Laser Interferometric Measurement Research Articles

Lomb-Scargle spectral analysis of plasma’s noise for space-based laser interferometric gravitational wave antennas

In space-based laser interferometric gravitational wave antennas, plasma from the solar wind is an important noise floor source for laser interferometric measurements between two distant spacecraft. In this study, we aim to analyze the impact of solar wind on the inter-satellite laser interferometric measurements of the Taiji mission, a space-based laser interferometric gravitational wave antenna proposed by the University of Chinese Academy of Sciences. Based on the 6.5-year electron number density data from the National Aeronautics and Space Administration Wind spacecraft and considering the uneven sampling characteristics of the data, we employed the Lomb–Scargle spectral analysis method to study the impact of solar wind plasma on intersatellite laser interferometric measurements within the frequency range of 1×10-6 Hz to 0.01 Hz. The study shows that the effect of the plasma on the intersatellite laser interferometric measurement is approximately 1 pm/Hz at 3.3 mHz, which is one order of magnitude smaller than the requirements on the displacement noise of the interferometric measurement of the Taiji mission, indicating that the noise due to plasma will not affect the aim of the Taiji mission to detect gravitational waves. The research can be applied to Taiji, Laser Interferometer Space Antenna, and future gravitational wave detection missions.

Frequency-modulated continuous-wave laser interferometry measurement method based on cross-correlation

Frequency-modulated continuous-wave (FMCW) laser interferometry technology holds significant potential for applications in the fields of ultraprecision manufacturing and high-precision sensing. This paper proposes a novel approach among current phase demodulation methods is based on cross-correlation to address the challenge of this technology. On the basis of nonlinear correction of a distributed feedback laser, the intercepted beat frequency signal was first preprocessed with Z-score signal normalization and a smoothing filter. Subsequently, the interference beat signal was subjected to processing using a correlation method to derive the correlation function. Finally, the phase difference between adjacent beat signals was determined by pinpointing the maximum value of the cross-correlation function, enabling accurate displacement demodulation. Experimental validation was performed by constructing an FMCW laser interferometric displacement measurement system. The results indicated that the standard deviation of the displacement error for the cross-correlation method was 2.41 nm during static measurements. Compared to conventional maximum-point method, the static measurement error of the cross-correlation method has been reduced by 1.43 times. In dynamic measurements in the 500 μm range, The measurement error of the cross-correlation method has been reduced by 6.04 times, avoiding the dynamic measurement positioning problem of conventional feature point demodulation methods and making the measurement results more accurate. This advancement holds substantial practical value in the realm of phase demodulation in laser interferometry.

Laser interferometer measurement and reconstruction of supersonic projectile acoustic pressure fields

Sensing acoustic fields with a laser interferometer offers several advantages over conventional techniques: the probe beam does not disturb the medium in which it operates, the interferometer optics can be placed far from the source, and interferometry typically has a wider bandwidth than microphones. These advantages are particularly useful in situations where precise measurements of high-amplitude shock-generating sources are required. In this work we use a laser interferometer to study the generation and propagation of shock wave signatures of ballistic projectiles. A laboratory experiment was conducted to collect interferometer data from a variety of supersonic projectiles over a range of standoff distances. Simultaneously-captured microphone data is compared to the interferometer measurements, and techniques for inversion and reconstruction of the sound pressure field are discussed.

Highly sensitive interferometry with strong anti laser jamming capability based on frequency shift optical feedback

With the proliferation of diverse laser equipment, the optical environment in which highly sensitive optical systems operate has become harsh and intricate. Mitigating laser jamming originating from the operational waveband is a challenging problem encountered by laser interferometric measurement systems. In this paper, we set forth a robust anti-jamming optical interferometry with high sensitivity. This method is based on frequency shift optical feedback, namely anti-jamming laser feedback interferometry (AJLFI). A rear-end pumping Nd:YVO4 microchip laser with bidirectional output channels is employed as the interferometric system source, and the photodetector is posterior to the laser cavity. This particular laser structure and the unique detector placement method from optical feedback interferometry make the laser cavity operate as a high-stop-band filter to filter out laser jamming in the operational waveband. In the AJLFI-based system we established, the jamming laser with a wavelength equaling that of the interferometric system suffers a notable attenuation of 44.8 dB. Concurrently, jamming laser falling within a range of ±10 nm from the wavelength of interferometric system gets an attenuation exceeding 44.43 dB. In addition, we set up the standard laser feedback interferometry(LFI)-based system and the Michelson heterodyne interferometry(MHI)-based system with the same experimental parameters as the AJLFI-based system to perform anti-jamming capability comparative experiments. In the experiments, a pulsed laser beam with a peak power of 1780.9 W is employed as laser jamming in the operating wavebands, which is precisely directed toward the target in conjunction with the probe light of the interferometric systems and scattered into the interferometric systems. The experimental findings demonstrate that the AJLFI-based system exhibits superior anti-jamming capability in both phase and amplitude measurements compared to conventional LFI-based and MHI-based systems.

