Resolution Of Displacement Measurement Research Articles

High-precision angular rate detection based on an optomechanical micro hemispherical shell resonator gyroscope.

Cavity optomechanics with picometer displacement measurement resolution has shown vital applications in high-precision sensing areas. In this paper, an optomechanical micro hemispherical shell resonator gyroscope (MHSRG) is proposed, for the first time. The MHSRG is driven by the strong opto-mechanical coupling effect based on the established whispering gallery mode (WGM). And the angular rate is characterized by measuring the transmission amplitude changing of laser coupled in and out from the optomechanical MHSRG based on the dispersive resonance wavelength shift and/or dissipative losses varying. The detailed operating principle of high-precision angular rate detection is theoretically explored and the fully characteristic parameters are numerically investigated. Simulation results show that the optomechanical MHSRG can achieve scale factor of 414.8 mV/ (°/ s) and angular random walk of 0.0555 °/ h1/2 when the input laser power is 3 mW and resonator mass is just 98 ng. Such proposed optomechanical MHSRG can be widely used for chip-scale inertial navigation, attitude measurement, and stabilization.

A Study of 2D Contour Measurement System at Tool Center Point of Machine Tools

This study proposes a 2D contour measurement system at the tool center point (TCP) that consists of a Blu-ray pickup head and position sensitive detector (PSD). The TCP displacement is equivalent to the relative position between the tool and workpiece. When the machine tools operate the machine part along the desired contour, the TCP displacement affects the machining geometric accuracy. To evaluate the TCP displacement, the contour errors are measured by the cross-grid encoder (KGM) in practice. However, it is difficult to install KGM as it is large and expensive. In this study, an optical measurement system (OMS) is constructed to measure the TCP displacement, named TCP-OMS. A Blu-ray pickup head was installed on the spindle as a tool, and a PSD was installed on the table as a workpiece. To enhance the measurement signal’s resolution and precision of TCP-OMS, the noise was reduced by an AC voltage stabilizer, a DC regulator, and a low-pass filter. The experimental results show that the resolution of displacement measurement was less than 1 μm, and the linearity regions of the X-orientation and Y-orientation were ±3 mm. The motion test on the circular paths were performed on an actual machine tool, and the repeatability tests of this measurement system were verified. The measurement data of circular paths were collected by TCP-OMS and KGM and the results were then compared. When the feed rate of the circular paths increased, the circular deviations were magnified, simultaneously. The axis reversal spikes were observed at the quadrants of a circular path. These measurement results of TCP-OMS matched with the measurement results of KGM. The TCP-OMS developed in this study is characterized by simple installation, compactness, and a low price. It is suitable for 2D contour measurement at the tool center point of machine tools.

On the Sensitivity of Microwave Fabry–Perot Interferometers for Displacement Detection

Microwave interferometers have been attractive devices for high-precision measurements of displacement-related physical quantities in a variety of scientific and engineering applications. However, due to the long operating wavelength, the displacement measurement resolution of microwave interferometers is limited to the micrometer scale. In this article, we propose and demonstrate a novel technology based on microwave interferometry for displacement measurements with potential picometer resolution. An open-ended (OE) transmission line resonator based on a homemade hollow coaxial cable is explored in proof-of-concept numerical and experimental investigations. The technique involves two stages of displacement sensitivity amplification: one is the open end-based phase sensitivity amplification, and the other is the destructive interference-based phase sensitivity amplification. We experimentally demonstrate a wavelength sensitivity amplification factor of 1800 through spectral interrogation where only the open end-based amplification is involved, and a phase sensitivity amplification factor of 1.4 million through phase interrogation where both the open end-based amplification and the destructive interference-based phase shift amplification are involved, i.e., two-stage phase shift amplified microwave interferometry (TPAMI). The numerical investigations and the experimental results match well.

