Search Results (37)

Optical interferometry provides high-precision displacement and angle measurement solutions for a wide range of cutting-edge industrial applications. One of the key factors to achieve such precision lies in highly accurate optical encoder signal processing, as well as the calibration and compensation techniques customized for specific measurement principles. Optical interferometric techniques, including laser interferometry and grating interferometry, are usually classified into homodyne and heterodyne systems according to their working principles. In homodyne interferometry, the displacement is determined by analyzing the phase variation of amplitude-modulated signals, and common demodulation methods include error calibration methods and ellipse parameter estimation methods. Heterodyne interferometry obtains displacement information through the phase variation of beat-frequency signals generated by the interference of two light beams with shifted frequencies, and its demodulation techniques include pulse-counting methods, quadrature phase-locked methods, and Kalman filtering. This paper comprehensively reviews the widely used signal processing techniques in optical interferometric measurements over the past two decades and conducts a comparative analysis based on the characteristics of different methods to highlight their respective advantages and limitations. Finally, the hardware platforms commonly used for optical interference signal processing are introduced. Full article

The primary measurement involves detecting tiny (picometer-level) pathlength fluctuations between satellites using heterodyne laser interferometry for space-based gravitational wave detection. The interference of two laser beams with a MHz-level frequency difference produces a MHz beat-note, in which the gravitational wave signal is encoded in the phase of the beat-note. The phasemeter then performs micro-radian accuracy phase measurement and communication information demodulation for this beat-note. To mitigate the impact of phase modulation, existing solutions mostly alleviate it by reducing the modulation depth and optimizing the structure of the pseudo-random noise (PRN) codes. Since the phase modulation is not effectively separated from the phase of the beat-note phase measurement, it has a potential impact on the phase extraction of the micro-radian accuracy of the beat-note. To solve this problem, this paper analyzes the influence mechanism of phase modulation on beat-note phase measurement and proposes a method to separate the modulated phase based on complex rotation. The beat-note is processed by complex conjugate rotation, which can effectively eliminate the PRN modulated phase. Simulation and analysis results demonstrate that this method can significantly enhance the purity of the measured phase in the beat-note while maintaining the ranging and communication functions. Targeting the application of the micro-radian phasemeter in space-based gravitational wave detection, this study presents the reconstruction and separation method of the ranging and communication phase in beat-note, which also provides a new direction for the final selection of modulation depth in the future. Full article

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

Space gravitational wave detection uses a three-satellite formation scheme, with the distance between satellites reaching hundreds of thousands or millions of kilometers. According to the principle of laser heterodyne interferometry, the distance change between the inter-satellite inertial references caused by the gravitational wave event is converted into the phase change of the heterodyne interference signal. The payload for measuring the phase change information is the phasemeter. The mission requires that the phasemeter’s ranging accuracy is 1 picometer, and the corresponding phase measurement accuracy is required to reach 2π μrad/Hz^1/2 @(0.1 mHz–1 Hz). Due to the inter-satellite Doppler effect, the dynamic range of the interference signal frequency reaches 5 MHz to 25 MHz. Due to the sampling jitter noise of the interference signal, it is necessary to suppress the noise through a single pilot tone. This paper introduces the development of the phasemeter, which uses a single pilot tone to suppress sampling jitter noise. The test results show that when the dynamic range of the interference signal frequency is 5 MHz to 25 MHz, the phasemeter meets the mission indicator requirement of 2π μrad/Hz^1/2 @(0.1 mHz–1 Hz). Full article

Space-based gravitational wave detection uses an equilateral triangular satellite constellation with inter-satellite laser heterodyne interferometry to measure displacement variations caused by gravitational waves. Inter-satellite laser communication is critical for data transmission, redundancy and clock synchronization, which suppresses clock noise and enhances detection sensitivity. This integrated approach ensures precise gravitational wave information extraction, supporting the high-accuracy requirements of space-based observatories. This study focuses on the modeling and simulation of inter-satellite laser communication for space-based gravitational wave detection. Based on the data-transmission requirements of such systems, the principles of inter-satellite laser communication are analyzed. The research includes the selection of pseudo-random noise (PRN) codes, the signal scheme design and the development of the mathematical models for signal transmission. A simulation model is subsequently constructed in Simulink to evaluate the system. The simulation results confirm the accuracy of the model’s functionalities, including spreading, phase modulation, noise addition, phase demodulation and despreading. Additionally, the model achieves a data-transmission rate of 62.5 kbps with a bit error rate (BER) better than ${10}^{-6}$ when the modulation index exceeds $3.4\times {10}^{-3}$, meeting the requirements for inter-satellite laser communication in space-based gravitational wave detection. Full article

