Interferometric Displacement Research Articles

Solving Phase Ambiguity in Interferometric Displacement Measurement With Millimeter-Wave FMCW Radar Sensors

The frequency-modulated continuous-wave (FMCW) radar sensor is subject to phase ambiguity in measuring large displacement of over half a wavelength, which is particularly severe in the millimeter-wave FMCW radar sensor due to its short wavelength. The state-of-the-art linear phase demodulation techniques were mostly developed for single tone quadrature continuous-wave (CW) radars such as the Modified differentiate and cross-multiply (MDACM) algorithm. This paper presents a novel linear interferometric displacement measurement technique which can synthesize the quadrature <inline-formula> <tex-math notation="LaTeX">${I}/{Q}$ </tex-math></inline-formula> signals across slow time from a single-channel FMCW radar. In this way, the linear phase demodulation technique developed for the CW radar can now be leveraged for the FMCW radar. The theoretical analysis and working principles are discussed. Exhaustive experiments are performed to validate the proposed technique. It is demonstrated that the displacement motions as large as 10 times of the wavelength can be precisely extracted from a single channel FMCW radar with micrometer accuracy and without any phase ambiguity.

Features of an acousto-optical two-channel laser displacement interferometer with multi-frequency photodetectors with subpycometer resolution

The article discusses the issues of improving acousto-optical (AO) heterodyne laser displacement interferometers (LDI) by using two independent multi-frequency photodetectors: high- frequency (HF) and low-frequency (LF) low-noise, working with "fast inaccurate" and "slow accurate" measuring channels, respectively. The "fast inaccurate" channel allows you to measure displacements with high velocity peed movements. The scheme of the "slow accurate" channel is based on the joint operation of a phase-locked frequency system and a small-range phase meter, providing high resolution for low velocity. Such a scheme of AO LDI most fully implements its capabilities in the control of start-stop cyclic movements of objects, providing high resolution at the initial and final stages of movements with low velocity. A metrological analysis of the "slow accurate" channel is carried out, the possibilities and conditions for achieving AO LDI at low velocity of subpicometer resolution 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.

Ultra-Precision and High-Speed Laser Interferometric Displacement Measurement Technology and Instrument

Ultra-Precision and High-Speed Laser Interferometric Displacement Measurement Technology and Instrument

Основы совершенствования схемотехники высокоточных быстродействующих акустооптических лазерных интерферометров перемещений с частотным согласованием составляющих блоков и двойного гетеродинирования на этапе фотопреобразования

The article discusses the development of the circuitry of acousto-optic (AO) laser displacement interferometers (LDI) and the values of resolution and speed of controlled displacements achieved by them. The issues of frequency matching of blocks of AO LDI are discussed: AO modulator, photodetector device (FDD) and frequency generator. The features of phototransformation of the FDD under its illumination by three spatially combined optical streams are studied. Of these, two streams are of different frequencies, created as a result of diffraction in the AO modulator and are used to measure the phase shift from the controlled displacements of the object in the AO LDI. The third optical stream is amplitude-modulated with a frequency close to the difference frequency of the first two optical streams. This technique leads to a twofold transfer (double heterodination) of the phase shift from the offsets to the electrical signal of the difference frequency between the three optical streams. The schemes of AO LDI with a constant value of the frequency of the amplitude-modulated optical flow and with its auto-tuning are considered. The features of the use of cooled FDD in AO LDI are discussed.

К вопросу достижения субпикометрической разрешающей способности акустооптическим двухканальным лазерным интерферометром перемещений с двумя разночастотными фотоприемниками

The article discusses an acousto-optical (AO) heterodyne laser displacement interferometer (LDI) with two different-frequency photodetectors: highfrequency (HF) and low-frequency (LF) low-noise, working with «fast inaccurate» and «slow accurate» measuring channels, respectively. The mode of operation of AO LDI at start-stop cyclic motions of objects is described, which provides high resolution at the initial and final stages of motions with low speeds of motion. A metrological analysis of the «slow accurate» channel is carried out taking into account the noise frequency characteristics of photodetectors with the formation of its so-called «optimistic» and «pessimistic» variants. Based on the metrological analysis carried out, the frequency ranges of the signal are determined, which allow achieving the resolution of AO LDI subpicometric values at low speeds.