Enhanced Detection Precision of the Taiji Program by Frequency Setting Strategy Based on a Hierarchical Optimization Algorithm

For space-based gravitational wave detection, a laser interferometric measurement system composed of a three-spacecraft formation offers the most rewarding bandwidth of astrophysical sources. There are no oscillators available that are stable enough so that each spacecraft could use its own reference frequency. The conversion between reference frequencies and their distribution between all spacecrafts for the synchronization of the different metrology systems is the job of the inter-spacecraft frequency setting strategy, which is important for continuously acquiring scientific data and suppressing measurement noise. We propose a hierarchical optimization algorithm to solve the frequency setting strategy. The optimization objectives are minimum total readout displacement noise and maximum beat-note frequency feasible range. Multiple feasible parameter combinations were obtained for the Taiji program. These optimized parameters include lower and upper bounds of the beat note, sampling frequency, pilot tone signal frequency, ultrastable clock frequencies, and modulation depth. Among the 20 Pareto optimal solutions, the minimum total readout displacement noise was 4.12 pm/Hz, and the maximum feasible beat-note frequency range was 23 MHz. By adjusting the upper bound of beat-note frequency and laser power transmitted by the telescope, we explored the effects of these parameters on the minimum total readout displacement noise and optimal local laser power in greater depth. Our results may serve as a reference for the optimal design of laser interferometry system instrument parameters and may ultimately improve the detection performance and continuous detection time of the Taiji program.

Research and Implementation of a Demodulation Switch Signal Phase Alignment System in Dynamic Environments.

In the space gravitational wave detection mission, inertial sensors play the role of providing an inertial reference for the laser interferometric measurement system. Among them, the capacitance sensor serves as the core key technology of the inertial sensor, used to measure the relative position of the test mass (TM) in the electrode cage. The capacitance sensor utilizes synchronous demodulation technology to extract signals from the AC induction signal. When the phase of the demodulation switch signal is aligned, the synchronous demodulator can most effectively filter out noise, thus directly influencing the performance of the capacitance sensor. However, since the TM is in a suspended state, the information read by the capacitance sensor is dynamic, which increases the difficulty of demodulation phase alignment. In light of this, a method is proposed for achieving the phase alignment of the demodulation switch signal in a dynamic environment. This is accomplished by adjusting the phase of the demodulation switch signal, and subsequently computing the phase difference between the AC induction signal and the demodulation switch signal. At the same time, a measurement and evaluation method for phase deviation is also proposed. Ultimately, an automatic phase alignment system for the demodulation switch signal in dynamic environments is successfully implemented on an FPGA platform, and tests are conducted on a hexapod PI console platform to simulate dynamic environments. The experimental results demonstrate that the system accurately achieves phase alignment in the static environment, with a phase deviation of 0.1394 rad. In the simulated dynamic environment, the phase deviation is 0.1395 rad.

Plasma noise in TianQin time-delay interferometry

TianQin is a proposed geocentric space-based gravitational wave observatory mission, which requires time-delay interferometry (TDI) to cancel laser frequency noise. With high demands for precision, solar-wind plasma environment at $\sim 10^5$ km above the Earth may constitute a non-negligible noise source to laser interferometric measurements between satellites, as charged particles perturb the refractivity along light paths. In this paper, we first assess the plasma noises along single links from space-weather models and numerical orbits, and analyze the time and frequency domain characteristics. Particularly, to capture the plasma noise in the entire measurement band of $10^{-4} - 1$ Hz, we have performed additional space-weather magnetohydrodynamic simulations in finer spatial and temporal resolutions and utilized Kolmogorov spectra in high-frequency data generation. Then we evaluate the residual plasma noises of the first- and second-generation TDI combinations. Both analytical and numerical estimations have shown that under normal solar conditions the plasma noise after TDI is less than the secondary noise requirement. Moreover, TDI is shown to exhibit moderate suppression on the plasma noise below $\sim 10^{-2}$ Hz due to noise correlation between different arms, when compared with the secondary noise before and after TDI.