Laser heterodyne interferometry plays a crucial role in measuring the velocity of water particles during the calibration of hydrophones with the optical method. The velocity of water particles acts as an indicator of acoustic-pressure variations and can be used to evaluate the stability of the acoustic field. The calibration of hydrophones requires a stable acoustic field environment; currently, though, the assessment of acoustic field stability is largely subjective. This study introduces the Normalized Dynamic Time-Warping (NDTW) algorithm, which objectively evaluates acoustic field stability. Sine-fitting is applied to the region of interest in the measured signal to obtain a reference signal. Subsequently, the NDTW algorithm is used to calculate the difference between the measured and reference signals, enabling the assessment of acoustic field stability. The NDTW algorithm effectively identifies subtle differences between signals and addresses the accumulation errors arising from varying signal lengths. The calibration results showed that for signals of high quality within the identified frequency band, the calibration outcomes obtained using the NDTW algorithm deviated from the reciprocity method by no more than 0.7 dB. For frequency bands with poor signal quality identified by the NDTW algorithm, the deviation between the calibration results and the reciprocity method exceeded 0.7 dB. Full article

Optical interferometry has emerged as a cornerstone technology for high-precision length measurement, offering unparalleled accuracy in various scientific and industrial applications. This review provides a comprehensive overview of the latest advancements in optical interferometry, with a focus on grating and laser interferometries. For grating interferometry, systems configurations ranging from single-degree- to multi-degree-of-freedom are introduced. For laser interferometry, different measurement methods are presented and compared according to their respective characteristics, including homodyne, heterodyne, white light interferometry, etc. With the rise of the optical frequency comb, its unique spectral properties have greatly expanded the length measurement capabilities of laser interferometry, achieving an unprecedented leap in both measurement range and accuracy. With regard to discussion on enhancement of measurement precision, special attention is given to periodic nonlinear errors and phase demodulation methods. This review offers insights into current challenges and potential future directions for improving interferometric measurement systems, and also emphasizes the role of innovative technologies in advancing precision metrology technology. Full article

The three spacecraft of the space gravitational wave antenna employ heterodyne interferometry to mitigate the effects of Doppler shift. Constrained by laser relative intensity noise (RIN) and the sampling frequency constraints of phase readout circuits, the widespread adoption of fixed offset frequencies effectively regulates the frequency of heterodyne interferometric beat notes within a reasonable frequency domain of [5 MHz, 25 MHz]. In this work, a high-precision fitness genetic algorithm for heterodyne interferometry is utilized to generate the initial offset frequency distribution scheme. To address issues with unreasonable switching times and offset frequency settings in the initial scheme for partial frequency domains, optimization strategies are proposed from three aspects: frequency domain selection extension, switch times control, and numerical low frequency. Results demonstrate that the optimization of frequency domain selection extension narrows the reasonable frequency domain to [5 MHz, 15 MHz] and [7 MHz, 17 MHz]. Optimization of switch times control ensures that switching times of offset frequency distribution scheme generated under the settings of [6 MHz, 17 MHz] and wider frequency domains can be controlled within a reasonable range of 6 to 13 times. Fixed offset frequency settings are generally reduced by 24.3% after low-frequency optimization. This methodology and result can provide a reliable reference for Program Taiji and even related space gravitational wave antenna projects. Full article

The wide application of displacement measurement in high-precision equipment production and high-precision metrology is placing increasing pressure on the resolution of heterodyne interferometers. However, as the core component of an interferometer, since measurement electronics includes the cross-physical process of photoelectric conversion, its resolution is rarely evaluated, either on an individual level or as a whole. Therefore, in this paper, we propose a picometer resolution test method for measurement electronics, that uses intensity modulation signals based on an AOM to replace the beat frequency interference signals, and an ordinary commercial guide rail to equivalently generate the pm-level displacement of the heterodyne interferometer under laboratory conditions. Based on the detailed analysis of the type of noise in the test device, the correlation between the light intensity and the nonlinear error was established, and nonlinearity was suppressed to 10% of the original level. Furthermore, this test method allows one to perform a 0.1 mrad phase step test at 1 MHz signal frequency, equivalent to a 2.5 pm resolution test in a double-pass heterodyne interferometer. Simultaneously, it can be directly applied to the resolution test for measurement electronics with a center frequency in the range of 1 MHz to 20 MHz. 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