Гомодинный квадратурный интерферометр перемещений. Эксперимент

In the previous work, the results of mathematical modeling of the optical scheme of a single-pass homodyne interferometer of displacements with the quadrature principle of phase registration are presented. The interferometer is built according to the Michelson scheme, and polarizing optical elements are used to obtain quadrature signals. The interferometer is supposed to be used as part of a new national standard of the kilogram based on watt balance method for precision measurements of the displacement and speed of the coil in the vertical direction. In this paper, experimental studies of the operation of a model of a homodyne quadrature displacement interferometer are presented. In this work, instead of a polarization beam splitter, a conventional (non-polarization) beam splitter and two polarizers are used in the optical scheme of a homodyne interferometer in the registration units. This added additional degrees of freedom when aligning optical channels for recording interference channels and made it possible to achieve the required signal shift by 90° with an accuracy of 0.1°. As a result, a displacement measurement error of 02. nm was experimentally achieved. Generalized expressions are obtained for quadrature signals for arbitrary azimuths of polarizers in three channels of recording interference signals. An assessment of the accuracy of displacement measurements using a quadrature homodyne interferometer was carried out and it was obtained that the expanded uncertainty of such measurements does not exceed 0.3 nm.

Periodic-Error-Free All-Fiber Distance Measurement Method With Photonic Microwave Modulation Toward On-Chip-Based Devices

High-accuracy distance measurements with compact configurations and robust operations are necessary in areas ranging from precision engineering to scientific missions. Here, we report a precise and accurate amplitude-modulation-based all-fiber distance measurement method without periodic errors. To realize an all-fiber configuration toward on-chip devices in the future, certain selective components for easy fabrication on the chip scale were employed. Despite this constraint, sub-100 nm precision was demonstrated with the help of the all-photonic microwave mixing technique introduced in our previous work. In this article, accuracy as another important factor for measuring distances was investigated to ensure better performance than in previous studies with an optical amplitude-modulation technique. By performing theoretical and experimental analyses of the periodic error while blocking electrical crosstalk signals and optimizing signal processing, accuracy of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.6~\mu \text{m}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1~\sigma $ </tex-math></inline-formula> ) was achieved in terms of measurement linearity according to a comparison with a laser displacement interferometer. With the best capabilities of precision and accuracy, the proposed all-fiber distance measurement method is expected to be utilized in diverse long-distance applications, such as large-machine axis tool work and formation flying by multiple satellites. Further, this study demonstrates the possibility of developing an on-chip-based distance-measuring device for the fourth industrial revolution.

Simultaneous mapping of nanoscale dielectric, electrochemical, and ferroelectric surface properties of van der Waals layered ferroelectric via advanced SPM

Ferroelectric surfaces involve a complex interplay between polarization and dielectric properties, internal and external surface charge screening, and ionic and electrochemical effects. There is currently no good way to simultaneously capture all the required information at appropriate length scales. To this end, we present an advanced scanning probe microscopy approach for simultaneously mapping surface potential, dielectric, and piezoelectric properties on the nanoscale. For quantitatively mapping electromechancial properties, we utilize interferometric displacement sensing piezoresponse force microscopy, which measures the effective piezoelectric coefficient free of background artifacts such as the cantilever body electrostatics. The dielectric and surface electrochemical properties are captured during G-mode electrostatic force microscopy/Kelvin probe force microscopy operated in the lift mode. We show the capabilities of this approach on the chemically phase separated composite sample consisting of a van der Waals layered ferroelectric CuInP2S6 phase and a non-polar In4/3P2S6 phase. Finally, we demonstrate domain structure evolution during thermally stimulated phase transition.

