Frequency-modulated Continuous-wave Laser Research Articles

Frequency-modulated continuous-wave laser interferometry measurement method based on cross-correlation

Frequency-modulated continuous-wave (FMCW) laser interferometry technology holds significant potential for applications in the fields of ultraprecision manufacturing and high-precision sensing. This paper proposes a novel approach among current phase demodulation methods is based on cross-correlation to address the challenge of this technology. On the basis of nonlinear correction of a distributed feedback laser, the intercepted beat frequency signal was first preprocessed with Z-score signal normalization and a smoothing filter. Subsequently, the interference beat signal was subjected to processing using a correlation method to derive the correlation function. Finally, the phase difference between adjacent beat signals was determined by pinpointing the maximum value of the cross-correlation function, enabling accurate displacement demodulation. Experimental validation was performed by constructing an FMCW laser interferometric displacement measurement system. The results indicated that the standard deviation of the displacement error for the cross-correlation method was 2.41 nm during static measurements. Compared to conventional maximum-point method, the static measurement error of the cross-correlation method has been reduced by 1.43 times. In dynamic measurements in the 500 μm range, The measurement error of the cross-correlation method has been reduced by 6.04 times, avoiding the dynamic measurement positioning problem of conventional feature point demodulation methods and making the measurement results more accurate. This advancement holds substantial practical value in the realm of phase demodulation in laser interferometry.

Interpolation linearization predistortion technology for FMCW LiDAR.

Frequency-modulated continuous-wave (FMCW) laser ranging technology is an important development direction of light detection and ranging (LiDAR) for the future. It has the advantages of high ranging accuracy, high resolution, wide range, and no ranging blind zone. A distributed feedback laser can be used as a high-quality light source in FMCW laser ranging systems because of its wide frequency modulation range, simple frequency modulation mode, and small package. Aiming at the nonlinear problem of the laser in the frequency modulation process, we present a novel, to our knowledge, predistortion algorithm based on interpolation linear fitting to enhance the linearity of the FMCW laser for LiDAR systems. The sweeping frequency curve of the laser is obtained using the Hilbert transform, and then the sweeping frequency curve is segmented and linearly fitted to calculate the interpolated driving current signals corresponding to linear frequency changes. Using this method, we achieved a nonlinearity error lower than 1e-7 for the swept-frequency signal and demonstrated that the ranging error is less than ±5c m at a distance of 100m in the FMCW system. In addition, we also demonstrated a 3D static object point cloud with high imaging quality. Compared with the iterative predistortion algorithm based on the function fitting, this method avoids fitting errors at the inflection points of the triangular swept-frequency signal and the complexity of multiple iterative calculations. It enables rapid generation of pre-distorted swept-frequency signals, making it particularly suitable for real-time applications of automotive LiDAR systems.

Enhancing Monte Carlo simulations of aerosol scattering using photon matrices

Within aerosol-rich environments, efficient simulation of frequency-modulated continuous wave (FMCW) laser detector echo characteristics is crucial. Conventional methods often need more efficiency. To address this, we propose a photon matrix-based approach for simulating intricate photon scattering processes, enhancing simulation accuracy. This study focuses on short-range FMCW laser detection under aerosol interference, assessing performance via signal-to-noise ratio (SNR). We analyze the impact of amplitude modulation coefficient and photon count on SNR. Surprisingly, the photon count minimally affects SNR, while the amplitude modulation coefficient significantly influences it. These findings shed light on optimizing FMCW laser detection in aerosol-laden environments. Attention to the amplitude modulation coefficient can notably enhance SNR and overall detection efficiency.

An absolute ranging method based on FMCW principle using dual laser interferometry

The FMCW (Frequency Modulated Continuous Wave) laser interferometer can achieve high-precision displacement measurement by calculating the phase of the interference signal. Due to the need for continuous superposition of signal phases, the optical path and power supply cannot be interrupted during the measurement process. To solve this problem, this article proposes a new absolute ranging method—the decimal comparison method. Two distributed feedback lasers with different central wavelengths are used to measure the same target. The digital signal processing technology is used to solve the sampled interference signals, and the initial phase value corresponding to the decimal of interference is taken. Combined with the central wavelength of the two laser sources, the length variation of the F–P cavity corresponding to the number of interference periods is calculated. Finally, the optical path difference of the target is calculated by the established mathematical model. The experimental results show that this method can realize the absolute measurement of laser interferometry and can expand the application range of FMCW interferometry.

