Heterodyne Laser Interferometer Research Articles

Green laser interferometric metrology system with sub-nanometer periodic nonlinearity.

This paper describes the design and realization of a heterodyne laser interferometer system that is applicable to metrology comparison. In this research, an iodine-stabilized Nd:YAG laser at 532 nm served as the light source. Two spatially separated beams with different offset frequencies are generated by two acousto-optic modulators to prevent any source mixing and polarization leakage. The interferometry components are integrated to a monolithic prism to reduce the difficulty of the light path adjustment and to guarantee the measuring accuracy. The experimental results show there is a sub-nanometer periodic nonlinearity, which mainly results from the ghost reflection. Placed in a vacuum chamber, the interferometer is applicable for measuring comparison using a piezo nanopositioner and a precision translation stage. Finally, a commercial interferometer is calibrated with the interferometer system.

Real-time compensation of the refractive index of air in distance measurement.

A two-color scheme of heterodyne laser interferometer is devised for distance measurements with the capability of real-time compensation of the refractive index of the ambient air. A fundamental wavelength of 1555 nm and its second harmonic wavelength of 777.5 nm are generated, with stabilization to the frequency comb of a femtosecond laser, to provide fractional stability of the order of 3.0 × 10(-12) at 1 s averaging. Achieved uncertainty is of the order of 10(-8) in measuring distances of 2.5 m without sensing the refractive index of air in adverse environmental conditions.

Improvement and validity of shock measurements using heterodyne laser interferometer

The improvement and validity of shock measurements using only the laser head (heterodyne laser interferometer) of a commercial laser Doppler vibrometer was investigated by comparing acceleration waveforms measured by a homodyne laser interferometer with those measured by a heterodyne laser interferometer. The acceleration waveforms were generated from the displacement waveforms obtained with a reference quadrature homodyne laser interferometer by applying a numeric differentiation process twice. The differences between the two acceleration waveforms were found to be small with the measurement uncertainty in case of high acceleration level. In a further investigation, the accuracy of the shock measurements taken by the homodyne and heterodyne laser interferometers were compared in computational simulation. The results indicated that the accuracy of the heterodyne laser interferometer was superior to that of the homodyne laser interferometer.

IQ quadrature demodulation algorithm used in heterodyne detection

In order to obtain better detection results of heterodyne, we used phase IQ quadrature demodulation algorithm to process the data which detected by laser heterodyne. Based on laser heterodyne interferometer, processing the data in the interferometer phase IQ quadrature demodulation algorithm from the signal to noise ratio, sampling rate, sampling rate, filter order and cutoff frequency, verify the effects of these system parameters to the phase precision, and choose the best parameters to obtain a better phase precision through experiment as: the signal to noise ratio is 25dB, the IF signal frequency is 98.3MHz, 98.5MHz, 99.1MHz, 99.5MHz and 100MHz, the sampling rate is 512–2048, the cutoff frequency and order of the filter are 0.11 and 40, respectively.

Simple method for reducing the first-order optical nonlinearity in a heterodyne laser interferometer.

A simple method was proposed by using a tunable attenuator fitted in the reference or measurement arm of a heterodyne laser interferometer to adjust the values of mixing laser beams while the spectrum of the measurement signal is monitored using a signal analyzer. The effectiveness of the proposed method in reducing the first-order optical nonlinearity was verified through experiments. Results indicated that the peak value of the first-order optical nonlinearity could be reduced from 5.15 to 0.24nm. It was therefore concluded that the proposed method was applicable to ultraprecision laser interferometry.

Analysis and verification of the nonlinear error resulting from the misalignment of a polarizing beam splitter in a heterodyne interferometer

In order to analyze and characterize the periodic nonlinear error resulting from the misalignment of a polarizing beam splitter (PBS) in a laser heterodyne interferometer more accurately, in this paper, starting from the light separating principle of thin-film PBS, we have found that the root cause of the periodic nonlinear error is the frequency mixing induced by the deviation from the Brewster angle of the incident angle or by the rotation of the incident plane when the PBS is misaligned. Moreover, we have established the direct function relationships between the periodic nonlinear error and different PBSs’ misalignment errors for the first time. The theoretical analysis shows that the periodic nonlinear error arising from the PBS’s yaw error is the largest and the maximal nonlinear errors are unequal even if the positive yaw angle is equal to the negative yaw angle. The nonlinear errors are much smaller under the PBS’s roll and pitch errors. The experiments of polarizing leakage and nonlinear error measurement under the PBS’s yaw error demonstrate that the experimental results are in agreement with the theoretical analysis.