Deep/Transfer Learning with Feature Space Ensemble Networks (FeatSpaceEnsNets) and Average Ensemble Networks (AvgEnsNets) for Change Detection Using DInSAR Sentinel-1 and Optical Sentinel-2 Satellite Data Fusion

Differential interferometric synthetic aperture radar (DInSAR), coherence, phase, and displacement are derived from processing SAR images to monitor geological phenomena and urban change. Previously, Sentinel-1 SAR data combined with Sentinel-2 optical imagery has improved classification accuracy in various domains. However, the fusing of Sentinel-1 DInSAR processed imagery with Sentinel-2 optical imagery has not been thoroughly investigated. Thus, we explored this fusion in urban change detection by creating a verified balanced binary classification dataset comprising 1440 blobs. Machine learning models using feature descriptors and non-deep learning classifiers, including a two-layer convolutional neural network (ConvNet2), were used as baselines. Transfer learning by feature extraction (TLFE) using various pre-trained models, deep learning from random initialization, and transfer learning by fine-tuning (TLFT) were all evaluated. We introduce a feature space ensemble family (FeatSpaceEnsNet), an average ensemble family (AvgEnsNet), and a hybrid ensemble family (HybridEnsNet) of TLFE neural networks. The FeatSpaceEnsNets combine TLFE features directly in the feature space using logistic regression. AvgEnsNets combine TLFEs at the decision level by aggregation. HybridEnsNets are a combination of FeatSpaceEnsNets and AvgEnsNets. Several FeatSpaceEnsNets, AvgEnsNets, and HybridEnsNets, comprising a heterogeneous mixture of different depth and architecture models, are defined and evaluated. We show that, in general, TLFE outperforms both TLFT and classic deep learning for the small dataset used and that larger ensembles of TLFE models do not always improve accuracy. The best performing ensemble is an AvgEnsNet (84.862%) comprised of a ResNet50, ResNeXt50, and EfficientNet B4. This was matched by a similarly composed FeatSpaceEnsNet with an F1 score of 0.001 and variance of 0.266 less. The best performing HybridEnsNet had an accuracy of 84.775%. All of the ensembles evaluated outperform the best performing single model, ResNet50 with TLFE (83.751%), except for AvgEnsNet 3, AvgEnsNet 6, and FeatSpaceEnsNet 5. Five of the seven similarly composed FeatSpaceEnsNets outperform the corresponding AvgEnsNet.

Comparison of three testing methods of rock materials equations of state

For rock materials, it is very important to use effective and reliable testing methods to obtain accurate Hugoniot parameters and further determine the equation of state (EOS) reflecting the intrinsic properties of materials. In this paper, taking marble as the experimental sample, three test methods of the Hugoniot EOS (i.e., symmetric, asymmetric, and reverse impacts) are proposed based on the first-class light gas gun experimental platform. The Displacement Interferometer System for Any Reflector is used to measure the speed history of the target plate and the arrival time of the shock wave. The electric probe is used to measure the speed of the flyer. Under the same launch conditions, at least three repeated experiments were conducted for each scheme. The experimental results showed that when the relative standard deviation (RSD) of the launch speed was controlled within 2%, the RSD of post-wave pressure and shock wave speed in the reverse impact method was the smallest, making it the best choice for the measurement of the Hugoniot EOS of rock materials. However, the symmetric impact can evaluate the impact flatness of the flying plate and the target plate by the time difference between the shock wave to reach different positions on the same plane of the target.

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.

A bilateral comparison of NIST and PTB laser power standards for scale realization confidence by gravitational wave observatories

The gravitational wave (GW) observatories calibrate interferometer displacement using photon momentum, with laser power serving as the measurand. These observatories are traceable to the International System of Units through a primary standard maintained by the US’s National Metrology Institute (NMI), the National Institute of Standards and Technology (NIST). The bilateral degree of equivalence of laser power measurements for various NMIs indicated in the 2010 EUROMET.PR-S2 supplementary comparison reveals scale realization uncertainty unacceptably large for GW event parameterization. We offer here an analysis to identify the source of the discrepancy between the Physikalisch-Technische Bundesanstalt (PTB) and NIST results. Using an improved transfer standard in a bilateral comparison, with representatives of the Laser Interferometer Gravitational-Wave Observatory (LIGO) receiving results prior to their comparison, NIST and PTB demonstrated a degree of equivalence of −0.15% with an uncertainty of 0.95% (k = 2) for combined 100 mW and 300 mW comparison results.

