• Photonics Research
  • Vol. 13, Issue 6, 1767 (2025)
Weijin Meng, Junkang Guo, Kai Tian, Yuqi Yu..., Zian Wang, Hu Peng and Zhigang Liu*|Show fewer author(s)
Author Affiliations
  • Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System, Xi’an Jiaotong University, Xi’an 710049, China
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    DOI: 10.1364/PRJ.554923 Cite this Article Set citation alerts
    Weijin Meng, Junkang Guo, Kai Tian, Yuqi Yu, Zian Wang, Hu Peng, Zhigang Liu, "Resonant cavity enhanced laser frequency-swept carrier ranging method for noncooperative targets," Photonics Res. 13, 1767 (2025) Copy Citation Text show less

    Abstract

    Conventional frequency-sweep interferometry is unreliable for noncooperative or long-distance targets owing to scattering on the target surface. Hence, this paper proposes a laser frequency-swept carrier (LFSC) ranging method based on resonant cavity enhancement for long-distance noncooperative target measurements and weak-signal detection. Experimental verification revealed that for a target comprising an oxidized black aluminum plate at a distance of 16 m, the standard deviation of 10 measurements was less than 70 μm, measurement accuracy exceeded 27 μm, and system ranging resolution exceeded 0.13 mm when the target feedback light was very weak. This method is useful for measurements of noncooperative targets, e.g., large-scale component assembly, industrial measurement, and biomedical testing.

    1. INTRODUCTION

    Lasers are widely used in ranging, vibration, and speed measurements owing to their unique properties such as monochromaticity, linear transmission, wave-particle duality, and noncontact operation. Laser frequency-sweep interferometry (FSI) has the advantages of a stable measurement process in addition to high measurement accuracy and resolution [1]. Hence, it can achieve precise measurements of physical quantities such as absolute distance, small vibration, and motion speed of the measurement target [2,3]. In addition, FSI has wide applications in fields such as gravitational wave detection and biological detection [4,5].

    However, to achieve precise measurements, FSI requires the use of objects with strong surface reflectivity, such as mirrors, to ensure that the target feedback laser has a high power, which makes it easy to interfere with the reference light and calculate the absolute distance, vibration, velocity, and other details of the target [68]. In the practical fields of industrial measurement and biomedical detection, the measurement light scatters on the surfaces of noncooperative targets, such as black surfaces, rough or cylindrical surfaces, and liquids [9,10], where it is difficult to install mirrors, and the target feedback laser power is low, resulting in poor interference signal quality and reduced measurement accuracy or even the inability to measure. Various methods have been proposed to improve the signal-to-noise ratio (SNR) of the interference signals and enhance the measurement accuracy for noncooperative targets. The most direct method is to increase the output light power to improve the feedback laser power, such as by using a high-power laser as the measurement light source or increasing the output light power through an optical power amplifier, e.g., an erbium-doped fiber amplifier [11]. High-sensitivity and high-gain detectors can also be used to detect weak feedback light signals [12]. These methods improve the measurement accuracy of noncooperative targets to some extent; however, the SNR of the interference signals and system measurement accuracy are not effectively improved. In addition, the use of these devices increases the cost and makes the system structure more complex, which is not conducive to practical application scenarios. Furthermore, to improve the signal quality and measurement accuracy, some signal processing algorithms have been applied for interference signal processing and target information calculation, such as frequency-domain fitting [8,10], time-domain filtering [13], and signal high-frequency modulation and demodulation algorithms using the phase solution method [14]. These methods have limited effectiveness in improving the measurement accuracy of the system, owing to the limitations of the measurement system. Therefore, a compact measurement method that can improve the quality of measurement signals from the system is required.

    By leveraging the principle of resonant cavity enhancement, a laser frequency-swept carrier (LFSC) that is generated through frequency-sweep feedback interferometry (FSFI) substantially enhances the SNR of the interference signal generated by the interaction between the feedback laser and probe laser, as shown in Fig. 1(b). When a weak feedback laser enters the resonant cavity, it collaborates with the internal resonant cavity of the laser to form a new resonant cavity with the measurement target [15,16]. The feedback laser is amplified through the oscillatory motion of the gain medium within the resonant cavity, which subsequently interferes with the probe laser to produce an interference signal with a superior SNR [17]. Another method to achieve laser feedback interferometry (LFI) is frequency-shift feedback interferometry, which is generally achieved using an acousto-optic modulator (AOM) [1820].