Research on absolute ranging technology of resampling phase comparison method based on FMCW

Abstract As an advanced optical precision ranging method, FMCW (frequency-modulated continuous-wave) laser interferometric ranging technology can achieve a large-scale and high-precision absolute distance measurement, so it has high research and application value in the field of coordinate measurement in large space. How to improve the resolution and stability of laser interferometry is a research difficulty in this technology. Based on FMCW laser interferometry relative distance technology, a method for achieving absolute distance measurement through phase comparison after repeated sampling is proposed. Using the FMCW laser distance measuring system, two interference optical paths of measuring interferometer and auxiliary interferometer are constructed, respectively. Synchronous sampling is performed on two interference signals, and the phase ratio of the two interference signals is obtained through the extracted frequency information. The optical path difference of the unknown measurement interferometer is derived from the known auxiliary interferometer information. This method uses a triangular wave modulation laser to reduce the influence of Doppler frequency shift and eliminate quantization errors. By using the fixed-point repeated sampling, the optical path difference information is quickly extracted, and the nonlinear error of laser interference frequency modulation is effectively reduced.

Broadband dual-chirp FMCW laser source based on DSB-SC modulation and cascaded FWM.

Based on dual-sideband suppressed-carrier (DSB-SC) modulation and two-stage cascaded four-wave-mixing (FWM), a scheme of broadband dual-chirp frequency-modulated continuous-wave (FMCW) laser source is proposed and experimentally demonstrated. First, via a Mach-Zehnder modulator biased at its null point, an original DSB-SC FMCW signal with 4.0 GHz swept-frequency range and 0.2 GHz/μs sweep rate is generated. Next, the original DSB-SC FMCW signal is sent to a 1 km dispersion compensation fiber for implementing first-stage FWM, a dual-chirp FMCW signal with 12.0 GHz swept-frequency range and 0.6 GHz/μs sweep rate is acquired and used as the pump for second-stage FWM. Finally, via second-stage FWM in a 200 m highly nonlinear fiber, a dual-chirp FMCW signal with a swept-frequency range of 36.0 GHz and sweep rate of 1.8 GHz/μs is generated. Taking the FMCW signal generated at different stages as the emitted signal, we evaluate the ranging resolution through fiber-based distance measurement, and the results demonstrate that the achieved ranging resolutions are 5.31 cm, 2.04 cm, and 1.18 cm, respectively. Through equalizing the optical power of generated FMCW signal over the swept-frequency range, the ranging resolution can be further improved.

Real-time high-precision FMCW laser range extraction method based on a hardware multiplier array.

Frequency-modulated continuous wave (FMCW) laser interferometry is an ideal large-scale absolute distance measurement method. It has advantages of high precision and noncooperative target measurement capability, with no blind spot for ranging. To meet the requirements of high-precision, high-speed 3D topography measurement technologies, a faster measurement speed of FMCW LiDAR at each measurement point is required. To solve the shortcomings of the existing technology, a real-time high-precision hardware solution method (including but not limited to FPGA and GPU) for lidar beat frequency signals is provided here based on hardware multiplier arrays to reduce lidar beat frequency signal processing time and to save energy and resource consumption during processing. A high-speed FPGA architecture was also designed for the frequency-modulated continuous wave lidar range extraction algorithm. The whole algorithm was designed and implemented in real time based on the principle of full-pipelines and parallelism. The results show that the processing speed of the FPGA system is faster than that of current top-performing software implementations.

Frequency-Modulated Continuous-Wave Laser Ranging With Sub-Nyquist Sampling Rate Using Asymmetric Chirped Waveforms

We propose a frequency-modulated continuous-wave (FMCW) laser range with sub-Nyquist sampling rates in which asymmetric chirped waveforms are used. Different de-chirped signals can be generated since the up-chirp and the down-chirp sections have different chirp rates. The distances are extracted at a sub-Nyquist sampling rate using a modified Vernier sampling, in which the sub-Nyquist sampling technique ratio is reconfigurable by changing the ratios of the chirp rates. A demonstrated experiment is carried out. The lengths of fiber can be measured with a sub-Nyquist sampling ratio of 1/10. Therefore, the proposed method reduces the sampling rate in the FMCW laser ranging system using Vernier sampling. Moreover, only a single-shot sampling is required, which reduces the complexity of the Vernier sampling.