Improving force sensitivity by amplitude measurements of light reflected from a detuned optomechanical cavity

The measurement of weak continuous forces exerted on a mechanical oscillator is a fundamental problem in various physical experiments. It is fundamentally impeded by quantum back-action from the meter used to sense the displacement of the oscillator. In the context of interferometric displacement measurements, we here propose and demonstrate the working principle of a scheme for coherent back-action cancellation. By measuring the amplitude quadrature of the light reflected from a detuned optomechanical cavity inside which a stiff optical spring is generated, back-action can be cancelled in a narrow band of frequencies. This method provides a simple way to improve the sensitivity in experiments limited by quantum back-action without injection of squeezed light or stable homodyne readout.

Correction of periodic displacement non-linearities by two-wavelength interferometry

Non-linearities in interferometric displacement measurements commonly affect both homodyne and heterodyne optical interferometers. Unwanted back reflections (ghost reflections) or polarisation leakage introduce non-linearity terms at harmonics of the illuminating wavelength that cannot be fully corrected for with standard non-linearity correction techniques. A two-wavelength interferometric approach, operating at 632.8 and 785 nm, is presented here that is capable of correcting such non-linearities. Non-linearities are separated from the difference between two displacement measurements made at differing wavelengths with a Fourier approach. Compared to a standard Heydemann ellipse fitting correction, the proposed approach reduces estimated residual non-linearities from 84 to 11 pm in the case of a linear displacement profile. In particular this approach is applicable to the correction of higher order non-linearities that are caused by multiple reflections, and that are therefore very sensitive to alignment conditions.

A nonlinear characteristic line model of the detonation process of aluminized explosives

Aiming at the non-ideal properties of aluminized explosive, a local isentropic hypothesis of the expansion of aluminized explosive detonation product was proposed, and a nonlinear characteristic line model for aluminized explosive detonation was established, which provides a new theoretical analysis method for studying the non-isentropic flow and the expansion of detonation products. A lot of studies have shown that for micron aluminum powder, the reaction mainly occurs in the expansion zone of detonation products. The aluminum powder was treated as inert in the detonation reaction zone in the model. Considering the reaction rate of the aluminum powder is relatively slow, the expansion process of the detonation products of aluminized explosive was divided into finite time regions. The energy released from the reaction of aluminum powder has a relaxation effect on the state of the products. Based on the relaxation effect, it was assumed that the detonation products flow was approximately isentropic in each time region. Due to the reaction of aluminum powder, the entropy in each time region was different. Based on the theory of isentropic flow of ideal explosive and local isentropic hypothesis, the non-isentropic expansion process of the detonation products of aluminized explosives can be analyzed theoretically. To verify the correctness of the model, metal plate experiments were conducted. Experiments on aluminized explosives and LiF explosives with a particle diameter of 5μm and 50μm to drive 0.5 mm and 1 mm metal plates were designed. The velocity history of the metal plate was measured by a laser displacement interferometer, and then the reaction degree of aluminum powder in the detonation products was calculated from the experimental results. Combined with the nonlinear characteristic line model of the detonation products of aluminized explosives, the velocity of the metal plate driven by aluminized explosives was calculated theoretically. Compared with the experimental results, the non-isentropic model can well describe the contribution of the secondary reaction of aluminum powder to the work ability of explosives, which verifies the correctness of the model for aluminized explosives (micron aluminum powder).

Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements.