    (a) Linearly frequency-swept principle. (b) System schematic diagram. (c) Theoretical model of resonant cavity for generating LFSC.

    Figure 1.(a) Linearly frequency-swept principle. (b) System schematic diagram. (c) Theoretical model of resonant cavity for generating LFSC.

    In recent years, scholars have extensively investigated the implementation of LFI using frequency-shift feedback and FSFI, and have applied them to various fields such as measurements of liquid flow rate, absolute distance, and vibration. Regarding the application of the frequency-shift feedback method, Zhang et al. [21] harnessed LFI and integrated it with all-fiber laser to achieve frequency-shift multiplexing. They successfully measured a two-dimensional vector field simulated using milk, surpassing the constraints of one-dimensional measurement and 2D vector information of fluid motion, and easily obtained the rate and direction of the fluid. Tian et al. [22] employed an LFI for the ultrasensitive detection of vibration information from targets at a distance of 300 m with an amplitude sensitivity of 0.72  nm/Hz1/2 at 1 kHz. Zhao et al. [23] developed an all-fiber Doppler velocimetry method based on frequency-shift feedback in a distributed-feedback laser, which could achieve noncontact measurement of high-speed objects with a feedback signal of 5.12 fW. As for FSFI, Wang et al. [24] utilized FSFI in conjunction with frequency-stabilized laser frequency-shift feedback compensation to attain a measurement standard deviation of less than 70 μm for noncooperative targets at a distance of 152 m. However, the structure of the system was relatively intricate, necessitating the use of a stable frequency laser and an AOM frequency shift to compensate for the measurement results. In addition, owing to the bandwidth and sweep-speed limitations of the laser source used in the system [25,26], the minimum achievable ranging resolution was approximately 1 mm, which is insufficient for certain high-precision measurement scenarios. Moreover, this approach requires the deployment of an auxiliary Mach–Zehnder interferometer (MZI) with at least twice the measurement distance for distance resolution, which is not conducive to the compactness of the system structure. Furthermore, Wang et al. [27] proposed a low-cost LFI-FMCW LiDAR system with a large working range for 3D imaging.

    In this study, we propose a novel noncooperative target ranging system that uses an LFSC based on resonant cavity enhancement. The system capitalizes on the interference between the weak target feedback laser and the probe laser within the resonant cavity, thereby amplifying the feedback and enhancing the SNR of the interference signal. Simultaneously, the interference signal within the cavity is modulated to the output laser frequency as a carrier signal to generate the LFSC. Unlike the conventional LFI, which detects amplitude modulation (AM) signals, our approach employs an MZI as a sensitive detector for frequency modulation (FM) signals. This method improves the ability to detect weak signals by approximately 150 times when compared with that of AM detection [28]. Furthermore, the system incorporates equal optical frequency resampling (EFRS) to mitigate the nonlinearities in the laser frequency sweep and precisely capture the peak of the signal spectrum. It utilizes an MZI of identical or smaller length as a reference interferometer to measure distant targets, thereby circumventing the constraints of the Nyquist sampling theorem and simplifying the system configuration. After a thorough theoretical analysis, simulation, and experimental validation, we confirmed the efficacy and precision of the system in long-distance noncooperative target ranging. Our method outperforms traditional FSI ranging and AM demodulation methods in terms of the detection accuracy and sensitivity, enabling high-precision and high-sensitivity measurements of noncooperative targets.

    2. METHODS AND SETUP

    A. Ranging System Principle

    The principle of the laser FSFI measurement system is illustrated in Fig. 1(b). A self-developed external cavity tunable laser (ECTL) is used as the frequency-swept laser source, which can achieve hop-free tuning. Furthermore, based on the Littman-Metcalf structural design characteristics [29] as shown in Fig. 1(c), the laser emitted from the front end of the ECTL is used as the probe laser. The probe laser undergoes diffuse reflection and scattering on the noncooperative target surface, and the feedback laser returns to the inside of the resonant cavity composed of a gain chip, grating, and mirror along the exit path. Because of the delay between the target feedback laser and probe laser, their signals interfere inside the resonant cavity [30]. Unlike traditional FSI, the LFSC ranging method does not require additional auxiliary interferometers and has a simpler system and more compact configuration, thus reducing the system complexity.

