Search Results (27)

As the primary electronic payload of laser interferometry system for space gravitational wave detection, the core function of the phasemeter is ultra-high precision phase measurement. According to the principle of laser heterodyne interferometry and the requirement of 1 pm ranging accuracy of the phasemeter, the phase measurement noise should reach 2π μrad/Hz^1/2@(0.1 mHz–1 Hz). The heterodyne interference signal first passes through the quadrant photoelectric detector (QPD) to achieve photoelectric conversion, then passes through the analog-to-digital converter (ADC) to achieve analog and digital conversion, and finally passes through the digital phase-locked loop (DPLL) for phase locking. The sampling timing jitter of the heterodyne interference signal caused by the ADC is the main noise affecting the phase measurement performance and must be suppressed. This paper proposes a sampling timing jitter noise suppression system (STJNSS), which can set system parameters for high-frequency signals used for inter-satellite clock noise transmission, the system clock of the phasemeter, and the pilot frequency for suppressing ADC sampling timing jitter noise, meeting the needs of the current major space gravitational wave detection plans. The experimental results after the integration of SJNSS and the phase meter show that the phase measurement noise of the heterodyne interferometer signal reaches 2π μrad/Hz^1/2@(0.1 mHz–1 Hz), which meets the requirements of space gravitational wave missions. Full article

In the detection of gravitational waves in space, during the science phase of the mission, the point-ahead angle mechanism (PAAM) serves to steer a laser beam to compensate for the angle generated by the relative motion of the two spacecrafts (SCs) during the approximately 10 s of flight time a laser beam will take from one SC to reach a distant SC of three million kilometers away. The Tilt-to-length (TTL) noise budget for the PAAM is constrained to less than $8 \mathrm{pm}/\sqrt{\mathrm{Hz}}$ within the frequency range of 1 mHz to 1 Hz. This constraint requires that the measurement noise of the interferometer remains below this threshold to guarantee the precision needed for gravitational wave detection in space. In the present work, an equal-arm heterodyne interferometer, which is fixed in a vacuum system with multilayer thermal shields, is proposed for the OPD (Optical Path Difference) measurement. The background measurement noise of the system is smaller than $60 \mathrm{pm}/\sqrt{\mathrm{Hz}}$ within the frequency range of 1 mHz to 1 Hz. This corresponds to an 84.6% noise reduction at 1 mHz compared to similar unshielded interferometers utilizing conventional bonding methods, demonstrating that the proposed system effectively suppresses measurement noises, particularly thermal noise, in the low-frequency range. Full article

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. Full article

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 (${10}^{-3} \mathrm{P}\mathrm{a}$), 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 $390 \mathrm{p}\mathrm{m}/\sqrt{\mathrm{H}\mathrm{z}}$ when the frequency is between 1 mHz and 1 HZ. By analogy, the optical path difference caused by the steering mirror reaches $5 \mathrm{p}\mathrm{m}/\sqrt{\mathrm{H}\mathrm{z}}$ in the 1 mHz to 1 Hz frequency band. The proposed TTL noise model is subsequently verified. Full article

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. Full article

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. Full article

Since the turn of the millennium, the development and commercial availability of optical frequency combs has led to a steadily increase of worldwide installed frequency combs and a growing interest in using them for industrial-related metrology applications. Especially, GPS-referenced frequency combs often serve as a “self-calibrating” length standard for laser wavelength calibration in many national metrology institutes with uncertainties better than u = 1 × 10⁻¹¹. In this contribution, the application of a He-Ne laser source permanently disciplined to a GPS-referenced frequency comb for the interferometric measurements in a nanopositioning machine with a measuring volume of 200 mm × 200 mm × 25 mm (NPMM-200) is discussed. For this purpose, the frequency stability of the GPS-referenced comb is characterized by heterodyning with a diode laser referenced to an ultrastable cavity. Based on this comparison, an uncertainty of u = 9.2 × 10⁻¹² (τ = 8 s, k = 2) for the GPS-referenced comb has been obtained. By stabilizing a tunable He-Ne source to a single comb line, the long-term frequency stability of the comb is transferred onto our gas lasers increasing their long-term stability by three orders of magnitude. Second, short-term fluctuations-related length measurement errors were reduced to a value that falls below the nominal resolving capabilities of our interferometers (ΔL/L = 2.9 × 10⁻¹¹). Both measures make the influence of frequency distortions on the interferometric length measurement within the NPMM-200 negligible. Furthermore, this approach establishes a permanent link of interferometric length measurements to an atomic clock. Full article

Delayed self-heterodyne/homodyne measurements based on an unbalanced interferometer are the most used methods for measuring the linewidth of narrow-linewidth lasers. They typically require the service of a delay of six times (or greater) than the laser coherence time to guarantee the Lorentzian characteristics of the beat notes. Otherwise, the beat notes are displayed as a coherent envelope. The linewidth cannot be directly determined from the coherence envelope. However, measuring narrow linewidths using traditional methods introduces significant errors due to the 1/f frequency noise. Here, a short fiber-based linewidth measurement scheme was proposed, and the influence of the noise floor on the measurement of the laser linewidth using this scheme was studied theoretically and experimentally. The results showed that this solution and calibration process is capable of significantly improving the measurement accuracy of narrow linewidth. Full article