Capacitive sensors are widely used in industrial applications, such as CNC machine tools, where reliable positioning in the micrometer range with nanometer accuracy is required. Hence, these sensors are operated in harsh industrial environments. The accuracy of these sensors is mainly limited by slope errors and nonlinearities. In practice, the required accuracy of these sensors is achieved by a calibration against a metrological high-quality reference such as interferometric displacement measurement systems. This usually involves the use of high-order polynomials as calibration functions based on empirical data. In metrology, this is only the second-best approach and has disadvantages in terms of stability over the measurement range of the instrument. In addition, the validity of these empirical calibrations over time is questionable, and the associated uncertainty can only be roughly estimated. This makes regular recalibration of such sensors at short intervals mandatory to ensure the reliability of the displacement measurement. In this paper, we report on our investigations of the different parameters that affect the accuracy of capacitive sensors. Since the capacitance of these sensors results from the electric fields that build up between the electrodes, these field lines are calculated using FEM simulation models for typical commercial sensors. In the following the influence of various geometric parameters such as edge radius, guard ring size and shape, or thickness of the electrodes are individually analyzed according to their impact on the accuracy of these sensors. Based on these simulations, the deviations of the capacitance as they arise for real detector geometries can then be compared with idealized, de facto unrealizable parallel plate capacitors. This methodology allows overall uncertainty of capacitive sensors to be decomposed into their individual components and sorted in terms of their contribution to the uncertainty budget. The individual FEM-based analysis then enables a systematic analysis of the sources of uncertainty and, thus, reveals possibilities to improve manufacturing processes for capacitive sensors, to put these sensors on a solid metrological basis, and to improve the performance of these displacement measurement systems in the long run, i.e., to provide better sensors for the application.

Tracing method based on heterodyne interferometer for scanning electron microscopes

In this study, a tracing method for a scanning electron microscope was developed based on a heterodyne interferometer, which can directly trace the measured values to the laser wavelength and then to the internationally defined meter length reference. In this method, a sample scanning motion is introduced, and the measuring mirror of the interferometer is fixed on the sample stage. The movement and displacement of the sample stage is recorded by the laser interferometer displacement measurement system, which synchronously collects the secondary electrons or backscattered electron signals excited on the sample surface. The feature size of the sample is measured, and the value can be traced directly to the international unit of length using the frequency-stabilized laser reference, which proves that the proposed method is an absolute measurement method. This study analyzed the specific technology implementation methods and experimental results, including positioning control of the displacement system and its measurement and control during the measurement process. Measurement uncertainty budgets are also discussed. Experimental measurements were carried out and their accuracy was verified. Results showed that this method could effectively obtain the performance parameters of the feature size intuitively and significantly improve the measurement accuracy.

Comparison of Submillinewton Thrust Measurements Between a Laser Interferometer and a Load Cell on a Pendulum Balance

Reliable measurements of thrust from systems to be flown on satellites are essential to ensure repeatable maneuvering capability of small nanosatellites. Thrusters can be used to vary spacecraft orientation, detumbling, and orbit change. Tests have been conducted in a low-pressure vacuum system using a cold gas prototype thruster and two independently calibrated methods: a four-point pendulum with a laser interferometer displacement sensor and a load cell, both of which have measurement capabilities from tens of micronewtons to tens of millinewtons. The agreement is very good, lending confidence in both methods. The advantages and disadvantages of both methods will be discussed. They include absolute accuracy, low thrust accuracy, temporal resolution, simplicity of operation, cost, and sensitivity to vibrations generated by laboratory equipment such as pumps, fans, bumps, and human movement.

Influence of installation error of grating interferometer on high-precision displacement measurement

We investigated a high-precision grating interferometer displacement measurement system that can be applied to high-end immersion lithography machines and explained its composition and measurement algorithm. By analyzing the optical path variation caused by the installation error of the grating interferometer, we calculated the influence of the installation error on the displacement measurement. A displacement measurement model of a grating interferometer using three read heads was established, and the influence of the model coefficients on the displacement measurement model was analyzed. The simulation results show that, under the condition that the error of the measurement model in the X direction and the Y direction is <0.1 nm, the translation error of the read head should be within ±100 μm, and the relative rotation deviation between the two read heads or two gratings placed along the diagonal should be within ±50 μrad. The methods and results of studying the influence of grating interferometer installation error on the displacement measurement provide a theoretical basis for the application of a grating interferometer displacement measurement system in immersive high-end lithography scanners.