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Keywords = heterodyne interferometer

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19 pages, 5033 KiB  
Article
Development and Verification of Sampling Timing Jitter Noise Suppression System for Phasemeter
by Tao Yu, Ke Xue, Hongyu Long, Mingzhong Pan, Zhi Wang and Yunqing Liu
Photonics 2025, 12(6), 623; https://doi.org/10.3390/photonics12060623 - 19 Jun 2025
Viewed by 305
Abstract
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 [...] Read more.
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/Hz1/2@(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/Hz1/2@(0.1 mHz–1 Hz), which meets the requirements of space gravitational wave missions. Full article
(This article belongs to the Special Issue Deep Ultraviolet Detection Materials and Devices)
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15 pages, 7516 KiB  
Article
Correction of Error Interference Fringes Based on Automatic Spectral Analysis
by Siqian Yang, Xinqiang Wang, Tingli Song, Wei Xiong, Song Ye and Fangyuan Wang
Optics 2025, 6(2), 26; https://doi.org/10.3390/opt6020026 - 6 Jun 2025
Viewed by 530
Abstract
When interferograms in space heterodyne spectrometers exhibit tilted or distorted fringes, significant errors may occur in the demodulated spectral information. To address this issue, we propose a method for interferogram correction based on automatic spectral analysis. Simulations on erroneous interferograms of monochromatic and [...] Read more.
When interferograms in space heterodyne spectrometers exhibit tilted or distorted fringes, significant errors may occur in the demodulated spectral information. To address this issue, we propose a method for interferogram correction based on automatic spectral analysis. Simulations on erroneous interferograms of monochromatic and polychromatic light demonstrate that this method effectively corrects fringe tilts and significantly improves spectral demodulation accuracy. The standard deviations between the corrected spectra and ideal spectra for monochromatic and polychromatic light are 0.016 and 0.019, respectively, compared to 0.104 and 0.127 for uncorrected spectra. Additionally, the method successfully corrects experimental interferograms of potassium and neon lamps, accurately demodulating characteristic peaks of potassium and neon emission lines. It also enables accurate displacement measurement in a Michelson interferometer experiment. This method, through automatic analysis and one-sided spectral correction, efficiently and accurately corrects erroneous interferograms and enhances spectral demodulation accuracy, showing broad application potential. Full article
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14 pages, 5039 KiB  
Article
Measurement of Optical Path Difference of Point-Ahead Angle Mechanism with a Multi-Layer Thermal Insulated Equal-Arm Heterodyne Interferometer
by Yue Guo, Jinke Yang, Hongxing Qi, Lingqiang Meng and Jianjun Jia
Appl. Sci. 2025, 15(9), 4863; https://doi.org/10.3390/app15094863 - 27 Apr 2025
Viewed by 413
Abstract
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 [...] Read more.
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 pm/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 pm/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
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21 pages, 5113 KiB  
Article
An Active Radar Interferometer Utilizing a Heterodyne Principle-Based Target Modulator
by Simon Müller, Andreas R. Diewald and Georg Fischer
Sensors 2025, 25(6), 1711; https://doi.org/10.3390/s25061711 - 10 Mar 2025
Viewed by 611
Abstract
The Active Radar Interferometer (AcRaIn) represents a novel approach in secondary radar technology, aimed at environments with high reflective clutter, such as pipes and tunnels. This study introduces a compact design minimizing peripheral components and leveraging commercial semiconductor technologies operating in the 24 [...] Read more.