Image-type displacement measurement resolution improvement without magnification imaging

The imaging-type displacement measurement (IDM) technique is better-suited to high-resolution measurement than the traditional moiré fringe technique. In Angular displacement measurement, IDM generally requires lens-magnified imaging processes to reach the proper resolution, which depends on overly large imaging lenses and highly complex, generally unreliable equipment, making the technique not conducive to industrial application. The resolution of an IDM device was improved in this study without the use of an imaging lens. The lensless imaging principle was established, then a new algorithm based on multi-line fusion and denoising was developed to improve the displacement subdivision resolution. The proposed algorithm was verified by both simulation and experimentation. The simulation shows that the proposed algorithm effectively reduces positioning operation noise. In the experiment, an angular measurement resolution of 0.039″ (25-bit) was achieved on a 70 mm diameter circular grating. The proposed method lays a foundation for further high-resolution displacement measurement techniques.

An image-based method for evaluating local deformations of saturated sand in undrained torsional shear tests

An image-based measurement system was developed to evaluate the induced local deformations of saturated sand specimens in undrained torsional shear tests. The images of specimens taken by a camera in front of a pressure chamber were noticeably distorted. To correct the errors caused by the curvature of the specimens and by the refraction of rays traveling through water, acrylic resin, and the atmosphere, a coordinate correction method was proposed to convert the apparent coordinates obtained from the distorted specimen image into the real coordinates under planar conditions. This method was verified using a rigid dummy specimen and was illustrated using a sand specimen as an example. The results obtained indicate that the resolution of displacement measurements is approximately 0.01 mm, representing approximately 3.3e-5 of the specimen height. Moreover, high measurement accuracy is obtained even if the dummy specimen has undergone a rotation of up to 26.4°. This measurement system was further extended to directly evaluate the local deformation of sand specimens through a transparent membrane. The direct and indirect evaluations indicate that the direct evaluation is more effective for quantitatively representing specimen deformation than indirect evaluation since membrane wrinkles and vertical slippage between the specimen and membrane occurred during liquefaction.

Probing the Theoretical Ultimate Limit of Coaxial Cable Sensing: Measuring Nanometer-Scale Displacements

Open-ended coaxial probes have been widely explored and commercialized for dielectric spectroscopy at microwave frequencies over the past decades. The working principle of the probes relies on the dependence of the fringing field on the complex permittivity of the material in front of the open end. In this article, inspired by the optical fiber extrinsic Fabry–Perot interferometer, we propose a novel sensing scheme based on an open-ended hollow coaxial cable resonator (OE-HCCR). The resonator is constructed using two reflectors along the coaxial line. The first reflector is a metal post at the RF input end, shorting the inner and outer conductors. The second reflector is the open end, where a metal plate is placed parallel and near the open end. The resonance frequency of the open-ended coaxial resonator depends strongly on the gap distance between the metal plate and the open end of the coaxial cable, due to the modulation of the phase of the reflection coefficient that characterizes the open end. Thus, by correlating the resonance frequency to the gap distance between the metal plate and the open end (or the movement of the metal plate), the OE-HCCR can be used as a displacement sensor device. Importantly, the displacement measurement resolution of the OE-HCCR is three orders of magnitude greater than that of the existing coaxial-cable-based displacement sensors within a certain dynamic range (~0.11 mm), affording a resolution that is comparable to fiber-optic sensors. The mathematical model of the OE-HCCR is discussed in detail, followed by a proof of concept for displacement measurements. The novel OE-HCCR device is suitable for sensing applications in harsh environments and will advance the field of physical/chemical sensing.

Self-Aligning and Self-Calibrating Capacitive Sensor System for Displacement Measurement in Inaccessible Industrial Environments

High-precision positioning often requires high speed and high resolution displacement measurements in order to compensate for the small vibrations of critical components. The displacement sensor must be precise and stable over a long period of time to avoid expensive recalibration. This requires tight mounting tolerances, which are especially difficult to meet in inaccessible environments. The proposed sensor system is based on a capacitive sensor and consists of three subsystems: 1) a mechanical “zoom-in” system that performs self-alignment of the capacitive sensor electrode in order to reduce the mounting tolerances of the sensor; 2) a real-time capacitance-to-digital converter that employs an internal reference and electrical zoom-in technique to effectively reduce the dynamic range of the measured capacitance, thus improving the power efficiency; and 3) a self-calibration circuit that periodically calibrates the internal references to eliminate their drift. In previous publications, the three subsystems have been introduced. This paper shows how the different subsystems can be integrated to achieve optimal performance and presents new repeatability and stability measurement results. The overall system demonstrates a displacement measurement resolution of 65 pm (in terms of capacitance 65 aF) for a measurement time of 20 $\mu \text{s}$ . Furthermore, the thermal drift of the sensor is within 6 ppm/K, owing to the self-calibration circuit. In measurement mode, the system consumes less than 16 mW.

