be used for nano-positioning, or for studying the rheology and physiochemical characteristics of hydrogels. Here, the gel is modelled as a continuum composite comprising a porous, charged, elastic skeleton saturated by an aqueous electrolyte. Electrostatics satisfy the Debye–Huckel approximation, with zero-slip boundary conditions between the skeleton, solvent, and walls. For large channel gaps, the steady electric-field-induced displacement of the top plate is proportional to the difference between the top- and bottom-wall ζ -potentials. Under oscillatory electrical stimulation, resonant peaks, with amplitudes from picometers to micrometers, reflect hydrogel elasticity and charge density. Such displacements are within the detection range of modern interferometric displacement sensors.