The Active Radar Interferometer (AcRaIn) represents a novel approach in secondary radar technology, aimed at environments with high reflective clutter, such as pipes and tunnels. This study introduces a compact design minimizing peripheral components and leveraging commercial semiconductor technologies operating in the 24 GHz ISM band. A heterodyne principle was adopted to enhance unambiguity and phase coherence without requiring synchronization or separate communication channels. Experimental validation involved free-space and pipe measurements, demonstrating functionality over distances up to 150 m. The radar system effectively reduced interference and achieved high precision in both straight and bent pipe scenarios, with deviations below 1.25% compared to manual measurements. By processing signals at intermediate frequencies, advantages such as improved efficiency, isolation, and system flexibility were achieved. Notably, the integration of amplitude modulation suppressed passive clutter, enabling clearer signal differentiation. Key challenges identified include optimizing signal processing and addressing logarithmic signal attenuation for better precision. These findings underscore AcRaIn’s potential for pipeline monitoring and similar applications. Full article
(This article belongs to the Special Issue Radar Target Detection, Imaging and Recognition)
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13 pages, 5760 KiB  
Article
Prism-Based Spatial Heterodyne Spectrometer with a Fixed Fringe Localization Plane
by Zihao Liu, Da Zhang, Huanyu Yang and Chunling Huo
Appl. Sci. 2025, 15(2), 598; https://doi.org/10.3390/app15020598 - 9 Jan 2025
Cited by 1 | Viewed by 987
Abstract
Spatial heterodyne spectroscopy (SHS) based on prism dispersion is a novel technique designed to overcome the limitations of traditional grating-based SHS, which is affected by grating diffraction. However, there are still some challenges with this technique, one of which is that the fringe [...] Read more.
Spatial heterodyne spectroscopy (SHS) based on prism dispersion is a novel technique designed to overcome the limitations of traditional grating-based SHS, which is affected by grating diffraction. However, there are still some challenges with this technique, one of which is that the fringe localization plane (FLP) moves with changes in wavelength. This paper proposes a prism-based tunable SHS where the FLP is fixed, utilizing prism–bimirror–mirror structures. The theoretical spectral resolving power, based on an example, is higher than 1300 in the spectral range from 10,000 cm−1 to 25,641 cm−1 and is approximately 27,595 at 25,641 cm−1. Furthermore, we propose solutions to simplify the motion control system and address the problem of spectral aliasing. Full article
(This article belongs to the Special Issue Advanced Spectroscopy Technologies)
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21 pages, 5065 KiB  
Article
Application of DS-DFT to the Fine Spectral Estimation of High-Noise Signals
by Lin Qin, Suihu Dang, Di Fu and Yutao Feng
Electronics 2024, 13(24), 5057; https://doi.org/10.3390/electronics13245057 - 23 Dec 2024
Viewed by 673
Abstract
This paper presented an extended double-subsegment discrete Fourier transform (DS-DFT) algorithm as a tool for the fine spectral estimation of high-noise environments, which was previously effective in low-noise scenarios, and as such, its application to the analysis of noisy signals observed by a [...] Read more.
This paper presented an extended double-subsegment discrete Fourier transform (DS-DFT) algorithm as a tool for the fine spectral estimation of high-noise environments, which was previously effective in low-noise scenarios, and as such, its application to the analysis of noisy signals observed by a satellite-based interferometer was investigated. The observation of satellite-borne Doppler asymmetric spatial heterodyne spectroscopy (DASH) was first simulated to obtain the signals of low- and high-noise levels; then, a practical criterion to classify noise levels in the interferograms based on the DS-DFT results was introduced and validated by calculating the SNR. For high-noise signals, DS-DFT remains robust by employing phase differences and amplitude ratios for fine frequency estimation. Full article
(This article belongs to the Topic Hyperspectral Imaging and Signal Processing)
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13 pages, 5636 KiB  
Article
Thin Copper Plate Defect Detection Based on Lamb Wave Generated by Pulsed Laser in Combination with Laser Heterodyne Interference Technique
by Xinhao Wang, Zhaojiong Zhu, Guqing Guo, Xiaocong Sun, Ting Gong, Yali Tian, Yueting Zhou, Xuanbing Qiu, Xiaohu He, Huiqin Chen, Christa Fittschen and Chuanliang Li
Sensors 2024, 24(10), 3103; https://doi.org/10.3390/s24103103 - 14 May 2024
Cited by 5 | Viewed by 1344
Abstract
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 [...] Read more.
