Laser frequency sweep linearization by iterative learning pre-distortion for FMCW LiDAR

Linearity improvement of chirped distributed feedback laser diodes based on an analog electro-optical phase-locked loop

A linearity improvement method for frequency-modulated distributed feedback laser diodes (DFB-LD) is proposed and demonstrated based on a pre-distortion signal and an electro-optical phase-locked loop (EO-PLL). The pre-distortion signal is used to reduce the deterministic frequency errors. The EO-PLL is further used to suppress the stochastic frequency noise and enhance the coherence of the DFB-LD. In the EO-PLL, the DFB-LD output is transmitted through a Mach-Zehnder interferometer (MZI) and detected by a photodetector (PD) to get a beat note signal, which denotes the nonlinearity of the chirp. A mixing signal, achieved by mixing the beat note signal with a fixed frequency reference signal, is then filtered by a proportional integral filter (PIF) and feedback to the DFB-LD to reduce the stochastic frequency noise in the chirp. The EO-PLL bandwidth can be adjusted by tuning the PIF response. Consequently, a linear chirp optical signal with an enhanced linearity is generated from the DFB-LD. In the experiment, 788- and 321-time linearity improvements are implemented when the loop bandwidths are about 100 and 550 kHz, respectively. Correspondingly, residual frequency errors of 1.65 and 4.85 MHz at 52- and 450-THz/s chirp rates are obtained.

A microcomb-empowered Fourier domain mode-locked LIDAR

Light detection and ranging (LIDAR) has emerged as an indispensable tool in autonomous technology. Among its various techniques, frequency-modulated continuous wave (FMCW) LIDAR stands out due to its capability to operate with ultralow return power, immunity to unwanted light, and simultaneous acquisition of distance and velocity. However, achieving a rapid update rate with submicrometer precision remains a challenge for FMCW LIDARs. Here, we present such a LIDAR with a sub-10-nanometer precision and a 24.6-kilohertz update rate by combining a broadband Fourier domain mode-locked (FDML) laser with a silicon nitride soliton microcomb. An ultrahigh-frequency chirp rate up to 320 petahertz per second is linearized by a 50-gigahertz microcomb to reach this performance. Our theoretical analysis also contributes to resolving the challenge of FMCW velocity measurements with nonlinear frequency sweeps and enables us to realize velocity measurement with an uncertainty below 0.4 millimeter per second. Our work shows how microcombs can unlock the potential of ultrafast frequency sweeping lasers.

Multi-band reconfigurable microwave photonic transceiver towards high-performance integrated radar

As an effective approach to overcome the electronic bottlenecks of conventional electrical radars, microwave photonic radars have demonstrated significant superiority in their perception and recognition capabilities. However, trade-offs exist among the reconfigurability, signal time-bandwidth product (TBWP), linearity, and phase coherence of current photonic radars, which ultimately weaken the overall performance. To address these challenges, a photonic transceiver based on electrically assisted synchronized lasers is proposed and demonstrated, which combines high resolution and multi-band reconfigurability. Optical coherent heterodyne linear frequency-modulated (LFM) radar signal generation and photonic dechirping reception are implemented through the synchronized lasers at the transmitter and receiver, respectively. In a proof-of-concept experiment, reconfigurable LFM signals covering the L- to Ka-band with improved linearity and phase coherence are generated. Furthermore, the proposed photonic transceiver operates in the Ka-band with an ultra-large signal TBWP of 4 × 106, enabling high-resolution ranging and inverse synthetic aperture radar (ISAR) imaging. A range resolution of 1.92 cm and an imaging resolution of 1.92 cm × 1.89 cm are obtained, which require a receiver sampling rate of only 5 MSa/s. Featuring a simple structure, flexible reconfiguration, and integration compatibility, the demonstrated photonic transceiver opens new opportunities for next-generation miniaturized radar application scenarios.

Time-variant parity-time symmetry in frequency-scanning systems

Parity-time (PT) symmetry is an active research area that provides a variety of new opportunities for different systems with novel functionalities. For instance, PT symmetry has been used in lasers and optoelectronic oscillators to achieve single-frequency lasing or oscillation. A single-frequency system is essentially a static PT-symmetric system, whose frequency is time-invariant. Here we investigate time-variant PT symmetry in frequency-scanning systems. Time-variant PT symmetry equations and eigenfrequencies for frequency-scanning systems are developed. We show that time-variant PT symmetry can dynamically narrow the instantaneous linewidth of frequency-scanning systems. The instantaneous linewidth of a produced frequency-modulated continuous-wave (FMCW) waveform is narrowed by a factor of 14 in the experiment. De-chirping and radar imaging results also show that the time-variant PT-symmetric system outperforms a conventional frequency-scanning one. Our study paves the way for a new class of time-variant PT-symmetric systems and shows great promise for applications including FMCW radar and lidar systems.

Photonic stepped-frequency radar with 150-m unambiguous detection and centimeter range resolution

Photonic stepped-frequency radars based on optical frequency-shifting modulation have shown attractive properties such as wide bandwidth, centimeter range resolution, inherent frequency-time linearity with low spectrum spurs, and reduced system complexity. However, existing approaches typically exhibit meter- or centimeter-level radar range ambiguity, inversely proportional to the frequency step, due to the large frequency shift determined by acousto-optic or electro-optic (EO) modulators. Here, we overcome this limitation by injecting a narrowband, stepped-frequency signal into an optical frequency-shifting fiber cavity to achieve, for the first time, to our knowledge, a broadband photonic stepped-frequency radar with 150-m unambiguous detection and centimeter range resolution, surpassing the reported photonic- and electronic-based counterparts. The demonstrated approach effectively resolves the trade-off between ambiguity range and shifting frequency while maintaining the signal quality and bandwidth, bringing its practicality into reach for outdoor applications.