    In an ideal scenario, the probe laser from the ECTL operates as a linearly frequency-swept laser. This implies that the laser frequency varies linearly with time, implying that the frequency change rate β(t)=2B/T remains constant, as depicted in Fig. 1(a). The local frequency of the laser is ν0; within one laser scanning cycle, the probe laser frequency νp can be expressed as νp(t)=ν0+β(t)·t.

    Taking the laser emission point as the initial position, owing to the distance from the target to be measured, there is a time delay τ between the target feedback laser and probe laser, as shown in Fig. 1(c). Therefore, the frequency of the target feedback laser νp(tτ) can be expressed as νf(t)=νp(tτ)=ν0+β(t)·(tτ).

    The probe and feedback lasers oscillate in the laser resonant cavity comprising R1, grating, and R2, which interfere with the generation of the interference signal, as shown in Fig. 1(c). According to the principle of wave superposition [31], the expression for the intensity of the interference signal can be obtained as I(t)=Ip(t)+Ip(tτ)+2Ip(t)·Ip(tτ)cos(Δϕ(t)),where Ip(t) is the intensity of the probe laser, and Δϕ(t) is the phase difference between the target feedback laser and probe laser.

    By utilizing the relationship between frequency and phase, the phase information of the local laser frequency in Eq. (1) and target feedback frequency in Eq. (2) can be obtained through integration. Therefore, the phase difference between the two can be expressed as Δϕ(t)=ϕ(t)ϕ(tτ)=2πν0τ+2πβ(t)τtπβ(t)τ2.

    Owing to the extremely high propagation speed of the laser, the time τ required for it to be reflected from the target back to the ECTL is very short. Therefore, for Δϕ(t), πβ(t)τ2 is a high-order infinitesimal and can be ignored. Therefore, the phase difference between the probe laser and feedback laser is Δϕ(t)=ϕ(t)ϕ(tτ)=2πν0τ+2πβ(t)τt.

    By substituting Eq. (5) into Eq. (3), the interference signal intensity can be expressed as I(t)=Ip(t)+Ip(tτ)+2Ip(t)·Ip(tτ)cos(2πν0τ+2πβ(t)τt).

    After an interference signal containing the distance information of the measurement target is formed in the laser resonant cavity, the frequency of the laser output light can be changed [18]. The optical frequency is modulated by the interference signal to form an LFSC [28,32], as shown in Fig. 1(c). By combining Eqs. (1) and (6), the mathematical expression of the LFSC frequency is obtained as νLFSC(t)=νp(t)+Ip(t)+Ip(tτ)+2Ip(t)·Ip(tτ)cos(2πν0τ+2πβ(t)τt)=ν0+β(t)·t+Acos(2πν0τ+2πω2t)+B,where A=2Ip(t)·Ip(tτ), B=Ip(t)+Ip(tτ), ω2=β(t)·τ, ω2 represents the frequency of the interference signal arising from the interference between the probe and target feedback lasers.

    An MZI, which is a highly sensitive device for FM signal monitoring, can be employed to demodulate the LFSC and extract the modulated target distance information. As shown schematically in Fig. 1(b), the LFSC output from the laser’s tail fiber is fed to the MZI, where the optical frequency signal of the delayed fiber is expressed as νLFSC(tτ)=ν0+β(t)·(tτ)+Acos(2πν0τ+2πβ(t)τ(tτ))+B.

    Similar to the process of generating the interference signals mentioned above, the phase difference between the LFSC and its delay laser in the MZI is ΔϕLFSC(t)=ϕ(t)ϕ(tτMZ)=2πω1t+Aω2(sin(2π(ω2t+ν0τMZ+B))sin(2π(ω2tω2τMZ+ν0τMZ+B))),where ω1=β(t)·τMZ, τMZ is the time delay of the MZI-delayed fiber, and ω1 is the frequency of the interference signal formed by the interference of the main optical frequency in the LFSC.

    By taking the derivative of the phase difference, the frequency components contained in the interference signal generated by the LFSC passing through the MZI can be obtained as shown in the following equation: ΔϕLFSC(t)=2πω1+Aω2(sin(2πω2t)(cosPcosQ)+cos(2πω2t)(sinPsinQ))=2π(ω1+2Aπω2τsin(2πω2t+ϕ0)).

