Heterodyne Laser Interferometer Research Articles

Determination of absolute turbulence amplitude by CO2 laser phase contrast imaging

Phase contrast imaging (PCI) has the important advantages of good sensitivity and applicability for the measurements of fluctuation and turbulence in magnetically confined plasma. However, the determination of the absolute amplitude of fluctuation is not well established. In this article, we propose to determine the absolute amplitude of fluctuation with calibration. The fluctuation measured by CO2 laser PCI (CO2-PCI) was confirmed by simultaneous measurements by using a HeNe heterodyne interferometer (HeNe-HI). In the test experiments, CO2-PCI and HeNe-HI measured sound fields, which are produced by the audio speaker (f=6∼18 kHz, k=0.09∼0.33 mm−1) and the piezoelectric transducer (f=72 kHz, k=1.3 mm−1). At f=13∼18 kHz, k=0.24∼0.33 mm−1, the differences between CO2-PCI and HeNe-HI were 20∼30%. At f=72 kHz, k=1.3 mm−1, the difference was less than ∼10%. On the other hand, the difference between PCI and HI becomes larger at f<13 kHz, k<0.24 mm−1. This is because in these regions some parts of the scattered and non-scattered radiation were not clearly separated inside and outside the groove of the phase plate. The procedure of the absolute value determination was applied to the detached plasma of LHD and compared with the measurement by using a CO2 laser heterodyne interferometer (CO2-HI). The signal of CO2- HI at f>20 kHz is almost at the same as the level of noise. On the other hand, the 2D-PCI signal is clearly higher than the level of noise in all the entire frequency region. At f < 20 kHz, the difference between CO2-HI and CO2-PCI becomes large. This is likely to be due to the wavenumber cut-off of CO2-PCI. Combining two diagnostics, it is possible to measure a wide range of fluctuations from the macroscopic to the microscopic scale.

3D push-pull heterodyne interferometer for SPM metrology.

A three-coordinate heterodyne laser interferometer has been developed to measure the displacement of the probe microscope scanner with a subnanometer resolution that provides traceability of measurements to the standard of meter through the wavelength of a stabilized He-Ne laser. Main sources of errors are investigated, and their influence is minimized so that the resulting measurement uncertainty of the system does not exceed 0.2nm, and the resolution is 0.01nm. The investigation of metrological characteristics of the three-coordinate interferometer was carried out with a scanning probe microscopy (SPM) NanoScan-3D using TGZ-type calibration gratings. The values measured with SPM fell within the 95% confidence interval given by Physikalisch-Technische Bundesanstalt (PTB) (Germany). SPM equipped with a laser interferometer was used to measure the characteristics of dynamic etalons of geometric dimensions.

Characterization of a Nanometer Displacement Gauge for the Dimensional Control of Large Optomechanical Structures

We present the design, implementation, and characterization of a heterodyne laser interferometer for nanometer displacement metrology. The purpose is to monitor the 3-D shape of a large optomechanical structure planned for future general relativity experiments. Reaching the target 10−11-m displacement uncertainty over 7-m distances and many days’ integration periods is a challenging task. The solution here investigated consists of a nonpolarizing Mach–Zehnder layout, featuring an optical cancelable circuit and a holey folding mirror. The instrument working principle and the method for online phase reconstruction are presented, as well as the complete hardware configuration used. The several sources of noise are investigated mathematically and, whenever possible, verified experimentally. The displacement gauge was tested up to one day of continuous data acquisition, showing nanometer-level performance down to 100 mHz, while air index variations and mechanical instabilities are currently the main limiting factors at lower frequencies. This experiment has brought into light many technical issues that will constitute precious “lessons learned” for the future improvements of the system.

Earthquake Magnitude Estimation Using a Total Noise Enhanced Optimization Model.

In this paper, a heterodyne laser interferometer, which is used as a sensor for high-precision displacement measurement, is introduced to measure ground vibration and seismic waves as a seismometer. The seismic wave is measured precisely through the displacement variation obtained by the heterodyne laser interferometer. The earthquake magnitude is estimated using only the P-wave magnitudes for the first 3 s through the total noise enhanced optimization (TNEO) model. We use data from southern California to investigate the relationship between peak acceleration amplitude () and the earthquake magnitude (). For precise prediction of the earthquake magnitude using only the value, the TNEO model derives the relation equation between and the magnitude, considering the noise present in each measured seismic data. The optimal solution is obtained from the TNEO model based objective function. We proved the performance of the proposed method through simulation and experimental results.

Measurement Method for Nonlinearity in Heterodyne Laser Interferometers Based on Double-Channel Quadrature Demodulation.

The phase quadrature measurement method is capable of measuring nonlinearity in heterodyne laser interferometers with picometer accuracy whereas it cannot be applied in the new kind of heterodyne interferometers with bidirectional Doppler frequency shift especially in the condition of non-uniform motion of the target. To solve this problem, a novel measurement method of nonlinearity is proposed in this paper. By employing double-channel quadrature demodulation and substituting the external reference signal with internal ones, this method is free from the type of heterodyne laser interferometer and the motion state of the target. For phase demodulation, the phase differential algorithm is utilized to improve the computing efficiency. Experimental verification is carried out and the results indicate that the proposed measurement method achieves accuracy better than 2 pm.