Non-Line-of-Sight Imaging and Vibrometry Using a Comb-Calibrated Coherent Sensor

Non-line-of-sight (NLOS) imaging has the ability to reconstruct hidden objects, allowing a wide range of applications. Existing NLOS systems rely on pulsed lasers and time-resolved single-photon detectors to capture the information encoded in the time of flight of scattered photons. Despite remarkable advances, the pulsed time-of-flight LIDAR approach has limited temporal resolution and struggles to detect the frequency-associated information directly. Here, we propose and demonstrate the coherent scheme-frequency-modulated continuous wave calibrated by optical frequency comb-for high-resolution NLOS imaging, velocimetry, and vibrometry. Our comb-calibrated coherent sensor presents a system temporal resolution at subpicosecond and its superior signal-to-noise ratio permits NLOS imaging of complex scenes under strong ambient light. We show the capability of NLOS localization and 3D imaging at submillimeter scale and demonstrate NLOS vibrometry sensing at an accuracy of dozen Hertz. Our approach unlocks the coherent LIDAR techniques for widespread use in imaging science and optical sensing.

Linearization of wavelength sweeping lasers for the construction of 4-D FMCW LiDAR images of slow-moving objects using baseband beat note signals

A FMCW LiDAR system of both the distributed feedback laser and external cavity laser is established in baseband beat notes, rather than up-conversion to an intermediate frequency to exclude flicker noise. Meanwhile, utilizing fast-scanning MEMS mirrors, high-quality real-time (1 fps) 4-D images of the slow-moving object (10 mm/s) can be directly constructed at the baseband with a central frequency as low as 100 kHz and a small Doppler shift. The proposed LiDAR architecture based on such a low-frequency baseband significantly improves the optical power budget on the transmitter side and eliminates the costly high-speed sampling circuits on the receiver side.

Photonic-electronic integrated circuit-based coherent LiDAR engine

Chip-scale integration is a key enabler for the deployment of photonic technologies. Coherent laser ranging or FMCW LiDAR, a perception technology that benefits from instantaneous velocity and distance detection, eye-safe operation, long-range, and immunity to interference. However, wafer-scale integration of these systems has been challenged by stringent requirements on laser coherence, frequency agility, and the necessity for optical amplifiers. Here, we demonstrate a photonic-electronic LiDAR source composed of a micro-electronic-based high-voltage arbitrary waveform generator, a hybrid photonic circuit-based tunable Vernier laser with piezoelectric actuators, and an erbium-doped waveguide amplifier. Importantly, all systems are realized in a wafer-scale manufacturing-compatible process comprising III-V semiconductors, silicon nitride photonic integrated circuits, and 130-nm SiGe bipolar complementary metal-oxide-semiconductor (CMOS) technology. We conducted ranging experiments at a 10-meter distance with a precision level of 10 cm and a 50 kHz acquisition rate. The laser source is turnkey and linearization-free, and it can be seamlessly integrated with existing focal plane and optical phased array LiDAR approaches.

Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR

LiDAR has high accuracy and resolution and is widely used in various fields. In particular, phase-modulated continuous-wave (PhMCW) LiDAR has merits such as low power, high precision, and no need for laser frequency modulation. However, with decreasing signal-to-noise ratio (SNR), the noise on the signal waveform becomes so severe that the current methods to extract the time-of-flight are no longer feasible. In this paper, a novel method that uses deep neural networks to measure the pulse width is proposed. The effects of distance resolution and SNR on the performance are explored. Recognition accuracy reaches 81.4% at a 0.1 m distance resolution and the SNR is as low as 2. We simulate a scene that contains a vehicle, a tree, a house, and a background located up to 6 m away. The reconstructed point cloud has good fidelity, the object contours are clear, and the features are restored. More precisely, the three distances are 4.73 cm, 6.00 cm, and 7.19 cm, respectively, showing that the performance of the proposed method is excellent. To the best of our knowledge, this is the first work that employs a neural network to directly process LiDAR signals and to extract their time-of-flight.

Continuous adiabatic frequency conversion for FMCW-LiDAR

Continuous tuning of the frequency of laser light serves as the fundamental basis for a myriad of applications spanning basic scientific research to industrial settings. These applications encompass endeavors such as the detection of gravitational waves, the development of precise optical clocks, environmental monitoring for health and ecological purposes, as well as distance measurement techniques. However, achieving a broad tuning range exceeding 100 GHz along with sub-microsecond tuning times, inherent linearity in tuning, and coherence lengths beyond 10 m presents significant challenges. Here, we demonstrate that electro-optically driven adiabatic frequency converters utilizing high-Q microresonators fabricated from lithium niobate possess the capability to convert arbitrary voltage signals into frequency chirps with temporal resolutions below 1 µs. The temporal evolution of the frequency correlates accurately with the applied voltage signal. We have achieved to generate 200-ns-long frequency chirps with deviations of less than 1 % from perfect linearity without requiring supplementary measures. The coefficient of determination isR 2 > 0.999 . Moreover, the coherence length of the emitted light exceeds 20 m. To validate these findings, we employ the linear frequency sweeps for Frequency-Modulated Continuous Wave (FMCW) LiDAR covering distances ranging from 0.5 to 10 m. Leveraging the demonstrated nanosecond-level tuning capabilities, coupled with the potential to tune the eigenfrequency of lithium-niobate-based resonators by several hundred GHz, our results show that electro-optically driven adiabatic frequency converters can be used in applications that require ultrafast and flexible continuous frequency tuning characterized by inherent linearity and substantial coherence length.

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 100 m 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.

