Heterodyne Laser Interferometer Research Articles

Suppression of frequency-mixing effect for pm-level heterodyne interferometers based on "zero coupling" optical path length control.

Optical path length (OPL) noise resulting from stray light significantly constrains interferometry displacement measurements in the low-frequency band. This paper presents an analytical model considering the presence of stray light in heterodyne laser interferometers. Due to the cyclic nonlinear coupling effect, there will be some special OPLs of stray light, minimizing the frequency-mixing impact to zero. Consequently, we propose a noise suppression scheme that locks the OPL of stray light at the zero coupling point. Therefore, we significantly enhanced the interference displacement measurement noise within the low-frequency band. Experimental results show that the interferometer achieves a displacement noise level lower than 6 pm/Hz1/2 covering 1 mHz.

Thin Copper Plate Defect Detection Based on Lamb Wave Generated by Pulsed Laser in Combination with Laser Heterodyne Interference Technique.

Thin copper plate is widely used in architecture, transportation, heavy equipment, and integrated circuit substrates due to its unique properties. However, it is challenging to identify surface defects in copper strips arising from various manufacturing stages without direct contact. A laser ultrasonic inspection system was developed based on the Lamb wave (LW) produced by a laser pulse. An all-fiber laser heterodyne interferometer is applied for measuring the ultrasonic signal in combination with an automatic scanning system, which makes the system flexible and compact. A 3-D model simulation of an H62 brass specimen was carried out to determine the LW spatial-temporal wavefield by using the COMSOL Multiphysics software. The characteristics of the ultrasonic wavefield were extracted through continuous wavelet transform analysis. This demonstrates that the A0 mode could be used in defect detection due to its slow speed and vibrational direction. Furthermore, an ultrasonic wave at the center frequency of 370 kHz with maximum energy is suitable for defect detection. In the experiment, the size and location of the defect are determined by the time difference of the transmitted wave and reflected wave, respectively. The relative error of the defect position is 0.14% by averaging six different receiving spots. The width of the defect is linear to the time difference of the transmitted wave. The goodness of fit can reach 0.989, and it is in good agreement with the simulated one. The experimental error is less than 0.395 mm for a 5 mm width of defect. Therefore, this validates that the technique can be potentially utilized in the remote defect detection of thin copper plates.

High-Bandwidth Heterodyne Laser Interferometer for the Measurement of High-Intensity Focused Ultrasound Pressure.

As a high-end medical technology, high-intensity focused ultrasound (HIFU) is widely used in cancer treatment and ultrasonic lithotripsy technology. The acoustic output level and safety of ultrasound treatments are closely related to the accuracy of sound pressure measurements. Heterodyne laser interferometry is applied to the measurement of ultrasonic pressure owing to its characteristics of non-contact, high precision, and traceability. However, the upper limit of sound pressure measurement is limited by the bandwidth of the interferometer. In this paper, a high-bandwidth heterodyne laser interferometer for the measurement of high-intensity focused ultrasound pressure is developed and tested. The optical carrier with a frequency shift of 358 MHz is realized by means of an acousto-optic modulator. The selected electrical devices ensure that the electrical bandwidth can reach 1.5 GHz. The laser source adopts an iodine frequency-stabilized semiconductor laser with high-frequency spectral purity, which can reduce the influence of spectral purity on the bandwidth to a negligible level. The interference light path is integrated and encapsulated to improve the stability in use. An HIFU sound pressure measurement experiment is carried out, and the upper limit of the sound pressure measurement is obviously improved.

Measurement of the Optical Path Difference Caused by Steering Mirror Using an Equal-Arm Heterodyne Interferometer

In space gravitational wave detection, the inter-satellite link-building process requires a type of steering mirror to achieve point-ahead angle pointing. To verify that the background noise does not drown out the gravitational wave signal, this paper designed a laser heterodyne interferometer specifically designed to measure the optical path difference of the steering mirror. Theoretically, the impact of angle and position jitter is analyzed, which is called tilt-to-length (TTL) coupling. This interferometer is based on the design concept of equal-arm length. In a vacuum (10−3 Pa), vibration isolation (up to 1 Hz), and temperature-controlled (approximately 10 mK) experimental environment, the accuracy is increased by about four orders of magnitude through a common-mode suppression approach and can reach 390 pm/Hz when the frequency is between 1 mHz and 1 HZ. By analogy, the optical path difference caused by the steering mirror reaches 5 pm/Hz in the 1 mHz to 1 Hz frequency band. The proposed TTL noise model is subsequently verified.