Synthetic model of nonlinearity errors in laser heterodyne interferometry.

The development of laser heterodyne interferometry raises the requirements of measurement resolution and accuracy. However, periodic nonlinearity errors mainly suppress the accuracy of laser heterodyne interferometry. Based on the generation mechanism of nonlinearity errors, the sources of nonlinearity errors in laser heterodyne interferometry are first analyzed in this paper. Then, a synthetic model is established to analyze the influences of various nonlinearity error sources on the first- and second-harmonic nonlinearity errors. The first-harmonic nonlinearity errors can be reduced and suppressed by adjusting the orientation error of optical elements in a heterodyne interferometer. Furthermore, the azimuthal misalignment of the polarization beam splitter (PBS) is the main source of the second-harmonic nonlinearity errors. Therefore, when in heterodyne interferometer, the azimuthal misalignment of the PBS should be avoided if possible. This study provides theoretical basis for reducing and compensating nonlinearity errors in a laser heterodyne interferometer.

Resolution-enhanced heterodyne laser interferometer with differential configuration for roll angle measurement.

A high resolution roll measurement heterodyne interferometer with differential configurations is proposed in this paper. The proposed interferometer is composed of a pair of measurement beams providing environmental noise immunity. The structure is designed and the mathematic model based on Jones' matrix for measuring the roll angle is established. Sensitivity is enhanced dramatically because of the opposite phase shift directions of two signals. An experimental setup is built and an amplification factor of 270 is obtained. Correspondingly, a roll angle resolution of 0.13 arcsec is attained using a phase meter with detecting resolution of 0.01°.

Note: Comparison experimental results of the laser heterodyne interferometer for angle measurement based on the Faraday effect.

A laser heterodyne interferometer for angle measurement based on the Faraday effect is proposed. A novel optical configuration, designed by using the orthogonal return method for a linearly polarized beam based on the Faraday effect, guarantees that the measurement beam can return effectively even though an angular reflector has a large lateral displacement movement. The optical configuration and measurement principle are presented in detail. Two verification experiments were performed; the experimental results show that the proposed interferometer can achieve a large lateral displacement tolerance of 7.4 mm and also can realize high precision angle measurement with a large measurement range.

Nonlinear Errors Resulting from Ghost Reflection and Its Coupling with Optical Mixing in Heterodyne Laser Interferometers.

Even after the Heydemann correction, residual nonlinear errors, ranging from hundreds of picometers to several nanometers, are still found in heterodyne laser interferometers. This is a crucial factor impeding the realization of picometer level metrology, but its source and mechanism have barely been investigated. To study this problem, a novel nonlinear model based on optical mixing and coupling with ghost reflection is proposed and then verified by experiments. After intense investigation of this new model’s influence, results indicate that new additional high-order and negative-order nonlinear harmonics, arising from ghost reflection and its coupling with optical mixing, have only a negligible contribution to the overall nonlinear error. In real applications, any effect on the Lissajous trajectory might be invisible due to the small ghost reflectance. However, even a tiny ghost reflection can significantly worsen the effectiveness of the Heydemann correction, or even make this correction completely ineffective, i.e., compensation makes the error larger rather than smaller. Moreover, the residual nonlinear error after correction is dominated only by ghost reflectance.

Measuring the Laser Polarization State and PBS Transmission Coefficients in a Heterodyne Laser Interferometer

By placing a polarizer between a dual-frequency laser source (DFLS) and a polarizing beam splitter (PBS), two optical beat signals are formed; then, the transmission coefficients of the PBS and the polarization state parameters of the DFLS can be simultaneously measured without coupling while achieving high accuracy. We obtained explicit equations for the ellipticity angles of the laser beam components and explained the relationship between the extreme values of the beat amplitude and the laser polarization state parameters, which obtain less uncertainties than the existing work. The method is validated experimentally. Measuring these parameters is important to compensate for nonlinearity errors in heterodyne laser interferometers and assess the quality of devices.

Laser heterodyne interferometer with rotational error compensation for precision displacement measurement.

A laser heterodyne interferometer with rotational error compensation is proposed for precision displacement measurement. In this interferometer, the rotational error of the measured object is obtained by using an angle detecting unit which is composed of a semi-reflective film, a polarizing beam splitter, a quarter-wave plate, a convex lens and a two-dimensional position sensitive detector. And the obtained rotational angle is used for compensating its influence on displacement measurement result. The optical configuration of the proposed interferometer is designed, and the mathematical model for displacement measurement with rotational error compensation is established. The coupling effect of axial displacement on rotational angle measurement and the rotational angle range used for compensation on displacement measurement are discussed in detail. To verify feasibility of the proposed interferometer, the experimental setup was constructed and several verification experiments were performed.