Wavelength Modulating Self-Mixing Interferometer

Self-mixing interference (SMI) was used to measure the displacement with a resolution of λ/2 by counting the interference signal peaks. In order to increase the measurement accuracy beyond λ/2, sinusoidal wavelength modulation (SWM) technique is introduced in SMI in this paper. Wavelength modulation of the laser beam is obtained by sinusoidal modulating the injection current of the laser diode. Fourier analysis method is proposed to demodulate the phase. Experimentally, the micro-movements of a high precision commercial PZT have been reconstructed, which can obtain a displacement measurement resolution of a few nanometers. It provides a potential displacement sensor with high accuracy and quite compact configuration.

Three-degree-of-freedom common-path laser measurement system

Common optical path arrangement was adopted to design a three-degree-of-freedom laser measurement system for measuring 1D displacement and 2D angles of a moving stage simultaneously on the basis of the principles of Michelson interference and laser auto-collimation. In the displacement measurement, the fine resolution of displacement measurement was achieved by using optical path difference doubling technique. Combined with polarization interference technology and signal differential processing, high-quality displacement output signal was obtained. In the angle measurement, changes in yaw and pitch of a moving stage caused the position change of the mirror which was mounted on the stage. The incident beam was reflected by the mirror and detected by a four-quadrant detector. According to the position change of the spot, yaw and pitch angles were obtained. The stability, resolution tests and the comparison experiments with the British Renishaw XL-80 laser interferometer were done. Experimental results show that the system has the resolution of 0.8 nm for displacement measurement and 0.2″ for angle measurement. Compared with the results of Renishaw XL-80 laser interferometer, the maximum deviation of displacement is less than 100 nm within the measurement range of 50 mm. The maximum deviations of yaw and pitch are 0.5″ and 0.4″.

Displacement Measurement of Sub-nanometre Resolution for Positioning System

A sub-nanometer resolution displacement measuring method, basing on fringe phase shifting, is developed in this paper. The system mainly consists of a grating interferometer and a phase-shift device. The principle of interfere fringe phase-shifting is to move the photoelectric sensor between the two interference fringes. The method leads to higher resolution in theory than that with laser interferometer. Measuring and positioning experiments to verify the method are made and the’ results indicate that the new displacement measuring method will improve the positioning accuracy about 16%. The displacement measurement resolution with the new method will reach to sub-nanometre in theory.

High-resolution spatiotemporal strain mapping reveals non-uniform deformation in micropatterned elastomers

Micropatterns are generated on a vast selection of polymeric substrates for various applications ranging from stretchable electronics to cellular mechanobiological systems. When these patterned substrates are exposed to external loading, strain field is primarily affected by the presence of microfabricated structures and similarly by fabrication-related defects. The capturing of such nonhomogeneous strain fields is of utmost importance in cases where study of the mechanical behavior with a high spatial resolution is necessary. Image-based non-contact strain measurement techniques are favorable and have recently been extended to scanning tunneling microscope and scanning electron microscope images for the characterization of mechanical properties of metallic materials, e.g. steel and aluminum, at the microscale. A similar real-time analysis of strain heterogeneity in elastomers is yet to be achieved during the entire loading sequence. The available measurement methods for polymeric materials mostly depend on cross-head displacement or precalibrated strain values. Thus, they suffer either from the lack of any real-time analysis, spatiotemporal distribution or high resolution in addition to a combination of these factors. In this work, these challenges are addressed by integrating a tensile stretcher with an inverted optical microscope and developing a subpixel particle tracking algorithm. As a proof of concept, the patterns with a critical dimension of 200 µm are generated on polydimethylsiloxane substrates and strain distribution in the vicinity of the patterns is captured with a high spatiotemporal resolution. In the field of strain measurement, there is always a tradeoff between minimum measurable strain value and spatial resolution. Current noncontact techniques on elastomers can deliver a strain resolution of 0.001% over a minimum length of 5 cm. More importantly, inhomogeneities within this quite large region cannot be captured. The proposed technique can overcome this challenge and provides a displacement measurement resolution of 116 nm and a strain resolution of 0.04% over a gage length of 300 µm. Similarly, the ability to capture inhomogeneities is demonstrated by mapping strain around a thru-hole. The robustness of the technique is also evaluated, where no appreciable change in strain measurement is observed despite the significant variations imposed on the measurement mesh. The proposed approach introduces critical improvements for the determination of displacement and strain gradients in elastomers regarding the real-time nature of strain mapping with a microscale spatial resolution.