Subcarrier modulation based phase-coded coherent lidar

This paper presents a lean subcarrier modulation-based phase-coded coherent lidar system with a non-quadrature receiver and sampling ratio lower than the Nyquist sampling ratio. Specifically, by utilizing the drawbacks of low Doppler tolerance in encoding signals, phase information can be obtained after pulse compression, and the mirror frequency introduced by real sampling can be negligible. Validation experiments based on inverse synthetic aperture lidar are performed, with the corresponding imaging results having a resolution superior to 4 cm, demonstrating our system's efficiency in phase acquisition that is free from frequency aliasing.

Integrated nonlinearity calibration optical-electrical engine for FMCW LiDAR application

We demonstrate an integrated optical-electrical calibration module for improving the nonlinearity of the optical source for frequency-modulated continuous-wave (FMCW) LiDAR applications. The linearity of the light source has a considerable influence on FMCW LiDAR range performance, and calibration is typically necessary. However, a majority of existing calibration techniques are based on separate devices, resulting in high cost and limited integration. Our module is made up of a silicon photonic chip with a long optical delay line, a tunable phase shifter, two balanced photodetectors, and some passive components. For this module, we also built the aided amplification and voltage bias circuits. After packaging this module, we used it with our nonlinearity calibration algorithm to analyze the laser's relative nonlinearity. After nonlinearity calibration, the laser relative nonlinearity 1-r2 could be improved to 10-6∼10-7. In the future, the calibration result of nonlinearity could be enhanced further by increasing the length of the on-chip optical delay line.

Symmetrical dual-sideband oppositely chirped differential FMCW LiDAR

A differential FMCW LiDAR for high-precision distance measurements of remote non-stationary targets is proposed and demonstrated experimentally. The required positive and negative symmetrically oppositely chirped laser beams are generated synchronously through a fixed-frequency laser by employing externally unified broadband optical phase modulation and symmetrical dual-sideband optical filtering. After coaxial transmission and reception, orthogonally polarized optical beat signals containing target distance and vector velocity data are de-chirped separately by optical in-phase and quadrature demodulations and then synchronously received by four-channel photoelectric balance detectors. After differential processing of the received beat signals and a fast Fourier transform, it is possible to implement real-time simultaneous range and vector velocity measurements. The inherent symmetrically oppositely chirped optical frequency make it possible to measure the target distance immune to the internal random phase noise introduced by the spectral linewidth of the frequency-swept laser and the external random phase noise introduced by atmospheric turbulence, speckle, and vibration. Meanwhile, the measurement of the target velocity is immune to the nonlinearity of the frequency-swept laser. These results encourage an approach to overcome the barriers of coherence length, nonlinearity, and external noise, and implement simultaneous real-time ranging and velocimetry of long-range, rapid-moving targets.

Laser swept-frequency interferometry with non-uniform fast Fourier transform and a linear regression frequency measurement method

The laser swept-frequency interferometric ranging method is commonly used in the field of large-scale, high-precision, and non-cooperative measurements. However, this method requires the laser chirp curve to be a stable straight line. Nonlinearities in the chirp can cause broadening of the target spectrum, which affects the accuracy of the frequency extraction of the beat signal, resulting in increased ranging error. Herein, a linear regression laser swept-frequency interferometry method based on the non-uniform fast Fourier transform is proposed, which effectively suppresses the influence of frequency modulation nonlinearity on ranging accuracy.

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.

Massively parallel FMCW lidar with cm range resolution using an electro-optic frequency comb

Frequency-modulated continuous wave (FMCW) light detection and ranging (lidar) is a promising solution for three-dimensional (3D) imaging and autonomous driving. This technique maps range and velocity measurement to frequency counting via coherent detection. Compared with single-channel FMCW lidar, multi-channel FMCW lidar can greatly improve the measurement rate. A chip-scale soliton micro-comb is currently used in FMCW lidar to enable multi-channel parallel ranging and significantly increase the measurement rate. However, its range resolution is limited due to the soliton comb having only a few-GHz frequency sweep bandwidth. To overcome this limitation, we propose using a cascaded modulator electro-optic (EO) frequency comb for massively parallel FMCW lidar. We demonstrate a 31-channel FMCW lidar with a bulk EO frequency comb and a 19-channel FMCW lidar using an integrated thin-film lithium niobate (TFLN) EO frequency comb. Both systems have a sweep bandwidth of up to 15 GHz for each channel, corresponding to a 1-cm range resolution. We also analyze the limiting factors of the sweep bandwidth in 3D imaging and perform 3D imaging for a specific target. The measurement rate achieved is over 12 megapixels per second, which verifies its feasibility for massively parallel ranging. Our approach has the potential to greatly benefit 3D imaging in fields where high range resolution is required, such as in criminal investigation and precision machining.

Advances in Silicon-Based Integrated Lidar

Silicon-based Lidar is an ideal way to reduce the volume of the Lidar and realize monolithic integration. It removes the moving parts in the conventional device and realizes solid-state beam steering. The advantages of low cost, small size, and high beam steering speed have attracted the attention of many researchers. In order to facilitate researchers to quickly understand the research progress and direction, this paper mainly describes the research progress of silicon-based integrated Lidar, including silicon-based optical phased array Lidar, silicon-based optical switch array Lidar, and continuous frequency-modulated wave Lidar. In addition, we also introduced the scanning modes and working principles of other kinds of Lidar, such as the Micro-Electro-Mechanical System, mechanical Lidar, etc., and analyzed the characteristics of the Lidars above. Finally, we summarized this paper and put forward the future expectations of silicon-based integrated Lidar.

Temperature influence on optical fiber and temperature compensation method for a frequency modulation continuous wave absolute distance measurement system

A temperature compensation method is proposed to solve the ranging precision decrease problem of the frequency-modulated continuous wave distance measurement system. The set of phases spread frequency sampling method is used to correct the beat frequency signal non-linearity. The influence model of temperature on the optical fiber auxiliary interferometer is studied. The experimental results show that distance measurement error decreases from 0.3432 mm to 0.02260 mm, and the mean measurement standard deviation decreases from 0.1088 mm to 0.01733 mm on a maximum measurement range of 1.6 m after compensation.