    Because ω1 represents the output light from the ECTL tail fiber, it corresponds to the interference signal frequency arising from the most dominant frequency component within the LFSC. Consequently, the SNR of the final interference signal detected by the MZI is maximized, whereas the power of the resonant cavity interference signal remains low. From the preceding equation, 2Aπτ1 and sin(2πω2t+ϕ0)(1,1); it is evident that the interference signal emitted by the MZI predominantly consists of three frequency components: ω1, ω1+ω2, and |ω1ω2|. As the amplitude A of the interference signal increases, indicating a higher power of the target feedback laser, the amplitude of the interference signal resulting from the interaction with the probe laser within the resonant cavity also increases. This leads to a corresponding enhancement in the SNR of the other frequency components.

    A series of signal processing steps is required to demodulate the signal detected by the MZI and compute the target distance information. The methodology used for the signal processing in this study is illustrated in Fig. 2. When the LFSC enters the MZI and yields a signal with ω1, ω1+ω2, and |ω1ω2| frequency components, the initial step involves bandpass filtering to isolate the signals containing the |ω1ω2| and ω1+ω2 components. Subsequently, these signals are mixed and bandpass filtered again to extract a signal with ω2 frequency components, which include the distance information of the target. However, the inherent nonlinearity in the optical frequency sweep leads to spectral broadening, which impedes the precise identification of spectral peaks and, in turn, affects the accuracy of the solution. EFRS of the signal is essential to mitigate this [33]. By leveraging the fixed delay length La of the reference interferometer and setting the resampling factor N, the spectral peak Pmax and total number of points M in the post-resampling spectrogram can be accurately determined. This ensures a precise calculation of the distance from the noncooperative target.

    LFSC demodulation algorithm flow.

    Figure 2.LFSC demodulation algorithm flow.

    B. Resonant Cavity Enhancement Mechanism

    As mentioned earlier, a weak feedback laser is amplified through oscillatory motion with the gain medium, which is based on the phase matching gain amplification mechanism of the resonant cavity. As shown in Fig. 1(c), when the reflectivity of a target is very low, the following electric field equation and carrier density equation can describe the behavior of the laser according to the Lang and Kobayashi model [16,34]: dE(t)dt=12(1+iα)(G(N)1τp)E(t)+κE(tτ)eiω0(tτ),dN(t)dt=JedN(t)τcG(N)|E(t)|2,where G(N) is the gain coefficient, which is related to the carrier density N. τp is the photon lifetime, κ is the feedback coefficient, τ is the feedback laser round-trip time, and α is the linewidth enhancement factor. J is the injected current density, τc is the carrier density lifetime, and d is the active area width.

    When the feedback laser is reflected by an external object and reenters the laser cavity, its round-trip phase change satisfies Δϕ=2mπ (m is an integer), that is to say, the phase difference is an integer multiple of 2π. This condition indicates that when the phase of the feedback laser is synchronized with the intrinsic mode inside the cavity, constructive interference between the feedback laser and the probe laser can be achieved, thereby enhancing the optical field intensity. The gain coefficient G(N) can be describes as G(N)=Γa(NN0),where Γ is the light field limiting factor, a is the differential gain coefficient, and N0 is the transparency carrier density. Under phase matching conditions, the feedback laser is in phase with the intracavity optical field, and the dynamic adjustment of carrier density maximizes the gain coefficient. The amplification factor of the feedback laser power is determined by the length d of the gain medium and the gain coefficient G(N). Under steady-state conditions, the amplified feedback optical power Pf_gain can be expressed as Pf_gain=Pf·R3·enGd,where Pf is the feedback laser power, R3 is the reflectivity of the targets, and n is the number of round-trips of feedback laser in the resonant cavity. The greater the number of round trips n of the feedback laser in the resonant cavity, the more significant the enhancement effect, and the higher the SNR of the interference signal generated by the feedback laser and the probe laser in the resonant cavity.

    For phase matching conditions, the feedback laser round-trip phase difference can be described as Δϕ=4πLextλ+ϕ0=2mπ,mZ,where Lext is the length of the external cavity, which can be described as R1-Grating-Target in Fig. 1(c). ϕ0 is the initial phase of the feedback laser. Therefore, the phase matching conditions can be achieved by adjusting the length of the external cavity or changing the driving current of the laser to adjust the wavelength. At the same time, the gain coefficient G(N) also can be improved by changing the driving current of the laser to increase the carrier density N under the stable state of the laser.