Neural Network-Based Laser Interferometer Compensation for Seismic Signal Detection

We propose a seismic wave detection method in the frequency domain using a heterodyne laser interferometer, which is used in ultraprecision fields as a displacement measurement device. In seismology, it is important to accurately measure seismic waves. To overcome the limited frequency range and low resolution of accelerometers and velocimeters and to enhance the precision of seismic data analysis, we use the heterodyne laser interferometer as a seismic detection apparatus. We apply the data fusion algorithm with the adaptive standard deviation ratio (ς) derived from the neural network to improve the laser interferometer’s measurement precision. Moreover, by using the interferometric characteristics, we analyze the seismic data in the frequency domain. To determine the location of the epicenter from the body wave propagation analysis, we apply the STA/LTA algorithm to the measurement data. The effectiveness of the proposed laser interferometric seismometer is shown through experiments to locate the precise epicenter.

Methodical errors caused by superposition of electrical and optical signals in a heterodyne laser interferometer

Distortions of the displacements measured by the heterodyne interferometer due to penetration of the electric excitation signal of the acousto-optic modulator into the path of registration and processing of optical signals are considered. The level of this type of noise is estimated and the ways of its elimination from data obtained using a three-coordinate heterodyne interferometer are proposed.

Laser-Interferometric Broadband Seismometer for Epicenter Location Estimation.

In this paper, we suggest a seismic signal measurement system that uses a laser interferometer. The heterodyne laser interferometer is used as a seismometer due to its high accuracy and robustness. Seismic data measured by the laser interferometer is used to analyze crucial earthquake characteristics. To measure P-S time more precisely, the short time Fourier transform and instantaneous frequency estimation methods are applied to the intensity signal () of the laser interferometer. To estimate the epicenter location, the range difference of arrival algorithm is applied with the P-S time result. The linear matrix equation of the epicenter localization can be derived using P-S time data obtained from more than three observatories. We prove the performance of the proposed algorithm through simulation and experimental results.

Nonlinear errors induced by intermodulation in heterodyne laser interferometers.

A striking abnormal harmonic is detected in the measurement signal spectrum of a heterodyne laser interferometer, which deviates from the conventional frequency-domain model. A nonlinearity model based on intermodulation is proposed to explain this abnormality and to analyze its influence. Analysis from this model demonstrates that the harmonics arising from intermodulation can result in not only nonlinear errors opposite in sign to the traditional first- and second-order nonlinearities, but also new third- and fourth-order nonlinearities; moreover, these periodic nonlinearities cannot be fully compensated anymore by the Heydemann correction.

An algorithm for circular test and improved optical configuration by two-dimensional (2D) laser heterodyne interferometer.

Circular test is an important tactic to assess motion accuracy in many fields especially machine tool and coordinate measuring machine. There are setup errors due to using directly centring of the measuring instrument for both of contact double ball bar and existed non-contact methods. To solve this problem, an algorithm for circular test using function construction based on matrix operation is proposed, which is not only used for the solution of radial deviation (F) but also should be applied to obtain two other evaluation parameters especially circular hysteresis (H). Furthermore, an improved optical configuration with a single laser is presented based on a 2D laser heterodyne interferometer. Compared with the existed non-contact method, it has a more pure homogeneity of the laser sources of 2D displacement sensing for advanced metrology. The algorithm and modeling are both illustrated. And error budget is also achieved. At last, to validate them, test experiments for motion paths are implemented based on a gantry machining center. Contrast test results support the proposal.

Metrological characterization of nm-range dynamic etalons using a heterodyne interferometer

Test structures used for calibration of scanning probe microscopes have certain limitations. They are short-lived, their work surface becomes coated with microparticles over time, and it gradually wears out by contact with the measuring probe, resulting in the etalon geometry deformation. Dynamic etalons allow calibrating SPMs in ranges from pm to nm. In this article we present the results of dynamic etalon metrological characteristics research using an SPM equipped with tree-coordinate heterodyne laser interferometer. Obtained data indicates stability of piezoelectric modulus and absence of piezoelectric hysteresis phenomena in the etalon samples used.

Lagrange multiplier‐based error compensation of heterodyne interferometer

The heterodyne laser interferometer is an ultra-precise measurement apparatus. However, its susceptibility to environmental error is an obstacle to improve its nanometre-scale measurement accuracy. To minimise the environmental error factor, a compensation algorithm using a Lagrange multiplier method is proposed. The improved accuracy of the proposed method was verified by means of experiments using nanometre-scale measurements of a capacitive displacement sensor.

Experimental study of the stripping breakup of droplets and jets after their ejection from a liquid surface

This paper presents the results of experiments on the breakup dynamics of droplets and jets moving in a gas medium after their shock-wave ejection from the surface of a liquid and molten metal. Velocities of jets, droplet clouds, and the free surface and the deceleration parameters of droplets and jets in the gas were measured using a heterodyne laser interferometer (photon Doppler velocimetry). The induction period and the droplet sizes after breakup were determined.

Recording the particle velocity spectrum at the time the shock wave reaches the surface of liquids of different viscosities

This paper presents the results of experimental studies of the cavitation breakdown of liquids in a wide range of shock-wave loading. The free surface velocity of liquids and the velocity spectrum of the cloud of particles and jets were measured using a laser heterodyne interferometer (photon Doppler velocimetry), and their size was determined. The spall strength of distilled water was determined.