Precise chirp control with model-based reinforcement learning for broadband frequency-swept laser of LiDAR

Artificial intelligence (AI) has been widely used in various fields of physics and engineering in recent decades. In this work, we introduce model-based reinforcement learning (MBRL), which is an important branch of machine learning in the AI domain, to the broadband frequency-swept laser control for frequency modulated continuous wave (FMCW) light detection and ranging (LiDAR). With the concern of the direct interaction between the optical system and the MBRL agent, we establish the frequency measurement system model on the basis of the experimental data and the nonlinearity property of the system. In light of the difficulty of this challenging high-dimensional control task, we propose a twin critic network on the basis of the Actor-Critic structure to better learn the complex dynamic characteristics of the frequency-swept process. Furthermore, the proposed MBRL structure would stabilize the optimization process greatly. In the training process of the neural network, we apply a delaying strategy to the policy update and introduce a smoothing regularization strategy to the target policy to further enhance the network stability. With the well-trained control policy, the agent generates the excellent and regularly updated modulation signals to control the laser chirp precisely and an excellent detection resolution is obtained eventually. Our proposed work demonstrates that the integration of data-driven reinforcement learning (RL) and optical system control gives an opportunity to reduce the system complexity and accelerate the investigation and optimization of control systems.

Frequency Modulation Control of an FMCW LiDAR Using a Frequency-to-Voltage Converter

An FMCW LiDAR (frequency-modulated continuous-wave light detection and ranging) is a sensor that can measure distance using optical interference frequency (fb). This sensor has recently attracted interest because it is robust to harsh environmental conditions and sunlight due to the wave properties of the laser. Theoretically, when the frequency of the reference beam is linearly modulated, a constant fb is obtained with respect to the distance. However, when the frequency of the reference beam fails to be linearly modulated, the distance measurement is not accurate. In this work, linear frequency modulation control using frequency detection is proposed to improve the distance accuracy. The FVC (frequency to voltage converting) method is used to measure fb for high-speed frequency modulation control. The experimental results show that linear frequency modulation control using an FVC improves FMCW LiDAR performance in terms of control speed and frequency accuracy.

Ultralinear 140-GHz FMCW signal generation with optical parametric wideband frequency modulation enabling 1-mm range resolution

We demonstrate ultralinear and ultrawideband frequency-modulated continuous-wave (FMCW) signal generation using an optical parametric wideband frequency modulation (OPWBFM) method. The OPWBFM method optically expands the bandwidths of FMCW signals beyond the electrical bandwidths of optical modulators via a cascaded four-wave mixing (FWM) process. Compared to the conventional direct modulation approach, the OPWBFM method simultaneously achieves high linearity and a short measurement time of the frequency sweep. On the other hand, it is also known that the OPWBFM method expands the phase noise of idlers as well as their bandwidths if an input conjugate pair has different phase noise. To avoid this phase noise expansion, it is crucial to synchronize the phase of an input complex conjugate pair of an FMCW signal using an optical frequency comb. For demonstration, we successfully generated an ultralinear 140-GHz FMCW signal by using the OPWBFM method. Moreover, we employ a frequency comb in the conjugate pair generation process, leading to the mitigation of phase noise expansion. By using a 140-GHz FMCW signal, we achieve a range resolution of ∼1 mm through fiber-based distance measurement. The results show the feasibility of an ultralinear and ultrawideband FMCW system with a sufficiently short measurement time.

Ultrafast tunable lasers using lithium niobate integrated photonics

Early works1 and recent advances in thin-film lithium niobate (LiNbO3) on insulator have enabled low-loss photonic integrated circuits2,3, modulators with improved half-wave voltage4,5, electro-optic frequency combs6 and on-chip electro-optic devices, with applications ranging from microwave photonics to microwave-to-optical quantum interfaces7. Although recent advances have demonstrated tunable integrated lasers based on LiNbO3 (refs. 8,9), the full potential of this platform to demonstrate frequency-agile, narrow-linewidth integrated lasers has not been achieved. Here we report such a laser with a fast tuning rate based on a hybrid silicon nitride (Si3N4)-LiNbO3 photonic platform and demonstrate its use for coherent laser ranging. Our platform is based on heterogeneous integration of ultralow-loss Si3N4 photonic integrated circuits with thin-film LiNbO3 through direct bonding at the wafer level, in contrast to previously demonstrated chiplet-level integration10, featuring low propagation loss of 8.5 decibels per metre, enabling narrow-linewidth lasing (intrinsic linewidth of 3 kilohertz) by self-injection locking to a laser diode. The hybrid mode of the resonator allows electro-optic laser frequency tuning at a speed of 12 × 1015 hertz per second with high linearity and low hysteresis while retaining the narrow linewidth. Using a hybrid integrated laser, we perform a proof-of-concept coherent optical ranging (FMCW LiDAR) experiment. Endowing Si3N4 photonic integrated circuits with LiNbO3 creates a platform that combines the individual advantages of thin-film LiNbO3 with those of Si3N4, which show precise lithographic control, mature manufacturing and ultralow loss11,12.