Accurate Ranging of Dual Wavelength FMCW Laser Fuze Under Different Types of Aerosol Interference

Laser fuze has the advantages of high distance accuracy and strong anti-electromagnetic interference capability, but it is easily disturbed by aerosols, such as smoke, which hinders its detection performance and application. This article proposes the dual wavelength frequency-modulated continuous wave (FMCW) laser detection technology as a solution. Compared with the single-wavelength FMCW laser fuze, the detection performance and the target recognition ability are enhanced under severe interference. First, the principles of dual wavelength FMCW laser detection are analyzed, followed by a block diagram of the fuze system. Second, the single scattering attenuation characteristics of spherical aerosol particles in reaction to different wavelengths of laser beams are discussed, and the scale distribution and complex refractive index characteristics and laws of four typical aerosol particles, including soot, ocean, dust, and water soluble, are analyzed. Finally, the echo characteristics of 0.3- and 10.6- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> wavelength laser beams with or without a target are simulated and analyzed under the condition of typical aerosol heavy interference, and the spectral characteristics of the beat signal of the dual wavelength laser echo are obtained. According to this characteristic, a system for target recognition and distance determination using a dual-wavelength FMCW laser beam against aerosol interference is designed. The simulation results indicate that, in the presence of severe interference, the proposed system can effectively distinguish aerosol interference from the target and realize the accurate distance of the target.

Hybrid Integrated Frequency-Modulated Continuous-Wave Laser With Synchronous Tuning

We report a wavelength widely-tunable hybrid integrated external cavity laser (ECL) with synchronous tuning to achieve a large frequency chirp bandwidth and high chirp linearity. Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> Vernier microring resonators (MRRs) in the ECL function as an optical bandpass filter to offer strong wavelength selectivity and fast frequency tunability. The wavelength tuning range is 56 nm, the maximum output optical power is 22.5 mW, the minimum intrinsic linewidth is 2.9 kHz, and the static frequency sweep bandwidth is 56 GHz. A frequency-modulated continuous-wave (FMCW) signal is generated under synchronous modulation with a chirp bandwidth of 7.68 GHz at a 1 kHz repetition rate, much larger than that produced by modulating the phase shifter or the Vernier filter alone. A chirp linearization method based on a non-uniform sampling algorithm and an iterative learning algorithm is employed to reduce the chirp nonlinearity to 1.02×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> , allowing for a detection resolution of 2.47 cm.

Simultaneous measurement of distance and speed via frequency-modulated continuous-wave LIDAR system based on H13C14N gas cell

• Simultaneous and accurate measurement of distance and speed with frequency-modulated continuous-wave laser. • The traditional method of finding the measurement signal's frequency by Fourier transform is replaced. • Accurately fitting the relationship between the phase of the beat signal and the frequency of tunable laser according to the characteristics of the gas absorption cell. • Up and down-scanning frequency rate are obtained by Fabry Perot cavity. • The measurement signal's frequency is obtained by fitting relationship result and frequency rate. Traditional frequency-modulated continuous-wave lidar is to measure the distance of the target through the spectrogram of the beat signal. In this paper, we propose a lidar system to obtain distance and speed at the same time. The distance and speed of the moving target are extracted by product of the delay time obtained by H 13 C 14 N standard gas cell and the fitting frequency modulation rate obtained by Fabry Perot cavity, which can avoid spectral broadening. The experimental results show that the speed resolution of the system was 10µm/s, the mean error of the speed measurement from 0.1mm/s to 100mm/s was less than 162µm/s, and the mean standard deviation was less than 523µm/s. When the speed was less than 10mm/s and the distance was about 4.5m, the mean standard deviation of the distance was less than 163µm. With the advantages of light computation requirements, a simple optical path and measurement results with good repeatability and accuracy, this system has high practical value in precision industrial manufacturing.