Linked Ball Bar for Flexible Motion Error Measurement for Machine Tools

A measuring instrument, Linked Ball Bar (LBB), is developed to measure machine tool motion errors quickly, flexibly, and robustly. The LBB employs the concept of double ball bar (DBB) and measures the distance between two balls attached to the spindle and table. The problem of short measurement range, the drawback of the DBB, is solved using a link. The measurement accuracy of the LBB is investigated. The analytical resolution of displacement measurement using the LBB is under 30 nm when the displacement direction coincides with the sensitivity direction. The difference between the LBB and the laser interferometer is less than 1 μm in the center measurement range of 75 mm. The repeatability of the LBB is ±0.4 μm and is at the same level as the interferometer. The kinematic error of a five-axis machine tool is measured using the LBB to demonstrate its validity. The parallelism between the C-axis and Z-axis identified using the LBB agrees with the result measured using the cylindrical square. The difference between the LBB and the cylindrical square is about 10 μm/m at the maximum. The LBB can provide quick and flexible measurements of the motion errors of five-axis machine tools.

Displacement measurement using a laser feedback grating interferometer.

A novel laser feedback grating interferometer (LFGI) with a phase-generated carrier demodulation technique is proposed in this paper. Laser feedback grating interference occurs when light emitted from a laser is diffracted by the double-diffraction system and re-enters the laser active cavity, thus generating a modulation of the lasing field. In order to improve the displacement measurement resolution, phase modulation is introduced by an electro-optic modulator in the external cavity of the LFGI. Detection of the displacement can be easily achieved by the time-domain orthogonal demodulation, which does not involve any complicated calculation and is insensitive to the sampling error. Experimental results show that the proposed system has a general nanometer-level resolution. It provides a potential displacement sensor with high resolution, simple mechanical structure, and good reliability.

Micro-displace sensor based on self-mixing interference of the fiber laser with phase modulation

Micro-displacement measurement based on self-mixing interference using a fiber laser system was demonstrated. The sinusoidal phase modulation technique was introduced into the fiber laser self-mixing interference measurement system to improve the measurement resolution. The phase could be demodulated by the Fourier analysis method. Error sources were evaluated in detail, and the system was experimentally applied to reconstruct the motion of a high-precision commercial piezoelectric ceramic transducer (PZT). The displacement measurement resolution was well beyond a half-wavelength. It provides a practical solution for displacement measurement based on all optical-fiber sensing applications with high precision.

Simultaneous measurement of temperature and infinitesimal displacement using the high cladding mode coupling loss in fiber Bragg grating

A novel application of fiber Bragg grating (FBG) cladding modes for simultaneously measuring infinitesimal displacement alteration and temperature is presented. The above 30-dB high cladding mode coupling loss with 0.1nm narrow bandwidth can be easily obtained using the photosensitive fiber with hydrogen loading technique. The wavelength shifts and the variations of coupling loss of the narrow resonances facilitate the measurement of infinitesimal displacement change, as well as the central wavelength of fiber Bragg grating can provide the surrounding temperature information. The 25μm displacement measurement resolution can be obtained if the wavelength interrogator of 1pm accuracy is used. The temperature sensing resolution can reach around 0.1°C in the range from 20 to 120°C.