The low-frequency fluctuations of the atomic density within the cell can induce the longterm drift of the K-Rb-²¹Ne spin-exchange relaxation-free (SERF) co-magnetometer output, such that the accurate measurement of in situ atomic density is of great significance for improving the performance of co-magnetometer. In this paper, the complex refractive index model of the spin ensembles under the hybrid optical pumping condition is established first, according to which the relation between atomic density and its complex refractive index is revealed and an optical heterodyne-based scheme for atomic density detection is proposed. The dependence of the atomic density on the demodulated phase signal from the optical heterodyne-based scheme is provided by numerical simulations. After that, a dual acousto-optics frequency shifter (AOFS)-based optical heterodyne interferometry is constructed with a noise level below 1 mrad/$\sqrt{\mathrm{Hz}}$ for frequencies > 1 Hz, and a compact SERF co-magnetometer is implemented as the testing medium, by which the atomic density detection with resolution of 0.40 K @ 473 K is reached and the experimental results agree well with theoretical simulations. Moreover, the detection scheme proposed in this paper has the properties of high detection sensitivity and immunity to laser power fluctuation, which are also proved experimentally. Full article

An accurate, easy setup, low-cost, and time-saving method for measuring glucose concentration was proposed. An all-grating-based glucose concentration measurement system contained moving-grating-based heterodyne interferometry and a grating-based self-align sensor. By combining the first-order diffraction lights from two separated moving gratings by a polarization beam splitter and creating S- and P-polarized light interference by an analyzer, the interference signal could be a heterodyne light source with a heterodyne frequency depending on the relative velocities of the two moving gratings. Next, a grating-based self-align sensor was used to make the optical configuration setup easy and accurate. Moreover, the sensor was deposited on GOx film to improve the measurement sensitivity and specificity for glucose. Finally, the phase change induced by the reaction of the sensor and glucose solutions was detected. The validity of this method was proved, and the measurement resolution can reach 2 mg/dL. Full article

Using polarization-maintaining fiber (PMF) in dual-frequency heterodyne interferometry has the advantages of reducing the laser’s own drift, obtaining high-quality light spots, and improving thermal stability. Using only one single-mode PMF to achieve the transmission of dual-frequency orthogonal, linearly polarized beam requires angular alignment only once to realize the transmission of dual-frequency orthogonal, linearly polarized light, avoiding coupling inconsistency errors, so that it has the advantages of high efficiency and low cost. However, there are still many nonlinear influencing factors in this method, such as the ellipticity and non-orthogonality of the dual-frequency laser, the angular misalignment error of the PMF, and the influence of temperature on the output beam of the PMF. This paper uses the Jones matrix to innovatively construct an error analysis model for the heterodyne interferometry using one single-mode PMF, to realize the quantitative analysis of various nonlinear error influencing factors, and clarify that the main error source is the angular misalignment error of the PMF. For the first time, the simulation provides a goal for the optimization of the alignment scheme of the PMF and the improvement of the accuracy to the sub-nanometer level. In actual measurement, the angular misalignment error of the PMF needs to be smaller than 2.87° to achieve sub-nanometer interference accuracy, and smaller than 0.25° to make the influence smaller than ten picometers. It provides theoretical guidance and an effective means for improving the design of heterodyne interferometry instruments based on PMF and further reducing measurement errors. Full article

In this study, we developed a glucose fiber sensor incorporating heterodyne interferometry to measure the phase difference produced by the chemical reaction between glucose and glucose oxidase (GOx). Both theoretical and experimental results showed that the amount of phase variation is inversely proportional to glucose concentration. The proposed method provided a linear measurement range of the glucose concentration from 10 mg/dL to 550 mg/dL. The experimental results indicated that the sensitivity is proportional to the length of the enzymatic glucose sensor, and the optimum resolution can be obtained at a sensor length of 3 cm. The optimum resolution of the proposed method is better than 0.6 mg/dL. Moreover, the proposed sensor demonstrates good repeatability and reliability. The average relative standard deviation (RSD) is better than 10% and satisfied the minimum requirement for point-of-care devices. Full article

Upon reentering the Earth’s atmosphere from space, a reentry vehicle becomes enshrouded in an ionization layer. This layer is known as the reentry plasma sheath and is caused by aerodynamic heating. Owing to the oscillation of charged particles in the reentry plasma sheath, the electromagnetic waves for communication between the vehicle and ground are attenuated. Analysis of the plasma density and attenuation of electromagnetic waves in a reentry plasma environment would require experimentation in an environment in which an actual aircraft reenters the atmosphere. Alternatively, an experiment in a large-scale plasma wind tunnel would be necessary. Unfortunately, these experiments would be extremely costly. Therefore, in this study, the reentry plasma was reproduced at laboratory scale using the hot refractory anode vacuum arc (HRAVA) method. In addition, the pressure in the vacuum chamber was used as a variable to probe the characteristics of the reentry plasma according to the altitude. The plasma density and attenuation of electromagnetic waves propagating through the plasma medium were measured using heterodyne interferometry and reflectometry capable of frequency analysis in the range of 10−35 GHz. The results confirmed that the plasma density and attenuation of the electromagnetic waves increased as the pressure in the vacuum chamber increased. Full article