Highly-time-resolved FMCW LiDAR with synchronously-nonlinearity-corrected acquisition for dynamic locomotion

Highly-time-resolved and precise tracking of position, velocity, and acceleration is urgently required when highly dynamic legged robots are walking, trotting, and jumping. Frequency-modulated continuous-wave (FMCW) laser ranging is able to provide precise measurement in short distance. However, FMCW light detection and ranging (LiDAR) suffers from a low acquisition rate and poor linearity of laser frequency modulation in wide bandwidth. A sub-millisecond-scale acquisition rate and nonlinearity correction in the wide frequency modulation bandwidth have not been reported in previous studies. This study presents the synchronous nonlinearity correction for a highly-time-resolved FMCW LiDAR. The acquisition rate of 20 kHz is obtained by synchronizing the measurement signal and the modulation signal of laser injection current with a symmetrical triangular waveform. The linearization of laser frequency modulation is conducted by resampling of 1000 intervals interpolated in every up-sweep and down-sweep of 25 µs, while measurement signal is stretched or compressed in every period of 50 µs. The acquisition rate is demonstrated to be equal to the repetition frequency of laser injection current for the first time to the best of authors' knowledge. This LiDAR is successfully used to track the foot trajectory of a jumping single-leg robot. The high velocity up to 7.15 m/s and high acceleration of 365 m/s² are measured during the up-jumping phase, while heavy shock takes place with high acceleration of 302 m/s² as the foot end strikes the ground. The measured foot acceleration of over 300 m/s², which is more than 30 times gravity acceleration, is reported on a jumping single-leg robot for the first time.

Phase-modulated continuous-wave coherent ranging method for optical phased array lidar

Light detection and ranging (lidar) is widely accepted as an indispensable sensor for autonomous vehicles. There are two fundamental challenges in a lidar system: optical beam steering technique and ranging method. Optical phased array (OPA) is considered as one of the most promising beam steering schemes due to its solid state, compact size, and high reliability. As for ranging method, time-of-flight and frequency-modulate continuous-wave (FMCW) are commonly utilized in numerous research. However, they are impractical to commercial OPA lidar due to either requiring excessive optical power or the poor stability, high complexity, and high insertion loss of the FMCW source. As a result, the development of OPA lidars is significantly hindered by the lack of a feasible ranging method. In this paper, we present a phase-modulated continuous-wave (PhMCW) ranging method with excellent ranging accuracy and precision. Ranging error as low as 0.1 cm and precision on the order of 3.5 cm are achieved. In addition, theoretical and experimental study on simultaneous velocity measurement is carried out and velocity error as low as 0.15 cm/s is obtained. Finally, we develop a proof-of-concept OPA-PhMCW lidar and obtain a point cloud with excellent fidelity. Our work paves a novel approach to solid-state, cost-effective and high-performance OPA lidars.

Optimization of laser stabilization via self-injection locking to a whispering-gallery-mode microresonator: experimental study

Self-injection locking of a diode laser to a high-quality-factor microresonator is widely used for frequency stabilization and linewidth narrowing. We constructed several microresonator-based laser sources with measured instantaneous linewidths of 1 Hz and used them for investigation and implementation of the self-injection locking effect. We studied analytically and experimentally the dependence of the stabilization coefficient on tunable parameters such as locking phase and coupling rate. It was shown that precise control of the locking phase allows fine-tuning of the generated frequency from the stabilized laser diode. We also showed that it is possible for such laser sources to realize fast continuous and linear frequency modulation by injection current tuning inside the self-injection locking regime. We conceptually demonstrate coherent frequency-modulated continuous wave LIDAR over a distance of 10 km using such a microresonator-stabilized laser diode in the frequency-chirping regime and measure velocities as low as sub-micrometer per second in the unmodulated case. These results could be of interest to cutting-edge technology applications such as space debris monitoring and long-range object classification, high-resolution spectroscopy, and others.

Dynamic wavelength calibration based on synchrosqueezed wavelet transform

With the developments of the tunable laser source (TLS), there are increasing demands for high-resolution dynamic wavelength calibration in recent years. Considering mutual constraints between wide measurement range and high calibration resolution, we propose a dynamic wavelength calibration method based on an auxiliary Mach-Zehnder interferometer (MZI) and the synchrosqueezed wavelet transform (SSWT). Our proposed method can achieve a calibration resolution of 5 fm and a tuning range of 10 nm. Moreover, the measurement range and spatial resolution of the optical frequency domain reflectometer (OFDR) system are improved to ∼80 m and ∼mm, respectively. Our proposed approach can substantially reduce the subtle spectrum distortion (tens of fm) in coherent optical spectrum analyzer (COSA) systems.

Low-pixel-count imaging FMCW lidar

We demonstrate the imaging capability of a frequency modulated continuous wave (FMCW) lidar based on a fiber bundle. The lidar constructs velocity and range images for hard targets at a rate of 60 Hz. The sensing range is up to 30 m with 20 mW output power. The instrument employs custom electronics with seven parallel heterodyne receivers. An example of image recovery is presented on 6-pixel "pictures" of a spinning disk and a drone hovering in the air. In experiments, we also tested the laser tuning linearity correction with a phase-locked loop. We see the practicality of such a low-pixel-count system as a boost in scanning rate of conventional lidars or for direct target imaging with a further upgrade of pixel count.

Hybrid integrated ultralow-linewidth and fast-chirped laser for FMCW LiDAR

Narrow linewidth and fast-chirped frequency are essential in frequency-modulated continuous-wave lasers. We introduce a laser that meets these requirements by coupling a distributed feedback laser with an external high-Q microring resonator, where a bulky stacked piezoelectric chip is attached to the resonator for fast tuning. The laser demonstrates an ultranarrow intrinsic linewidth of 22 Hz in the self-injection-locked state. Actuated by the bulky piezoelectric chip, the maximum triangular actuation bandwidth can reach 100 kHz. The driving voltage is filtered to avoid a resonant mechanical mode, obtaining the minimum residual linearity error at 10 kHz with a 4.2 GHz tuning range. A light detection and ranging system was set up for a proof-of-concept experiment, demonstrating a high detection precision with standard deviations of 2.7 and 4.0 cm for targets at 15 and 30 m, respectively.