    C. Simulation

    Simulations were conducted to validate the theoretical analysis and substantiate the accuracy of the LFSC-ranging theoretical model. In this measurement system, a frequency-swept laser source ECTL was utilized. As the resonant cavity length of the laser is altered by the motor, the probe laser frequency does not vary linearly with time owing to factors such as the nonuniform rotation of the motor. This results in nonlinear frequency modulation of the ECTL. Consequently, the rate of frequency change β(t) is not constant, unlike in our previous discussion. To simulate a system that reflects the actual situation, the system simulation parameters were set as listed in Table 1.

    Simulation Parameter Settings

    ParameterSymbolValue
    Center wavelengthν01550 nm
    BandwidthB40 nm
    PeriodT1 s
    Sampling ratefs20 MHz
    Quadratic coefficienta3×1011
    Cubic coefficientb1.5×1011
    Reference fiber lengthLa5 m
    Target distanceL30 m
    Resampling factorN10

    Figure 3 displays the interference signal spectrum of the LFSC as it passes through the MZI and its demodulation results after signal processing. Figure 3(a) reveals that the signal detected by the MZI predominantly consists of three frequency components: ω1, ω1+ω2, and |ω1ω2|. Notably, the interference signal at the frequency ω1, generated by the delay fiber of the MZI, exhibits the highest SNR. Concurrently, an increase in the power of the interference signal, resulting from the interaction between the target feedback laser and probe laser, leads to an enhancement in the SNR of the signals at the frequencies ω1+ω2 and |ω1ω2|. Additionally, the SNR of the other frequency components improves incrementally, as shown in Fig. 3(b), which aligns with the outcomes of the theoretical model analysis.

    Simulation results. (a) Interference signal spectrum of LFSC through MZI. (b) Interference signal spectra under different feedback laser powers. (c) Time-domain diagram of interference signal before resampling. (d) Time-domain diagram of interference signal after resampling. (e) Spectra of original interference signal and resampled signal. (f) Resampled signal spectrum after subdivision transformation.

    Figure 3.Simulation results. (a) Interference signal spectrum of LFSC through MZI. (b) Interference signal spectra under different feedback laser powers. (c) Time-domain diagram of interference signal before resampling. (d) Time-domain diagram of interference signal after resampling. (e) Spectra of original interference signal and resampled signal. (f) Resampled signal spectrum after subdivision transformation.

    As illustrated by the signal processing method shown in Fig. 2, the signal detected by the MZI can be processed through sequential bandpass filtering, mixing, and further bandpass filtering to yield a signal that carries the target distance information. This process is visualized in the spectral diagram presented in Fig. 3(e). However, because of spectral broadening, the peak value is not accurately extracted for calculating the target distance. The spectrum can be accurately extracted after EFRS of the time-domain signal, as shown in Fig. 3(f). And the time-domain signals before and after resampling are shown in Figs. 3(c) and (d). When calculating the target distance, we set the resampling factor N to 10 and recreated the frequency spectrum of the resampled signal, as shown in Fig. 3(f). At this point, the horizontal axis is no longer the frequency but π/NτMZ. The peak point Pmax of the spectrum is 6×106. The target distance is calculated as L=NLaPmaxM=10×5×6×106107=30m.

    The final calculated target distance is 30 m, which is consistent with the simulation parameters, indicating the accuracy of the theoretical model and LFSC demodulation algorithm.

    D. Experimental Setup

    The schematic of the laser feedback measurement system is shown in Fig. 4(a). The frequency-swept laser source used in the system was a self-developed ECTL. The specific structures are shown in Fig. 4(b). The motor rotates the mirror to continuously change the cavity length within one sweeping cycle, thereby achieving continuous tuning. The tuning range and laser linewidth characteristics of the ECTL are shown in Fig. 5. The center wavelength of the ECTL used in the system was 1550 nm, with a tuning range of 34 nm (1530–1564 nm) and tuning rate of 68 nm/s. The linewidth of the ECTL measured using the delayed self-interference method was 160 kHz, and the theoretical coherence length was 1.875 km. Owing to the design characteristics of the ECTL, the zeroth order diffracted light emitted from the grating can be used as a probe laser to detect the target. The power of the probe laser was approximately 200 μW. Simultaneously, the feedback laser returned from the target is reflected back to the resonant cavity through the grating surface and interferes with the probe laser. The gain chip (Thorlabs, SAF1550S2) has an isolator integrated at its tail end, which does not affect the working state of the resonant cavity owing to the reflection of light by the subsequent devices. The laser output through the tail fiber has the same properties as those of the probe laser; however, it has a higher power of approximately 20 mW, which can be used to demodulate the target distance and other information more easily. To measure the optical path, the probe laser emitted through the ECTL is irradiated onto the surface of the noncooperative target to be measured through a polarization controller (PC, LBTEK, FLP25-NIR-M) and a variable optical attenuator (VOA, Daheng Optics, GCO-0703M). A PC is used to adjust the polarization states of the probe and feedback lasers, which improves the SNR of the interference signal. In addition, the VOA can be used to adjust the power of the probe laser. The VOA can prevent the feedback laser power from being too high in order to avoid affecting the working state of the laser resonant cavity. In addition, it can be used to determine the detection limit of the measurement system for weak light signals.