Development of a Micro-Thruster Test Facility which fulfils the LISA requirements

In the context of investigations for a sufficient attitude control thruster for LISA, we have developed a thruster test facility which consists of a highly precise thrust balance coupled with plasma diagnostics. In parallel to the test facility development, investigations to downscale a High Efficiency Multistage Plasma Thruster (HEMP-T) are also being carried out. The thruster has been used to demonstrate the measurement capabilities of the facility. The setup allows a parallel operation of all instruments and can also be used for other types of μN propulsion systems including cold gas thrusters. The thrust balance consists of two pendulums. As read out a heterodyne laser interferometer is used. Differential wave front sensing (DWS) enables the measurement of the pendulum tilt which, via suitable calibration using an electrostatic comb, can be converted to a thrust. The whole setup is a symmetric configuration enabling a common-mode rejection of the dominant noise sources (e.g. seismic noise etc.). The thrust balance has a demonstrated precision of 0.1 μN. Based on our unique design, this precision can be attained down to 10-3 Hz. Thus, the measurement setup is especially suitable for characterising the thrust noise of potential eLISA propulsion candidates. We give an overview of the design, the present performance and the future plans.

Multi-channel phasemeter and its application in the heterodyne laser interferometry

The mission to detect gravitational wave in space requires a not only sophisticated but also ultra-precise laser interferometric measurement system. Within a single spacecraft, tens of interferometric beat signals are generated at the same time and they also need to be processed simultaneously. In this paper, a multi-channel phasemeter which can parallelly process the signals is constructed. The test shows that a sensitivity of 2π μrad/√Hz could be achieved in the frequency range of 0.1 to 10 Hz. We also utilize the phasemeter to evaluate the performance of a heterodyne laser interferometer.

Development of a Highly Precise Micronewton Thrust Balance

In this paper, we present our ongoing micronewton thrust balance development, which fulfils the laser interferometer space antenna requirements. In the context of the development of highly precise thrusters for attitude control of satellites for future space missions, test facilities for the characterization and qualification of thrusters need to be developed in parallel. The presented thrust balance has a resolution of $0.1~\mu $ N in a bandwidth between 1 and $10^{-3}$ Hz. As a general measurement principle, we chose a pendulum balance. The setup consists of two pendulums to enable a common mode rejection. To suppress the eigenfrequency of the pendulums, a damping system based on an eddy current brake is part of the balance assembly. A heterodyne laser interferometer is used as the translation sensor. Different measurements were performed to investigate the noise performance of the pendulum. The results are presented and analyzed. The measurement system was used to measure the thrust of a micro-high efficiency multistage plasma thruster.

Heterodyne Interferometer for the Metrological Assurance of the Devices Measuring Physical Properties of Nanostructured Materials

Nano-hardness tester with three-coordinate laser heterodyne interferometer integrated in the commercially available industrial scanning probe is developed. It allows ensuring traceability of measurements in nanometer range to the primary standard of meter. This device may be used for the characterization of indentor's tips. Corresponding method is presented.

Laser heterodyne interferometer for simultaneous measuring displacement and angle based on the Faraday effect.

A laser heterodyne interferometer for simultaneous measuring displacement and angle based on the Faraday effect is proposed. The optical configuration of the proposed interferometer is designed and the mathematic model for measuring displacement and angle is established. The influences of the translational, lateral and rotational movements of the measuring reflector on displacement and angle measurement are analyzed in detail. The experimental setup based on the proposed interferometer was constructed and a series of experiments of angle comparison and simultaneous measuring displacement and angle were performed to verify the feasibility of the proposed interferometer for precision displacement and angle measurement.

Error Compensation Based on Lagrange Multiplier in Heterodyne Laser Interferometer

In this paper, we propose a signal compensation algorithm. In heterodyne laser interferometer, the unexpected error restricts the precision such as nonlinearity and environmental error. To improve the accuracy in length measurement, we use the method of Lagrange multiplier which solves the constrained optimization problem and allows to minimize an objective function. With the method of Lagrange, we apply it to a length measurement and show the result of simulation.

Detection of Seismic Wave with Laser Interferometer

In this paper, we propose a seismic wave detection process using a laser interferometer as a seismometer. The laser interferometer system is an important equipment with its remarkable accurate capability for displacement measurement. During the process of the seismic wave measurement, however, environmental and nonlinearity error are occurred in a heterodyne laser interferometer. Through the extended Kalman filter compensation, the distortion is reduced. With a recursive STA/LTA algorithm, the PS-time of the seismic wave is determined and then the epicenter distance can be derived. Through some simulations, it is demonstrated that the proposed algorithm can reduce error factors and improve the measurement accuracy of a seismometer.

An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer.