Rapid Linear Frequency Swept Frequency-Modulated Continuous Wave Laser Source Using Iterative Pre-Distortion Algorithm

We present a simple iterative pre-distortion algorithm for achieving a rapid linear frequency sweep of semiconductor lasers. The algorithm achieves the desired frequency swept linearity with only four iterations. We derive a general formula for iterative pre-distortion by establishing the relationship between the laser output frequency and the drive current. The linear frequency-swept laser source obtained by this algorithm can be used in FMCW LiDAR systems. Experimentally, we investigated the algorithm using a 1550 nm distributed feedback (DFB) laser, achieving frequency swept excursion of 30.26 GHz, and frequency swept slope of 504 THz/s. We analyzed the linearity of the frequency swept results for the fourth iteration, achieving less than 5 MHz root mean square (RMS) value of frequency swept nonlinearity.

Broadband linear frequency-modulated waveform generation based on optical frequency comb assisted spectrum stitching

In this paper, we propose and demonstrate a novel spectrum stitching method for broadband linear frequency-modulated waveform (LFMW) generation. An optical frequency comb (OFC) is modulated by a narrowband LFMW whose bandwidth matches the free spectral range of the OFC. Optical injection locking is employed in extracting one broadband frequency sweeping component from the modulated OFC. In this way, seamless spectrum stitching is realized and a broadband LFMW with a multi-fold time-bandwidth product (TBWP) is obtained. Our scheme has a simple structure, which requires only a single OFC, a modulation module and a baseband waveform generator. An LFMW as broad as 20 GHz is generated from a baseband LFMW with 2GHz bandwidth experimentally. The TBWP is 100 times as large as that of the baseband LFMW. Moreover, the power fluctuation and the phase jumps are both eliminated, ensuring an excellent pulse compression performance. Benefiting from the injection locking technique, the linearity reaches 2.0 × 10^-6. The central frequency tuning ability of our scheme is also demonstrated.

Linearization of nonlinear frequency modulated continuous wave generation using model-based reinforcement learning

The prevalence of machine learning (ML) opens up new directions for plenty of scientific fields. The development of optics technologies also benefits from it. However, due to the complex properties of nonlinear and dynamic optical systems, optical system control with ML is still in its infancy. In this manuscript, to demonstrate the feasibility of optical system control using reinforcement learning (RL), i.e., a branch of ML, we solve the linearization problem in the frequency modulated continuous wave (FMCW) generation with the model-based RL method. The experiment results indicate an excellent improvement in the linearity of the generated FMCW, showing a sharp peak in the frequency spectrum. We confirm that the RL method learns the implicit physical characteristics very well and accomplishes the goal of the linear FMCW generation effectively, indicating that the marriage of ML and optics systems could have the potential to open a new era for the development of optical system control.

FMCW LiDAR with an FM nonlinear kernel function for dynamic-distance measurement

Frequency-modulated continuous-wave (FMCW) LiDAR is an absolute-distance measurement technology with the advantages of high-precision, non-cooperative target measurement capabilities and the ability to measure distance and speed simultaneously. However, the existing range extraction method for FMCW LiDAR is associated with problems, such as requiring a high sample rate and dispersion mismatch. Here, we propose and demonstrate a dynamic range extraction method based on an FM nonlinear kernel function, which improves measurement accuracy without the use of a long auxiliary interferometer (as is required for the traditional method), reduces the influence of dispersion mismatch and the Doppler effect caused by target movement and can simultaneously measure the target motion information dynamically, with a lower measurement error than that of the existing range extraction method under the same conditions.

Video-rate high-precision time-frequency multiplexed 3D coherent ranging

Frequency-modulated continuous wave (FMCW) light detection and ranging (LiDAR) is an emerging 3D ranging technology that offers high sensitivity and ranging precision. Due to the limited bandwidth of digitizers and the speed limitations of beam steering using mechanical scanners, meter-scale FMCW LiDAR systems typically suffer from a low 3D frame rate, which greatly restricts their applications in real-time imaging of dynamic scenes. In this work, we report a high-speed FMCW based 3D imaging system, combining a grating for beam steering with a compressed time-frequency analysis approach for depth retrieval. We thoroughly investigate the localization accuracy and precision of our system both theoretically and experimentally. Finally, we demonstrate 3D imaging results of multiple static and moving objects, including a flexing human hand. The demonstrated technique achieves submillimeter localization accuracy over a tens-of-centimeter imaging range with an overall depth voxel acquisition rate of 7.6 MHz, enabling densely sampled 3D imaging at video rate.

Directly modulated optical negative feedback lasers for long-range FMCW LiDAR

Frequency sweep operation of directly modulated optical negative feedback lasers is numerically and experimentally investigated for frequency-modulated continuous-wave (FMCW) light detection and ranging (LiDAR) with a high signal-to-noise ratio (SNR), particularly over a long range. Low FM noise corresponding to a spectral linewidth of ∼2.0 kHz is sustained even with injection current modulation of an optical negative feedback laser through optical feedback from a Fabry-Perot etalon, and a beat note spectrum with a 30-dB SNR is achieved even when a 300-m delay fiber is used as a ranging sample. These results encourage an approach to provide directly modulated frequency-swept lasers for long-range FMCW LiDAR.

A large-scale microelectromechanical-systems-based silicon photonics LiDAR

Three-dimensional (3D) imaging sensors allow machines to perceive, map and interact with the surrounding world¹. The size of light detection and ranging (LiDAR) devices is often limited by mechanical scanners. Focal plane array-based 3D sensors are promising candidates for solid-state LiDARs because they allow electronic scanning without mechanical moving parts. However, their resolutions have been limited to 512 pixels or smaller². In this paper, we report on a 16,384-pixel LiDAR with a wide field of view (FoV, 70° × 70°), a fine addressing resolution (0.6° × 0.6°), a narrow beam divergence (0.050° × 0.049°) and a random-access beam addressing with sub-MHz operation speed. The 128 × 128-element focal plane switch array (FPSA) of grating antennas and microelectromechanical systems (MEMS)-actuated optical switches are monolithically integrated on a 10 × 11-mm² silicon photonic chip, where a 128 × 96 subarray is wire bonded and tested in experiments. 3D imaging with a distance resolution of 1.7 cm is achieved with frequency-modulated continuous-wave (FMCW) ranging in monostatic configuration. The FPSA can be mass-produced in complementary metal–oxide–semiconductor (CMOS) foundries, which will allow ubiquitous 3D sensors for use in autonomous cars, drones, robots and smartphones.