Phase Measurement Method Based on Digital Dual Frequency Comb for High-Precision High-Speed Heterodyne Interferometry

The heterodyne interferometer is widely used as a precise displacement sensor in ultraprecision processing. However, there is a trade-off between measurement speed and measurement precision in the existing interference signal processing methods. In this work, a novel phase measurement method based on digital dual frequency comb is proposed. The proposed method uses the intrinsic frequency comb signal and a narrowband low-pass filter to form a band-pass filter bank, which divides the broadband brought by high-speed movement into multiple narrow bands. The signal-to-noise ratio (SNR) is improved for phase calculation. In addition, two groups of intrinsic frequency comb signals are used simultaneously for phase measurement and the rotation of the output, preventing the inaccurate phase measurement of the input signal whose frequency is the average of two frequencies in the frequency comb signal. The heterodyne laser interferometer can maintain high precision at high measurement speed. The simulation results show that the precision of the proposed method is more than 50% higher than that of the phase-locked loop method. The experiment with a circuit board combined with 100 Msps sampling 16-bit A/D converter shows that the phase measurement precision of the input signal frequency in the bandwidth range of 2.5–37.5 MHz can reach 0.77 mrad, equivalent to the displacement measurement precision of the double-pass interferometer (19 pm) at a measurement speed of less than 2.77 m/s.

A Novel Analog Interpolation Method for Heterodyne Laser Interferometer

Laser interferometer technology is used in the precision positioning stage as an encoder. For better resolution, laser interferometers usually work with interpolation devices. According to the interpolation factor, these devices can convert an orthogonal sinusoidal signal into several square-wave signals via digital processing. The bandwidth of the processing will be the limitation of the moving speed of the positioning stage. Therefore, the user needs to make a trade-off between the interpolation factor and the moving speed. In this investigation, a novel analog interpolation method for a heterodyne laser interferometer has been proposed. This method is based on the principle of the lock-in amplifier (LIA). By using the proposed interpolation method, the bandwidth of the laser encoder system can be independent of the interpolation factor. This will be a significant benefit for the ultra-high resolution encoder system and the laser interferometers. The concept, design, and experiment are revealed in this manuscript. The experimental results show that the proposed interpolation method can reach nanometer resolution with a heterodyne laser interferometer, and the bandwidth of the signal is independent of the resolution.

A high precision phase extraction method in heterodyne interferometer based on FPGA

The high-precision phase extraction method directly determines the final measurement performance of the heterodyne laser interferometer. This paper proposes a digital quadrature phase-locked (DQPL) method with sub-nanometer precision based on FPGA hardware and compiled on the LABVIEW FPGA platform. DQPL method can accurately extract the phase difference of the two optical signals in the heterodyne laser interferometer. The validity and stability of the method have been verified by simulations and experiments. The experimentally obtained measurement resolution is 0.074 nm, and the measurement standard deviation obtained by the Monte Carlo method is 0.22 nm.

Primary accelerometer calibration with two-axis automatic positioning stage

In this study, we developed an automated, multipoint primary accelerometer calibration system using a two-axis positioning stage and a heterodyne laser interferometer. The proposed system offers low-cost, convenient, and automated multipoint accelerometer calibration, enabling less calibration lead time. The positioning stage also offers better positioning repeatability of 1μm, which is impossible through manual alignments. We measured the surface deformation of a laser reflection adaptor for a single-ended accelerometer by measuring more than 450 measurement positions. Visualizing the deformation of laser reflection surfaces facilitates understanding the effects of deformation or non-linear motion, which are among the most significant uncertainty components in high-frequency accelerometer calibrations.

Fiber-based two-wavelength heterodyne laser interferometer.

Displacement measuring interferometry is a crucial component in metrology applications. In this paper, we propose a fiber-based two-wavelength heterodyne interferometer as a compact and highly sensitive displacement sensor that can be used in inertial sensing applications. In the proposed design, two individual heterodyne interferometers are constructed using two different wavelengths, 1064 nm and 1055 nm; one of which measures the target displacement and the other monitors the common-mode noise in the fiber system. A narrow-bandwidth spectral filter separates the beam paths of the two interferometers, which are highly common and provide a high rejection ratio to the environmental noise. The preliminary test shows a sensitivity floor of 7.5pm/Hz at 1 Hz when tested in an enclosed chamber. We also investigated the effects of periodic errors due to imperfect spectral separation on the displacement measurement and propose algorithms to mitigate these effects.

Quasi-monolithic heterodyne laser interferometer for inertial sensing.

We present a compact heterodyne laser interferometer developed for high-sensitivity displacement sensing applications. This interferometer consists of customized prisms and wave plates assembled as a quasi-monolithic unit to realize a miniaturized system. The interferometer design adopts a common-mode rejection scheme to provide a high rejection ratio to common environmental noise. Experimental tests in vacuum show a displacement sensitivity level of 11p m/H z at 100m H z and as low as 0.6p m/H z above 1p m. The prototype unit is 20m m×20m m×10m m in size and weighs 4.5g, allowing subsequent integration in compact systems.