The laser ranging interferometer onboard the Gravity Recovery and Climate Experiment Follow-On mission proved the feasibility of an interferometric sensor for inter-satellite length tracking with sub-nanometer precision, establishing an important milestone for space laser interferometry and the general expectation that future gravity missions will employ heterodyne laser interferometry for satellite-to-satellite ranging. In this paper, we present the design of an on-axis optical bench for next-generation laser ranging which enhances the received optical power and the transmit beam divergence, enabling longer interferometer arms and relaxing the optical power requirement of the laser assembly. All design functionalities and requirements are verified by means of computer simulations. A thermal analysis is carried out to investigate the robustness of the proposed optical bench to the temperature fluctuations found in orbit. Full article

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 $3.31\times {10}^{-11}$$\mathrm{m}$/$\sqrt{\mathrm{Hz}}$ at 100 $\mathrm{m}$$\mathrm{Hz}$ is achieved after applying our noise subtraction algorithm to a benchtop prototype interferometer that showed a noise level of $2.76\times {10}^{-10}$$\mathrm{m}$/$\sqrt{\mathrm{Hz}}$ at 100 $\mathrm{m}$$\mathrm{Hz}$ when tested in vacuum at levels of $3\times {10}^{-5}$ 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. Full article

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. Full article

In this paper, a novel, compact, and high-precision axial error measurement using a frequency-modulated interferometer is developed. Normally, heterodyne interferometers are a powerful system for small displacement measurements due to their property of being less sensitive to temperature and pressure variations. However, the maximum measurement speed of the heterodyne interferometer is around 5 m/s because it is usually limited by the difference in frequency between the two components of the laser beam, which is no larger than 3 MHz or 20 MHz corresponding laser source based on the Zeeman effect and acousto-optic modulator, respectively. The proposed measuring system is realized by modulating the frequency of the laser diode source at a high modulation frequency and using lock-in amplifiers to extract the harmonics of the interference signal. The measurement speed is proportional to the modulation frequency. Thus, the higher the modulation frequency, the higher the measuring speed attains. The frequency-modulated interferometer is then applied to measure the axial error of an ultra-precision spindle. The proposed system can be a capable solution for noncontact and high-precision spindle error measurements in the machining process. Full article

A polarization-insensitive recirculating delayed self-heterodyne method (PI-RDSHM) is proposed and demonstrated for the precise measurement of sub-kilohertz laser linewidths. By a unique combination of Faraday rotator mirrors (FRMs) in an interferometer, the polarization-induced fading is effectively reduced without any active polarization control. This passive polarization-insensitive operation is theoretically analyzed and experimentally verified. Benefited from the recirculating mechanism, a series of stable beat spectra with different delay times can be measured simultaneously without changing the length of delay fiber. Based on Voigt profile fitting of high-order beat spectra, the average Lorentzian linewidth of the laser is obtained. The PI-RDSHM has advantages of polarization insensitivity, high resolution, and less statistical error, providing an effective tool for accurate measurement of sub-kilohertz laser linewidth. Full article

In this study, a compound speckle interferometer for measuring three-degree-of-freedom (3-DOF) displacement is proposed. The system, which combines heterodyne interferometry, speckle interferometry and beam splitting techniques, can perform precision 3-DOF displacement measurements, while still having the advantages of high resolution and a relatively simple configuration. The incorporation of speckle interferometry allows for non-contact displacement measurements by detecting the phase of the speckle interference pattern formed from the convergence of laser beams on the measured rough surface. Experiments were conducted to verify the measurement capabilities of the system, and the results show that the proposed system has excellent measurement capabilities suitable for future real-world applications. Full article

Laser interferometers can achieve a nanometer-order uncertainty of measurements when their frequencies are locked to the reference frequencies of the atom or molecule transitions. There are three types of displacement-measuring interferometers: homodyne, heterodyne, and frequency modulation (FM) interferometers. Among these types of interferometer, the FM interferometer has many advantageous features. The interference signal is a series of time-dependent harmonics of modulation frequency, so the phase shift can be detected accurately using the synchronous detection method. Moreover, the FM interferometer is the most suitable for combination with a frequency-locked laser because both require frequency modulation. In previous research, low modulation frequencies at some tens of kHz have been used to lock the frequency of laser diodes (LDs). The low modulation frequency for the laser source means that the maximum measurement speed of the FM interferometers is limited. This paper proposes a novel contribution regarding the application of a high-frequency modulation for an LD to improve both the frequency stability of the laser source and the measurement speed of the FM interferometer. The frequency of the LD was locked to an I₂ hyperfine component at 1 MHz modulation frequency. A high bandwidth lock-in amplifier was utilized to detect the saturated absorption signals of the I₂ hyperfine structure and induce the signal to lock the frequency of the LD. The locked LD was then used for an FM displacement measuring interferometer. Moreover, a suitable modulation amplitude that affected the signal-to-noise ratio of both the I₂ absorption signal and the harmonic intensity of the interference signal was determined. In order to verify the measurement resolution of the proposed interferometer, the displacement induced by a piezo electric actuator was concurrently measured by the interferometer and a capacitive sensor. The difference of the displacement results was less than 20 nm. To evaluate the measurement speed, the interferometer was used to measure the axial error of a high-speed spindle at 500 rpm. The main conclusion of this study is that a stable displacement interferometer with high accuracy and a high measurement speed can be achieved using an LD frequency locked to an I₂ hyperfine transition at a high modulation frequency. Full article