A large focal plane switch array is constructed to steer the laser beam of a LiDAR system, leading to 3D imaging with 16,384 pixels, improving the resolution and coverage of solid-state LiDARs.

Demonstration of high output power DBR laser integrated with SOA for the FMCW LiDAR system

We demonstrated a high output power distributed-Bragg-reflector (DBR) laser integrated with semiconductor optical amplifier (SOA) for the frequency-modulated continuous-wave (FMCW) light detection and ranging (LiDAR) system. In order to acquire higher output power, different from the conventional SG-DBR laser, the front mirror in this work is a section of uniform grating to get higher transmissivity. Therefore, the output power of the laser reaches 96 mW when the gain current and SOA current are 200 mA and 400 mA, respectively. Besides, we fabricated a spot size converter (SSC) at the laser output port to enhance the fiber coupling efficiency, which reached 64% coupled into the lensed fiber whose beam waist diameter is 2.5 μm. A tuning range of 2.8 nm with free spectral range (FSR) of 0.29 nm and narrow Lorentzian linewidth of 313 kHz is achieved. To realize distance and velocity measurement, we use the iterative learning pre-distortion method to linearize the frequency sweep, which is an important part of the FMCW LiDAR technology.

Experimental Investigation on the Ranging Resolution of a FMCW Lidar

In some previous reports about frequency-modulated continuous-wave (FMCW) Lidar, observing the longer waveform of a de-chirped signal is considered an effective scheme for further improving the ranging resolution. In this work, the ranging resolution of a FMCW Lidar is experimentally investigated, and the feasibility of such a scheme is tested. During the experiment, a FMCW signal is generated via a Mach–Zehnder modulator in the transmitted port. In the received port, the de-chirped signal is extracted based on a homodyne detection scheme and is analyzed by an electrical spectrum analyzer. Two different methods are adopted to determine the ranging resolution. One is based on a single target, for which the ranging resolution is obtained through inspecting the shift of spectral peak position as the target moves. The other is based on two targets, for which the ranging resolution is acquired through inspecting the variation of spectrum distribution as the spacing of two targets changes. The experimental results demonstrate that extending the observed duration of the de-chirped signal cannot improve the ranging resolution, and the corresponding physical mechanism is revealed.

Active control of a diode laser with injection locking using a laser line filter

We present a simple and effective method to implement an active stabilization of a diode laser with injection locking, which requires minimal user intervenes. The injection-locked state of the diode laser is probed by a photodetector, of which sensitivity is enhanced by a narrow laser-line filter. Taking advantage of the characteristic response of laser power to spectral modes from the narrow laser-line filter, we demonstrate that high spectral purity and low-intensity noise of the diode can be simultaneously maintained by active feedback to the injected laser. Our method is intrinsically cost-effective and does not require bulky devices, such as Fabry-Pérot interferometers or wavemeters, to actively stabilize the diode laser. Based on the successful implementation of this method in our quantum gas experiments, it is conceivable that our active stabilization will greatly simplify potential applications of injection locking of diode lasers in modularized or integrated optical systems.

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.

Compact multifunction digital OFDR system without using an auxiliary interferometer

This paper describes an integrated, accurate, and inexpensive semiconductor laser -based optical frequency domain reflectometry (OFDR) system design. The system utilizes the fiber under test for both sensing and frequency sweep linearization functions, allowing the system to mitigate and compensate for phase errors without the need for an auxiliary interferometer, as is the case for traditional OFDR systems. Benefiting from the unique and embedded design, this system reaches the minimal OFDR system with only one optical interferometer and its corresponding optic-electric components without sacrificing accuracy. In addition, conventional design requires an external auxiliary interferometer, which may experience different noises from the main measuring interferometer, deteriorating the overall performance. Experimental results demonstrate the enhanced performance of the compact design as compared with the former methods, as well as the reduced complexity and improved cost-effectiveness.

3D chaos lidar system with a pulsed master oscillator power amplifier scheme

We investigated the characteristics of chaos-modulated pulses amplified by a pulsed master oscillator power amplifier (MOPA) for application in a new chaos lidar system in this study. Compared with the loss modulation applied in a continuous-wave (CW) time-gating scheme, the pulsed MOPA scheme could generate chaos-modulated pulses with much higher peak power, resulting in an improved peak-to-standard deviation of sidelobe level (PSL_std) in correlation-based lidar detection. When the pulsed MOPA scheme was applied at a duty cycle of 0.1% and pulse repetition frequency of 20 kHz, which correspond to specifications compliant with eye safety regulations, it outperformed the CW time-gating scheme with respect to PSL_std by 15 dB. For the first time, we applied the chaos lidar system with the pulsed MOPA scheme to execute high-resolution, high-precision three-dimensional (3D) face profiling from a distance of 5 m. We also added the corresponding PSL_std value to each pixel in the point clouds to generate false-color images; thus, we obtained 3D images of a scene with multiple objects at a range of up to 20 m.