Characteristics of a heterodyne laser interferometer laboratory model for the development of a space gravimetry project

We investigate displacement measurements of up to 17 μm on a heterodyne laser interferometer laboratory model. The measurement error for small (up to 200 nm) linear displacements is found to be 270 pm at a 10-s averaging time. The results obtained can be used for developing a space laser interferometric system for the global Earth’s gravity field mapping.

Micro-Movement Measured by Laser Heterodyne Interferometer Based on Acousto-Optic Effect

In this experiment, the stable output of a dual-frequency laser source is obtained by an acousto-optic modulator due to the Bragg diffraction effect. Furthermore, the non-polarized dual-laser heterodyne interferometer is designed to measure the micro-movement of stacked piezoelectric (PZT) ceramic. This micro-movement can be dynamically determined by comparing the phase difference between the conference beam and measuring beam. The results indicate that the micro-movement of PZT ceramic changes linearly with the driven-voltage in the range of 0–30 V and the sensitivity of movement to voltage is 58.3 nm/V, which is very close to the theoretical value and this laser heterodyne interferometer can be applied for calibrating parameters of PZT ceramic.

Investigation and Mitigation of Noise Contributions in a Compact Heterodyne Interferometer

We present a noise estimation and subtraction algorithm capable of increasing the sensitivity of heterodyne laser interferometers by one order of magnitude. The heterodyne interferometer is specially designed for dynamic measurements of a test mass in the application of sub-Hz inertial sensing. A noise floor of / at 100 is achieved after applying our noise subtraction algorithm to a benchtop prototype interferometer that showed a noise level of / at 100 when tested in vacuum at levels of Torr. Based on the previous results, we investigated noise estimation and subtraction techniques of non-linear optical pathlength noise, laser frequency noise, and temperature fluctuations in heterodyne laser interferometers. For each noise source, we identified its contribution and removed it from the measurement by linear fitting or a spectral analysis algorithm. The noise correction algorithm we present in this article can be generally applied to heterodyne laser interferometers.

Development of the Heterodyne Laser Encoder System for the X-Y Positioning Stage.

This investigation develops a laser encoder system based on a heterodyne laser interferometer. For eliminating geometric errors, the optical structure of the proposed encoder system was carried out with the internal zero-point method. The designed structure can eliminate the geometric errors, including positioning error, straightness error, squareness error, and Abbe error of the positioning stage. The signal processing system is composed of commercial integrated circuits (ICs). The signal type of the proposed encoding system is a differential signal that is compatible with most motion control systems. The proposed encoder system is embedded in a two-dimensional positioning stage. By the experimental results of the positioning test in the measuring range of 27 mm × 27 mm, with a resolution of 15.8 nm, the maximum values of the positioning error and standard deviation are 12.64 nm and 126.4 nm, respectively, in the positioning experiments. The result shows that the proposed encoder system can fit the positioning requirements of the optoelectronic and semiconductor industries.

A Heterodyne Interferometer with Separated Beam Paths for High-Precision Displacement and Angular Measurements

As standard concepts for precision positioning within a machine reach their limits with increasing measurement volumes, inverse concepts are a promising approach for addressing this problem. The inverse principle entails other limitations, as for high-precision positioning of a sensor head within a large measurement volume, three four-beam interferometers are required in order to measure all necessary translations and rotations of the sensor head and reconstruct the topography of the reference system consisting of fixed mirrors in the x-, y-, and z-directions. We present the principle of a passive heterodyne laser interferometer with consequently separated beam paths for the individual heterodyne frequencies. The beam path design is illustrated and described, as well as the design of the signal-processing and evaluation algorithm, which is implemented using a System-On-a-Chip with an integrated FPGA, CPU, and A/D converters. A streamlined bench-top optical assembly was set up and measurements were carried out to investigate the remaining non-linearities. Additionally, reference measurements with a commercial homodyne interferometer were executed.

Calibration of laser Doppler vibrometer and laser interferometers in high-frequency regions using electro-optical modulator

We proposed a new primary calibration method of a laser Doppler vibrometer (LDV) using the optical modulated excitation of an electro-optical modulator and validated this approach by comparing mechanical modulated excitation with homodyne laser interferometer at the National Metrology Institute of Japan (NMIJ). The velocity sensitivity of the LDV was evaluated with the uncertainty budget at a high-frequency range up to 1 MHz, which is indicated as the upper limit of 50 kHz in ISO (International Organization for Standardization) 16063–41. As the results, we confirmed that velocity sensitivities between optical and mechanical modulated excitations are flat within their uncertainty from 100 Hz up to 1 MHz. Moreover, in order to evaluate the accurate phase shift of the accelerometer up to 20 kHz using optical modulated excitation, we also revealed the reliability of two time shifts between homodyne and heterodyne laser interferometers.