Effect of Earth-Moon’s gravity on TianQin’s range acceleration noise. II. Impact of orbit selection

The paper is a sequel to our previous work (Zhang et al. Phys. Rev. D 103, 062001 (2021)). For proposed geocentric space-based gravitational wave detectors such as TianQin, gLISA, and GADFLI, the gravity-field disturbances, i.e., the so called ``orbital noise'', from the Earth-Moon system on the sensitive intersatellite laser interferometric measurements should be carefully evaluated and taken into account in the concept studies. Based on TianQin, we investigate how the effect, in terms of frequency spectra, varies with different choices of orbital orientations and radii through single-variable studies, and present the corresponding roll-off frequencies that may set the lower bounds of the targeted detection bands. The results, including the special cases of geostationary orbits (gLISA/GADFLI) and repeat orbits, can provide a useful input to orbit and constellation design for future geocentric missions.

Workshop-suited geometric errors identification of three-axis machine tools using on-machine measurement for long term precision assurance

In this paper we present a novel methodology for fast geometric errors identification of three-axis machine tools (MTs) using on-machine measurement. For this purpose, a new design of a three-dimensional artifact is proposed. The artifact allows to identify the linear positioning error and the two straightness errors of any linear axis of MTs with cartesian kinematics and the perpendicularity error between the axes. The prerequisite for the measurement is that the roll, pitch and yaw errors of all axes have already been measured and are negligibly small. The presented methodology is especially suitable for regular control of the machine accuracy in order to ensure the precision of the machining in the long term.As part of this work, an artifact was made of thermo-invariant material (Invar) and calibrated with an accurate coordinate measuring machine (CMM). This artifact was used to identify the geometric errors of an MT with three linear axes, with the raw data being collected using a 3D touch trigger probe. The measured errors were compared with results from laser interferometer and ballbar measurements. Moreover, the measurement uncertainty of presented methodology was analysed and compared with those of the laser interferometer and ballbar.

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

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

Laser Interferometric Measurement of Machine Tools

This paper deals with a positioning accuracy measurement on a machine tool to perform calibration. The principle of laser interferometric measurement is introduced, a Renishaw XL-80 laser interferometer is applied to perform measurements. The methodology of using the system is presented through a practical measurement. The deviations in certain positions are determined, thus the pitch error table of the machine tool can be refreshed. Thereafter a test running is performed in order to check the accuracy of the machining centre.

Study on the Control of Micro-Environmental Parameters in Long Distance Laser Interferometry

Fluctuation in environmental parameters has become an important factor affecting the performance of ultra precision measurement. Aiming at the long-distance and high-speed laser interferometer measurement system, a method combining structure design and closed-loop control is proposed to reduce the measurement error caused by environmental parameters. The uniform pressure structure is designed, and the control system of micro environmental parameters is established. The simulation and experimental research on the uniformity of temperature and pressure on the optical path measured by laser interferometer are carried out. The simulation and experimental results show that this method can achieve temperature uniformity and stability above 0.01°C and pressure uniformity and stability above 1Pa, and can be widely used in micro environment parameter control of long-distance ultra precision measurement.

New Model-Based Method to Improve the Moving Performance of the Planar Near-Field Scanning Frame

A new model-based method is proposed to improve the moving performance of the planar near-field scanning frame. First, the geometric error model of the planar near-field scanning frame is established based on homogeneous coordinate transformation and multi-body system theory. Then, 21 underdetermined parameters in the geometric error model are derived by using the laser interferometer measurement system with unique light path and configurations. Based on the established error model, online error compensation in combination with structural optimization are proposed to reduce geometric errors efficiently. Finally, the proposed method is utilized to derive a novel planar near-field scanning frame. Scanning planeness in XY plane with z = 10 mm is calculated by using the Monte Carlo simulation method, results show that the calculated scanning planeness satisfies demands for the planar near-filed scanning frame, which validates the effectiveness of the proposed method.