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
(This article belongs to the Section Fault Diagnosis & Sensors)
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13 pages, 16919 KiB  
Article
A Picometre-Level Resolution Test Method without Nonlinearity for Heterodyne Interferometer Measurement Electronics
by Yunke Sun, Wenjun Li, Xu Xing, Jianing Wang, Pengcheng Hu and Jiubin Tan
Photonics 2024, 11(4), 331; https://doi.org/10.3390/photonics11040331 - 2 Apr 2024
Cited by 1 | Viewed by 1811
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Optical Devices/Components/Coatings for Ultra-Precision Equipment)
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14 pages, 5775 KiB  
Article
Measurement of the Optical Path Difference Caused by Steering Mirror Using an Equal-Arm Heterodyne Interferometer
by Weizhou Zhu, Yue Guo, Qiyi Jin, Xue Wang, Xingguang Qian, Yong Xie, Lingqiang Meng and Jianjun Jia
Photonics 2023, 10(12), 1365; https://doi.org/10.3390/photonics10121365 - 11 Dec 2023
Cited by 5 | Viewed by 2045
Abstract
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 [...] Read more.
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 (103 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. Full article
(This article belongs to the Special Issue Optical Interferometry)
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11 pages, 2991 KiB  
Article
High-Bandwidth Heterodyne Laser Interferometer for the Measurement of High-Intensity Focused Ultrasound Pressure
by Ke Wang, Guangzhen Xing, Ping Yang, Min Wang, Zheng Wang and Qi Tian
Micromachines 2023, 14(12), 2225; https://doi.org/10.3390/mi14122225 - 11 Dec 2023
Cited by 1 | Viewed by 1794
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Progress and Application of Ultra-Precision Laser Interferometry)
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19 pages, 5968 KiB  
Article
Drift Error Compensation Algorithm for Heterodyne Optical Seawater Refractive Index Monitoring of Unstable Signals
by Shiwen Zhang, Liyan Li, Yuliang Liu and Yan Zhou
Sensors 2023, 23(20), 8460; https://doi.org/10.3390/s23208460 - 14 Oct 2023
Cited by 4 | Viewed by 1282
Abstract
The refractive index measurement of seawater has proven significance in oceanography, while an optical heterodyne interferometer is an important, highly accurate, tool used for seawater refractive index measurement. However, for practical seawater refractive index measurement, the refractive index of seawater needs to be [...] Read more.
The refractive index measurement of seawater has proven significance in oceanography, while an optical heterodyne interferometer is an important, highly accurate, tool used for seawater refractive index measurement. However, for practical seawater refractive index measurement, the refractive index of seawater needs to be monitored for long periods of time, and the influence of drift error on the measurement results for these cases cannot be ignored. This paper proposes a drift error compensation algorithm based on wavelet decomposition, which can adaptively separate the background from the signal, and then calculate the frequency difference to compensate for the drift error. It is suitable for unstable signals, especially signals with large differences between the beginning and the end, which is common in actual seawater refractive index monitoring. The authors identify that the primary cause of drift error is the frequency instability of the acousto-optic frequency shifter (AOFS), and the actual frequency difference was measured through experimentation. The frequency difference was around 0.1 Hz. Simulation experiments were designed to verify the effectiveness of the algorithm, and the standard deviation of the optical length of the results was on the scale of 10−8 m. Liquid refractive index measurement experiments were carried out in a laboratory, and the measurement error was reduced from 36.942% to 0.592% after algorithm processing. Field experiments were carried out regarding seawater refractive index monitoring, and the algorithm-processing results are able to match the motion of the target vehicle. The experimental data were processed with different algorithms, and, according to the comparison of the results, the proposed algorithm performs better than other existing drift error elimination algorithms. Full article
(This article belongs to the Special Issue Optical Sensors and Measuring Systems: Design and Applications)
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16 pages, 10808 KiB  
Article
Design and Analysis of a Stable Support Structure for a Near-Infrared Space-Borne Doppler Asymmetric Spatial Heterodyne Interferometer
by Jian Sun, Wei Wang, Chenguang Chang, Di Fu, Xiongbo Hao, Juan Li, Yutao Feng and Bingliang Hu
Appl. Sci. 2023, 13(18), 10446; https://doi.org/10.3390/app131810446 - 19 Sep 2023
Viewed by 1195
Abstract
As spectral resolution increases, the dimension of the Doppler Asymmetric Spatial Heterodyne (DASH) interferometer increases. The existing approach for stably mounting the interferometer is limited to mounting a normal-sized DASH interferometer. In this study, a novel and stable structure is proposed, with its [...] Read more.