Tracking Length and Differential-Wavefront-Sensing Signals from Quadrant Photodiodes in Heterodyne Interferometers with Digital Phase-Locked-Loop Readout

We propose a method to track signals from quadrant photodiodes (QPD) in heterodyne laser interferometers that employ digital phase-locked loops for phase readout. Instead of separately tracking the four segments from the QPD and then combining the results into length and Differential Wavefront Sensing (DWS) signals, this method employs a set of coupled tracking loops that operate directly on the combined length and angular signals. Benefits are increased signal-to-noise ratio in the loops and the possibility to adapt the loop bandwidths to the different dynamical behavior of the signals being tracked, which now correspond to physically meaningful observables. We demonstrate an improvement of up to 6 dB over single-segment tracking, which makes this scheme an attractive solution for applications in precision inter-satellite laser interferometry in ultra-low-light conditions.

Laser metrology concept consolidation for NGGM

The measurement of the static and temporal variation of Earth’s gravity field yields important information on water storage, seasonal and sub-seasonal water cycles, their impact on water levels and delivers key data to Earth’s climate models. The satellite missions GOCE (ESA), GRACE (US-GER) and just recently GRACE Follow-On (US-GER) resulted in a significant improvement on our understanding of the system Earth. To further improve the measurement accuracy of the time-variable gravity field, ESA is investigating the concept of a ‘Next Generation Gravity Mission’ (NGGM), consisting of two pairs of satellites and a heterodyne laser interferometer for inter-satellite ranging. Based on the heritage of the development of the laser ranging interferometer for GRACE Follow-On and the former and ongoing studies for NGGM, two schemes for the Laser Metrology Instrument (LMI) for NGGM, namely the transponder and the retroreflector scheme have been investigated and are presented in this paper. The results include the instrument ranging performance analyses, the laser link acquisition, an instrument reliability assessment and redundancy approach as well as the Technology Readiness Level assessment of the individual instrument units.

Measurement optimization of high accuracy check master based on interferometry method in National Standardization Agency of Indonesia: a preliminary study for measuring range of 10 mm to 400 mm

High accuracy check master is a type of geometry gauge that often used to check the accuracy of Coordinate Measuring Machine (CMM) in the high-class metrological institutes and manufacturing industries. This type of geometry gauge is composed of several high-accuracy short gauge blocks and a large rod as its foundation. Conventionally, the measurement of high accuracy check master can be carried on by using measuring machine. Since the bench has limit up to 400 mm, the measurement of high accuracy check master more than 400 mm range is performed in two-step. Firstly, from nominal range of 10 mm to 400 mm and the other range by utilizing extension. In some cases, this measurement method has bigger expanded uncertainty value, i.e. more than 2 µm. Since the check master has important role to verify the accuracy of CMM, the quality of calibration system of high accuracy check master is required to be improved. This paper describes only to achieve high accuracy of measurement up to 400 mm. In the developed measuring system, the heterodyne laser interferometer is used as the reference. The optical configuration of laser is combined with the measuring machine as a moving part. In order to improve the accuracy of measurement, the refractive index of air and the temperature compensation are recalculated manually by Edlen’s formula and linear expansion equation, respectively. Using this method, the expanded uncertainty from calibration 400 mm high accuracy check master is less than 1 µm. The results had a good agreement to the measurement results from manufacturer with international certification, experimentally. In conclusion, this method can be applied to calibrate the high accuracy check master of 400 mm range.

Seismic Discrimination between Earthquakes and Explosions Using Support Vector Machine.

The discrimination between earthquakes and explosions is a serious issue in seismic signal analysis. This paper proposes a seismic discrimination method using support vector machine (SVM), wherein the amplitudes of the P-wave and the S-wave of the seismic signals are selected as feature vectors. Furthermore, to improve the seismic discrimination performance using a heterodyne laser interferometer for seismic wave detection, the Hough transform is applied as a compensation method for the periodic nonlinearity error caused by the frequency-mixing in the laser interferometric seismometer. In the testing procedure, different kernel functions of SVM are used to discriminate between earthquakes and explosions. The outstanding performance of a laser interferometer and Hough transform method for precision seismic measurement and nonlinearity error compensation is confirmed through some experiments using a linear vibration stage. In addition, the effectiveness of the proposed discrimination method using a heterodyne laser interferometer is verified through a receiver operating characteristic curve and other performance indices obtained from practical experiments.