Correct return of the measuring beam is essential for laser interferometers to carry out measurement. In the actual situation, because the measured object inevitably rotates or laterally moves, not only the measurement accuracy will decrease, or even the measurement will be impossibly performed. To solve this problem, a novel orthogonal return method for linearly polarized beam based on the Faraday effect is presented. The orthogonal return of incident linearly polarized beam is realized by using a Faraday rotator with the rotational angle of 45°. The optical configuration of the method is designed and analyzed in detail. To verify its practicability in polarization interferometry, a laser heterodyne interferometer based on this method was constructed and precision displacement measurement experiments were performed. These results show that the advantage of the method is that the correct return of the incident measuring beam is ensured when large lateral displacement or angular rotation of the measured object occurs and then the implementation of interferometric measurement can be ensured.

Design of a real-time two-color interferometer for MAST Upgrade.

A single chord two-color CO2/HeNe (10.6/0.633 μm) heterodyne laser interferometer has been designed to measure the line integral electron density along the mid-plane of the MAST Upgrade tokamak, with a typical error of 1 × 10(18) m(-3) (∼2° phase error) at 4 MHz temporal resolution. To ensure this diagnostic system can be restored from any failures without stopping MAST Upgrade operations, it has been located outside of the machine area. The final design and initial testing of this system, including details of the optics, vibration isolation, and a novel phase detection scheme are discussed in this paper.

Model and Measurement Method of Optical Nonlinearities Caused by the Heterodyne and Homodyne Interference Terms in the Heterodyne Interferometer

The heterodyne laser interferometer is widely applied in ultra-precision displacement measurement, but its accuracy is seriously restricted by the optical nonlinearity which arises from the optical mixing in the reference and measurement arms. In an ideal heterodyne laser interferometer, the beam from the laser source consists of two orthogonally linear-polarized components with slightly different optical frequencies and the two components can be completely separated by the polarizing optics, one traverses in the reference arm, the other traverses in the measurement arm, both of them are in the form of a pure optical frequency. However, in a real heterodyne laser interferometer, due to the imperfect laser polarization, the optics defect and the misalignment, the two components of the laser beam cant be perfectly separated, therefore both of the reference arm and the measurement arm contain a portion of the two laser components, which leads to an optical mixing in the two arms of the heterodyne interferometer and causes the cyclic nonlinearity of several to tens of nanometers.

P-S Time Observation based on Laser Interferometer Seismic Signal Data

In seismic signal detection, it is important to detect seismic wave and P-S wave arrival time. Seismometers or accelerometers which are used as seismic wave measurement system have some limits to detect seismic signal. In order to overcome these limits, we propose the seismic wave measurement device based on a heterodyne laser interferometer. Heterodyne laser interferometer is used as the distance measurement device which has measurable range from nanometer to several meters. Therefore we model seismic wave detection system based on heterodyne laser interferometer to measure P-S time for epicenter. Finally, we use STA/LTA algorithm to detect P-S time accurately. It is shown that heterodyne laser interferometer can be used as seismic detection device.

Measurement and control of the movable coil position of a joule balance with a system based on a laser heterodyne interferometer

A system based on laser heterodyne interferometer is proposed in this paper to measure and control the movable coil position of a joule balance. A damping system is used to suppress the movement of the movable coil in the horizontal direction while a piezoelectric ceramic control unit with PID controller is used to inhibit the vibration and long term drift of the movable coil in the vertical direction. The effectiveness of the proposed method in measuring and controlling the movable coil position of a joule balance is proved through experiments. Experimental results indicate that the displacement of the movable coil in the vertical direction can be reduced from 400 to 50 nm while its drift is successfully inhibited.

Measurement method for roll angular displacement with a high resolution by using diffraction gratings and a heterodyne interferometer.

The roll angle measurement is difficult to be achieved directly using a typical commercial interferometer due to its low sensitivity in axial direction, where the axial direction is orthogonal to the plane of the roll angular displacement. A roll angle measurement method combined diffraction gratings with a laser heterodyne interferometer is discussed in this paper. The diffraction grating placed in the plane of a roll angular displacement and the interferometer arranged in the plane's orthogonal direction, constitute the measurement pattern for the roll angle with high resolution. The roll angular displacement, considered as the linear, can be tested precisely when the corresponding angle is very small. Using the proposed method, the angle roll measurement obtains the high resolution of 0.002″. Experiment has proved its feasibility and practicability.

Magnetostrictive deformation of a transformer: A comparison between calculation and measurement

Magnetostriction, which refers to the deformation of the core material of transformers and electrical machines, is a main contributor to the total noise. In this work, a technique is proposed to calculate the magnetostrictive deformations of the core of the aforementioned devices. This technique is based on finite element approach with an artificial neural network model of the magnetostrictive behaviour of the core material. The strain measurements are carried out by using a dual heterodyne laser interferometer setup. The proposed technique is then applied to a single-phase test transformer core. As a validation, the vibration of the magnetised core of the same setup is measured by using a laser scanning vibrometer.