Phase noise compensation experiment with frequency modulated continuous wave laser in atmospheric propagation

Experimental research is performed on a phase noise compensation (PNC) method to improve the signal-to-noise ratio of a frequency modulated continuous wave (FMCW) ladar under long-distance-detection and atmospheric propagation conditions. In the PNC method, a local self-coherent reference is generated where phase noise of the laser source is recorded. Then the phase noise of long-distance-target echo can be compensated by mean of the recorded source phase noise. The laser source of the ladar is chirped modulated from 1550-nm seed laser, whose bandwidth is 10 GHz. In the experiments, the target for test is an optical corner cube retro-reflector that placed over 10 km away from the ladar. The local self-coherent reference, also refer as auxiliary reference, is the heterodyne signal between the chirped laser source and the delay of itself. The delay path is a 5-km soundproofed fiber optic ring. A 2D data processing technique is proposed for ranging with the concatenately generated phase method applied to implement PNC. To verify the proposed technique under long-distance atmospheric propagation conditions, experiments are performed with the distances of the target as 12 and 19.5 km respectively, and the spectral linewidth of the seed laser as 100 Hz and 3 kHz respectively. By comparing the experimental results, the proposed technique is effective in compensating FMCW laser phase noise, even when the target is further and the phase noise of seed laser is worse.

Virtual Simulation of the Effect of FMCW Laser Fuse Detector's Component Performance Variability on Target Echo Characteristics under Smoke Interference.

The laser transmitter and photoelectric receiver are the core modules of the detector in a laser proximity fuse, whose performance variability can affect the accuracy of target detection and identification. In particular, there is no study on the effect of detector’s component performance variability on frequency-modulated continuous-wave (FMCW) laser fuse under smoke interference. Therefore, based on the principles of particle dynamic collision, ray tracing, and laser detection, this paper builds a virtual simulation model of FMCW laser transmission with the professional particle system of Unity3D, and studies the effect of performance variability of laser fuse detector components on the target characteristics under smoke interference. Simulation results show that the difference in the performance of the fuse detector components causes the amplitude variation and peak migration of the beat signal spectrum, and the change in the visibility of the smoke can also affect the results, which indicates that the factors affecting the signal-to-noise ratio (SNR) of the echo signal are related to the smoke interference and performance variability of the detector. The proposed simulation model is supported by experimental results, which reflect the reliability of the proposed findings. Therefore, this study can be used for the optimization of the parameters in the laser fuse antismoke interference to avoid false alarms.

Long distance high resolution FMCW laser ranging with phase noise compensation and 2D signal processing.

A long distance high resolution frequency-modulated continuous wave (FMCW) laser rangefinder with phase noise compensation and two-dimensional (2D) data processing skills is developed. Range-finding ladar consists of a continuously chirped laser source, an auxiliary reference interferometer, and a monostatic optical transceiver for target illumination and return photon collection. To extend the range unambiguity and lower the electronic processing bandwidth, a two-step laser frequency chirping scheme is adopted, where a long pulse width, small frequency bandwidth laser chirping signal are used in step 1 for coarse distance estimation, and a short pulse width and large frequency bandwidth laser chirping signal are applied afterwards for step 2 high resolution distance realization. An auxiliary reference interferometer is to record the phase noise originated from the laser source to compensate for phase errors induced in the target return photons. The 2D data processing skill helps to coherently sum up all the phase noise removed echo photons to achieve high resolution range peak extraction with high detection sensitivity. Experimental demonstration shows that the proposed FMCW ladar at 1550 nm wavelength with a laser chirping bandwidth of 10 GHz and electronic processing bandwidth of 200 MHz can measure a corner cube test target in an outdoor atmospheric environment, and the measurement results are 12013.905 m with a 2.4 cm range resolution under strong return photon levels and 12013.920 m with a 2.5 cm range resolution under weak return photon levels.

Computed tomography for distributed Brillouin sensing.

A method to reconstruct the spatial distribution of Brillouin gain spectrum from its Radon transform is proposed, which is a type of optical computed tomography. To verify the concept, an experiment was performed on distributed Brillouin fiber sensing, which succeeded in detecting a 55-cm strain section along a 10-m fiber. The experimental system to obtain the Radon transform of the Brillouin gain spectrum is based on a Brillouin optical correlation-domain analysis with a linear frequency-modulated continuous-wave laser. Combining distributed fiber sensing with computed tomography, this method can realize a high signal-to-noise ratio Brillouin sensing.