Analysis of Laser Interferometer Measurement Uncertainty by Simulating Error Sources

Analysis of Laser Interferometer Measurement Uncertainty by Simulating Error Sources

High-Frequency Guided Wave Propagation and Scattering in Silicon Wafers

Abstract Thin monocrystalline silicon wafers are employed for the manufacturing of solar cells with high conversion efficiency. Micro-cracks can be induced by the wafer cutting process, leading to breakage of the fragile wafers. High-frequency guided waves allow for the monitoring of wafers and detection and characterization of surface defects. The material anisotropy of the monocrystalline silicon leads to variations of the guided wave characteristics, depending on the guided wave mode and propagation direction relative to the crystal orientation. Selective excitation of the first antisymmetric A0 wave mode at 5 MHz center frequency was achieved experimentally using a custom-made wedge transducer. Strong wave pulses with limited beam skewing and widening were measured using noncontact laser interferometer measurements. This allowed the accurate characterization of the Lamb wave propagation and scattering at small artificial surface defects with a size of less than 100 µm. The surface extent of the defects of varying size was characterized using an optical microscope. The scattered guided wave field was evaluated, and characteristic parameters were extracted and correlated with the defect size, allowing in principle detection of small defects. Further investigations are required to explain the systematic asymmetry of the guided wave field in the vicinity of the indents.

Precise Compensation for Positional Accuracy of Ultra-Precision Air-Bearing Motion Stage Based on the Self-Calibration Method

In this paper, a high-efficiency self-calibration method was proposed, which was successfully applied to the ultra-precision air-bearing motion stage. Firstly, digital grating focusing, camera vision measurement and position synchronous output signal control were integrated, which can effectively improve the acquisition accuracy of stage positional data. Then, based on the least square algorithm the systematic error compensation value of motion stage can be quickly obtained through the fitting processing of three different measurement views. The experimental results showed that the proposed self-calibration measurement system can successfully realize ultra-precision air-bearing stage accurate location, and the orthogonality and shrinkage were controlled within 1 arcsec and 300 nm, respectively. This compensation method can effectively avoid the problems of high cost and poor environmental anti-interference in the laser interferometer measurement system, and will have a broad application prospect in the fields of high-end lithography and ultra-precision machining.

Motion measurement system of compliant mechanisms using computer micro-vision

Position sensing is essential to testify the validity of the mechanical design and verify the performance in micromanipulation. A practical system for non-contact micro-motion measurement of compliant nanopositioning stages and micromanipulators is proposed using computer micro-vision. The micro-motion measurement method integrates optical microscopy and an optical flow-based technique, in which the motions of complaint mechanisms are precisely detected and measured. Simulations are carried out to validate the robustness of the proposed method, while the micro-vision system and a laser interferometer measurement system are also built up for a series of experiments. The experimental results demonstrate that the proposed measurement system possesses high stability, extensibility, and precision with 0.06 µm absolute accuracy and 0.05 µm standard deviation.

Enhanced density in a stabilized high-current plasma beam

Externally generated, axial magnetic fields used to confine high-current plasma beams in compact linear devices are usually 0.5 Tesla or less and can be insufficient to suppress plasma instabilities. Such an issue is addressed in this study by closely winding the current-carrying cable around a small chamber attached to the end of a linear device. The magnetic field generated inside the small chamber during the high-current pulse reached 0.8 Tesla at the peak current of 10.83 kA. Formation of a steady plasma beam through a mixture of argon, hydrogen and helium was photographed by a high-speed camera at the instant of the peak current. The beam width profile starts from over 24.8 mm at the upstream location and becomes thinner with distance down-stream. At the location of laser-interferometer measurement, at the right-most viewing window on the test chamber, the beam width was estimated as 7.4 mm and plasma density was evaluated to be 1.0 × 1022 m−3, an increase of two orders of magnitude compared to a previous study. A simple relationship was derived for the plasma density as a function of beam width. Based on examination of the metal target at the far end, the final beam width was estimated as 50 µm, with the plasma density evaluated to be 4.31 × 1022 m−3, with a calculated ion energy of 4.35 keV, consistent with x-ray spectrum measurements.

三通道调频连续波激光干涉位移测量系统

三通道调频连续波激光干涉位移测量系统

Long stroke displacement measurement with reduced coupling error supporting high precision control of a beam flexure-based micro-stage.

This paper presents a novel beam flexure-based X-Y-θ micro-stage integrated with a laser interferometric type displacement measurement approach for reducing the measurement error induced by the rotational motion and cross-axis load effect. Aiming at achieving high-precision real-time control of the proposed system, an active disturbance rejection controller is developed such that the inevitable parasitic and coupling errors can be treated as disturbances and actively compensated by using the extended state observer. Finally, the verification experiments are deployed on the fabricated prototype, where the results indicate that the proposed approach achieves excellent performance in terms of motion accuracy and disturbance rejections.