As spectral resolution increases, the dimension of the Doppler Asymmetric Spatial Heterodyne (DASH) interferometer increases. The existing approach for stably mounting the interferometer is limited to mounting a normal-sized DASH interferometer. In this study, a novel and stable structure is proposed, with its effecti1veness exemplified for a near-infrared (NIR) DASH interferometer. The mathematical model of a flexible structure was established. The parameters of the support structure were optimized by requiring the mechanical stress of the flexible structure and shear stress at the bonding surface to be less than the strength value. The spring constants were optimally designed to adjust natural frequency and minimize stress. The finite element analysis (FEA) results show that the maximum mechanical stress was 65.56 MPa. The maximum shear stress was 3.4 MPa. All stress values had a high safety margin. The mechanical material and adhesive area were optimally designed. Therefore, the thermal resistance of the structure was improved by 7.5 times. The test results indicate that the proposed flexible support structure could satisfy the requirements of the launch environment. The results from FEA and vibration tests were consistent with the model calculation results. Compared to existing structures, the mechanical performance and thermal resistance were improved. Full article
(This article belongs to the Section Mechanical Engineering)
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14 pages, 6227 KiB  
Article
Glucose Concentration Measurement by All-Grating-Based System
by Hung-Chih Hsieh, Yi-Ming Lu and Ke-Cheng Huang
Sensors 2023, 23(9), 4216; https://doi.org/10.3390/s23094216 - 23 Apr 2023
Viewed by 2010
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Advanced Sensing Technology in Blood Glucose Monitoring)
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9 pages, 3468 KiB  
Technical Note
An Efficient Calibration System of Optical Interferometer for Measuring Middle and Upper Atmospheric Wind
by Guangyi Zhu, Yajun Zhu, Martin Kaufmann, Tiancai Wang, Weijun Liu and Jiyao Xu
Remote Sens. 2023, 15(7), 1898; https://doi.org/10.3390/rs15071898 - 31 Mar 2023
Cited by 3 | Viewed by 1985
Abstract
Detection of the Doppler shift of airglow radiation in the middle and upper atmosphere is one of the most important methods for remote sensing of the atmospheric wind field. Laboratory and routine field calibration of an optical interferometer for wind measurement is very [...] Read more.
Detection of the Doppler shift of airglow radiation in the middle and upper atmosphere is one of the most important methods for remote sensing of the atmospheric wind field. Laboratory and routine field calibration of an optical interferometer for wind measurement is very important. We report a novel calibration system that simulates a frequency shift of airglow emission lines introduced by wind in the middle and upper atmosphere for calibrating passive optical interferometers. The generator avoids the shortcomings of traditional motor-driven Doppler-shift generators in terms of stability and security while improving accuracy and simplifying assemblies. A simulated wind speed can be determined simultaneously using the light-beat method. The wind error simulated by the generator mainly comes from the light source, which is about 0.63 m/s. An experimental demonstration was conducted using a calibrated Fabry–Perot interferometer and showed that the root mean square of the measurement uncertainty is 0.91 m/s. The novel calibration system was applied to calibrate an asymmetric spatial heterodyne spectrometer (ASHS)-type interferometer successfully. The results demonstrate the feasibility of the system. Full article
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13 pages, 3844 KiB  
Article
A Novel Analog Interpolation Method for Heterodyne Laser Interferometer
by Chung-Ping Chang, Syuan-Cheng Chang, Yung-Cheng Wang and Pin-Yi He
Micromachines 2023, 14(3), 696; https://doi.org/10.3390/mi14030696 - 21 Mar 2023
Cited by 3 | Viewed by 2255
Abstract
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. [...] Read more.
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
(This article belongs to the Special Issue Precision Mechatronics: Design, Control and Applications)
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