Self-mixing interferometry based on nanometer fringes and polarization flipping

Self-mixing interferometry (SMI) based on nanometer fringes and polarization flipping is realized. The interferometer comprises a single-mode He-Ne laser and a high-amplitude reflectivity feedback mirror. The nanometer fringes are obtained by tilting the external feedback mirror. The fringe density is 35 times higher than that derived with conventional two-beam interference, and each fringe corresponds to a λ/70 displacement in external cavity length. Moreover, polarization flipping occurs when the external feedback mirror moves in the opposite direction. Such movement can be used to easily distinguish displacement direction. Experimental results show an optical resolution of displacement measurement of 9.04 nm with a range of 100 µm. The proposed SMI presents promising application prospects in precisely measuring displacement and calibrating other micro-displacement sensors because of its optical wavelength traceability.

Quadrature demodulation technique for self-mixing interferometry displacement sensor

A new, to the best of our knowledge, signal processing method based on quadrature demodulation technique is presented for laser diode self-mixing interferometry(LDSMI) displacement sensor. Phase modulation of the laser beam is obtained by an electro-optic modulator (EOM) in the external cavity. Detection of the target's displacement can be easily achieved by sampling the interference signal at those times which satisfied certain conditions. The major advantage of the technique is that it does not involve any complicated calculation and insensitive to the sampling error. Experimental results show that the proposed method can effectively improve the displacement measurement resolution of the laser diode self-mixing displacement sensor to a few nanometers.

Intersatellite laser ranging with homodyne optical phase locking for Space Advanced Gravity Measurements mission

In this paper, we present the scheme and the preliminary results of an intersatellite laser ranging system that is designed for the Earth's gravity recovery mission proposed in China, called Space Advanced Gravity Measurements (SAGM). The proposed intersatellite distance is about 100 km and the precision of inter-satellite range monitoring is 10 nm/Hz(1/2) at 0.1 Hz. To meet the needs, we designed a transponder-type intersatellite laser ranging system by using a homodyne optical phase locking technique, which is different from the heterodyne optical phase-locked loop used in GRACE follow-on mission. Since an ultrastable oscillator is unnecessary in the homodyne phase-locked loop, the measurement error caused by the frequency instability of the ultrastable oscillator need not be taken into account. In the preliminary study, a heterodyne interferometer with 10-m baseline (measurement arm-length) was built up to demonstrate the validity of the measurement scheme. The measurement results show that a resolution of displacement measurement of about 3.2 nm had been achieved.

Measurement of small displacement based on surface plasmon resonance heterodyne interferometry

Abstract This paper proposes an optical method for measuring small displacements using the surface plasmon resonance (SPR) heterodyne interferometry. A heterodyne light beam reflected by a mirror passes through a hemisphere glass and then enters into a surface plasmon resonance apparatus at the resonant angle. A small displacement of the mirror will introduce a phase-difference variation between p - and s -polarizations of the light emerging from the SPR apparatus. The phase-difference variation can be precisely measured with the heterodyne interferometric technique, and the associated displacement can be estimated. The feasibility of this method was verified by experiment, and the displacement measurement resolution of about 1.4 nm over a traveling range of 6 μm was achieved. Our method of measurement has the merits of both common-path interferometry and heterodyne interferometry.

Phase subdivision of absolute coding grating in displacement measurement

A phase subdivision of absolute coding grating is proposed to improve the resolution and precision of displacement measurement. The used grating consists of multiple code channel grating of Gray code, and the basic code channel is high frequency Rochi grating. Fourier analysis method is adopted to extract the phase value of grating in decoding, and the wrapped phase distribution of basic code channel is obtained by Fourier transform, filtering, and inverse Fourier transform, then the unwrapped phase distribution could be recovered using the phase order information of Gray code. High resolution of phase subdivision can be achieved via linear fitting of phase distribution. Analysis of the basic principle and the subdivision of the phase to improve the resolution of displacement measurement have also been described in this paper. Experimental results show that the resolution and precision of absolute coding grating is enhanced greatly after phase subdivision and calibration.