Hybrid integrated low-noise linear chirp frequency-modulated continuous-wave laser source based on self-injection to an external cavity

A hybrid integrated low-noise linear chirp frequency-modulated continuous-wave (FMCW) laser source with a wide frequency bandwidth is demonstrated. By employing two-dimensional thermal tuning, the laser source shows frequency modulation bandwidth of 10.3 GHz at 100 Hz chirped frequency and 5.6 GHz at 1 kHz chirped frequency. The intrinsic linewidth of 49.9 Hz with 42 GHz continuous frequency tuning bandwidth is measured under static operation. Furthermore, by pre-distortion linearization of the laser source, it can distinguish 3 m length difference at 45 km distance in the fiber length measurement experiment, demonstrating its application potential in ultra-long fiber sensing and FMCW light detection and ranging.

A Spectrum Correction Algorithm Based on Beat Signal of FMCW Laser Ranging System.

The accuracy of target distance obtained by a frequency modulated continuous wave (FMCW) laser ranging system is often affected by factors such as white Gaussian noise (WGN), spectrum leakage, and the picket fence effect. There are some traditional spectrum correction algorithms to solve the problem above, but the results are unsatisfactory. In this article, a decomposition filtering-based dual-window correction (DFBDWC) algorithm is proposed to alleviate the problem caused by these factors. This algorithm reduces the influence of these factors by utilizing a decomposition filtering, dual-window in time domain and two phase values of spectral peak in the frequency domain, respectively. With the comparison of DFBDWC and these traditional algorithms in simulation and experiment on a built platform, the results show a superior performance of DFBDWC based on this platform. The maximum absolute error of target distance calculated by this algorithm is reduced from 0.7937 m of discrete Fourier transform (DFT) algorithm to 0.0407 m, which is the best among all mentioned spectrum correction algorithms. A high performance FMCW laser ranging system can be realized with the proposed algorithm, which has attractive potential in a wide scope of applications.

Application Research of Frequency-Modulated Continuous-Wave Displacement Sensor Based on Zero-Crossing Phase Detecting Algorithm

Frequency-modulated continuous-wave (FMCW) interference, as a new technology of laser interferometry, has the advantages of length traceability, large range, high accuracy, simple structure, and optical fiber transmission. Based on the formula of FMCW laser interference displacement, a zero-crossing phase detection algorithm is proposed, which can accurately calculate the initial phase of a cosine signal in a modulation period, and it is successfully applied to the contact laser interference displacement sensor. The experimental results show that the FMCW technology based on the zero-crossing phase detection algorithm can achieve the technical specifications of the contact displacement sensor with a measurement range greater than 15 mm and the standard deviation is less than 0.01 μm. The conversion of noncontact measurement to contact measurement can realize the direct measurement of workpieces with complex surface conditions on the production line, breaking through the limitation of optical measurement and expanding the application of optical fiber interferometry.

High-precision optical fiber pressure sensor using frequency-modulated continuous-wave laser interference

This work presents a high-precision fiber optic pressure sensor based on frequency-modulated continuous-wave (FMCW) laser interference. The pressure sensor is primarily composed of a diaphragm-type Fabry–Pérot (F–P) cavity, with the diaphragm fabricated using high-elasticity SUS631 stainless steel. The external air pressure causes the center of the elastic diaphragm to deform, and this deformation results in a change in the F–P cavity length. The FMCW laser-interference method was used to demodulate the change in the length of the cavity and realize high-precision pressure measurements. The experimental results showed that when the pressure measurement is in the range of 0 kPa–600 kPa, an accuracy of 3.8 Pa can be obtained. In addition, the sensor had very good linearity with pressure change (R2 = 0.999 94), repeatability, and stability.

FMCW laser ranging method based on a frequency multiplier.

A reference interferometer is often introduced into the frequency-modulated continuous wave (FMCW) ranging system to deal with nonlinear laser modulation. In this system, the beat signal of the reference interferometer is regarded as the system clock to resample the measurement signal. According to Nyquist sampling theorem, the optical path difference (OPD) of the reference interferometer should be more than twice the target distance. We propose a resampling method that uses a frequency multiplier to help shorten the OPD of the reference interferometer. A quadruple frequency circuit board with two multipliers is added into the system to generate a new clock for this system. Results show that a target at a distance of 6.4 m can be measured when the OPD of the reference interferometer is provided by a 3 m delay fiber, and the ranging standard deviation of 9.4 µm is achieved.