Fibre-coupled, multiplexed methane detection using range-resolved interferometry

We describe the first use of range-resolved interferometric signal processing for measurement of spectral transmission. This was applied to gas sensing using tunable diode laser spectroscopy, allowing the simultaneous and independent measurement of methane concentrations in multiple gas cells. The system uses a single injection-current modulated diode laser and a single photodetector. For three gas cells, we show the ability of the system to measure methane at noise equivalent concentrations of less than 200 ppm for a 0.5 s measurement period and a potential noise equivalent concentration (1σ) of <20 ppm with 150 s averaging time. We further show that cross-talk between cells is below the experimental uncertainty for the system.

Frequency-modulated continuous-wave laser ranging using low-duty-cycle signals for the applications of real-time super-resolved ranging

A frequency-modulated continuous-wave laser ranging method using low-duty-cycle linear-frequency-modulated (LFM) signals is proposed. A spectrum consisting of a dense Kronecker comb is obtained so that the frequency of the beat signal can be measured with finer resolution. Since the dense comb is provided, super-resolved laser ranging can be achieved using a single-parametric frequency estimation method. Therefore, the run times of the estimation are reduced which promises real-time applications. A proof-of-concept experiment is carried out, in which an LFM signal with a bandwidth of 5 GHz and a duration of 1 µs is used. The duty-cycle of the LFM signal is 10%. The time delay of a scanning variable optical delay line is obtained in real time from the frequency of the highest comb tooth, of which the measurement resolution is 20 ps. Moreover, a single-parametric nonlinear least squares method is used to fit the envelope so that the time delay can be estimated with super-resolution. The standard deviation of the estimation displacements is 2.3 ps, which is 87 times finer than the bandwidth-limited resolution (200 ps). Therefore, the variation of the time delay can be precisely monitored. The proposed method may be used to achieve real-time high-resolution laser ranging with low-speed electronic devices.

A Novel Method of Measuring Instantaneous Frequency of an Ultrafast Frequency Modulated Continuous-Wave Laser

Ultrafast linear frequency modulated continuous-wave (FMCW) lasers are a special category of CW lasers. The linear FMCW laser is the light source for many sensing applications, especially for light detection and ranging (LiDAR). However, systems for the generation of high quality linear FMCW light are limited and diverse in terms of technical approaches and mechanisms. Due to a lack of characterization methods for linear FMCW lasers, it is difficult to compare and judge the generation systems in the same category. We propose a novel scheme for measuring the mapping relationship between instantaneous frequency and time of a FMCW laser based on a modified coherent optical spectrum analyzer (COSA) and digital signal processing (DSP) method. Our method has the potential to measure the instantaneous frequency of a FMCW laser at an unlimited sweep rate. In this paper, we demonstrate how to use this new method to precisely measure a FMCW laser at a large fast sweep rate of 5000 THz/s by both simulation and experiments. We find experimentally that the uncertainty of this method is less than 100 kHz and can be improved further if a frequency feedback servo system is introduced to stabilize the local CW laser.

Massively parallel coherent laser ranging using a soliton microcomb

Coherent ranging, also known as frequency-modulated continuous-wave (FMCW) laser-based light detection and ranging (lidar)¹ is used for long-range three-dimensional distance and velocimetry in autonomous driving^2,3. FMCW lidar maps distance to frequency^4,5 using frequency-chirped waveforms and simultaneously measures the Doppler shift of the reflected laser light, similar to sonar or radar^6,7 and coherent detection prevents interference from sunlight and other lidar systems. However, coherent ranging has a lower acquisition speed and requires precisely chirped⁸ and highly coherent⁵ laser sources, hindering widespread use of the lidar system and impeding parallelization, compared to modern time-of-flight ranging systems that use arrays of individual lasers. Here we demonstrate a massively parallel coherent lidar scheme using an ultra-low-loss photonic chip-based soliton microcomb⁹. By fast chirping of the pump laser in the soliton existence range¹⁰ of a microcomb with amplitudes of up to several gigahertz and a sweep rate of up to ten megahertz, a rapid frequency change occurs in the underlying carrier waveform of the soliton pulse stream, but the pulse-to-pulse repetition rate of the soliton pulse stream is retained. As a result, the chirp from a single narrow-linewidth pump laser is transferred to all spectral comb teeth of the soliton at once, thus enabling parallelism in the FMCW lidar. Using this approach we generate 30 distinct channels, demonstrating both parallel distance and velocity measurements at an equivalent rate of three megapixels per second, with the potential to improve sampling rates beyond 150 megapixels per second and to increase the image refresh rate of the FMCW lidar by up to two orders of magnitude without deterioration of eye safety. This approach, when combined with photonic phase arrays¹¹ based on nanophotonic gratings¹², provides a technological basis for compact, massively parallel and ultrahigh-frame-rate coherent lidar systems.

Multi-point spectroscopic gas sensing based on coherent FMCW interferometry

We present an innovative spectroscopic method based on coherent optical frequency-modulated continuous-wave (FMCW) interferometry that can realize multi-point gas detection with high spatial resolution, high sensitivity, and high selectivity. This method takes full advantage of the intrinsic capability of spatial localization of the coherent FMCW, meanwhile efficiently decodes the spectral information from the reflected optical signals. Gas sensors are deployed by adopting bus topology, i.e., distributed along a single backbone fiber in the measurement arm of the FMCW interferometer. For validation, a multi-point acetylene gas sensing system with three sensing nodes is experimentally demonstrated. The transmission spectra of the three gas sensors are accurately extracted, and their corresponding gas concentrations are efficiently retrieved with a low crosstalk below -30 dB. The demonstrated system achieves a sensitivity of 55 ppm (noise equivalent absorbance of 0.004) over a distance of 52 m, with a sensing spatial resolution of 30 cm and a spectral resolution of 0.5 GHz. Our proposed method promotes a novel way for the development of multi-point spectroscopic gas sensing systems for challenging applications such as gas leakage detection and gas emission monitoring, where spatially resolved chemical analysis over a large area is required.