    (a) Schematic of the FSFI ranging system with LFSC demodulation device. ECTL: external cavity tunable laser; PC: polarization controller; VOA: variable optical attenuator; FC: fiber coupler; BPD: balanced photodetector; DAQ: data acquisition. (b) Schematic of LFSC.

    Figure 4.(a) Schematic of the FSFI ranging system with LFSC demodulation device. ECTL: external cavity tunable laser; PC: polarization controller; VOA: variable optical attenuator; FC: fiber coupler; BPD: balanced photodetector; DAQ: data acquisition. (b) Schematic of LFSC.

    Tuning range and laser line width property of the ECTL. (a) Laser output power signal from ECTL tail fiber. (b) GAC peak signal and wavelength variation during ECTL positive frequency scanning process. (c) GAC peak signal and wavelength variation during ECTL reverse frequency scanning process. (d) Laser line width property of the ECTL.

    Figure 5.Tuning range and laser line width property of the ECTL. (a) Laser output power signal from ECTL tail fiber. (b) GAC peak signal and wavelength variation during ECTL positive frequency scanning process. (c) GAC peak signal and wavelength variation during ECTL reverse frequency scanning process. (d) Laser line width property of the ECTL.

    Furthermore, the LFSC output from the ECTL tail fiber passes through FC1 with a splitting ratio of 10:90, and 10% of the optical signal enters the gas absorption cell (GAC, Wavelength Reference, HCN-13-H(5.5)-25-FOCAC) whereas 90% of the optical signal enters the MZI, which uses a 1.5 m delay fiber as the reference interferometer length. Figure 6 shows the original measurement signal of the target at 15.5 m as well as the time-domain and frequency-domain graphs of the signal after signal processing. The interference signal from the MZI, shown in Figs. 6(a) and 6(b), is converted into an electrical signal for detection using a balanced photodetector (BPD2, Thorlabs, PDB450C-AC). It is then input to a data acquisition (DAQ) module for data processing and analysis. The spectrum of the interference signal includes frequencies ω1, ω1+ω2, and |ω1ω2|, as shown in Fig. 6(c). The time domain and spectrogram of the signal obtained after filtering and mixing are shown in Figs. 6(d) and 6(e), respectively. In terms of signal calibration, the measurement system uses the GAC to calibrate the tuning range of the interference signal output by the MZI. As shown in Fig. 4(a), the MZI and GAC work synchronously; hence, the GAC signal peak can be used to calibrate the length of the MZI output interference signal corresponding to the sweeping rise or fall of the ECTL. This plays an important role in evaluating the accuracy of the measurement system in the later stages. Finally, the signals output by BPD1 and BPD2 are collected by the DAQ module (PI, PXI-8880), and information such as the target distance is obtained through EFRS, as shown in Fig. 6(f). The GAC and MZI signals are shown on the right side of the figure [Fig. 4(a)].

    Experimental data when the distance from the measurement target is 15.5 m. (a) LFSC interference signal from the MZI. (b) Normalized LFSC interference signal from the MZI. (c) Spectra of LFSC interference signal. (d) Time-domain signal diagram of mixed signals with frequencies of ω1+ω2 and |ω1−ω2|. (e) Spectra of mixed signals with frequencies of ω1+ω2 and |ω1−ω2|. (f) Time-domain plot of resampled signal with frequency 2ω2 after bandpass filtering.

    Figure 6.Experimental data when the distance from the measurement target is 15.5 m. (a) LFSC interference signal from the MZI. (b) Normalized LFSC interference signal from the MZI. (c) Spectra of LFSC interference signal. (d) Time-domain signal diagram of mixed signals with frequencies of ω1+ω2 and |ω1ω2|. (e) Spectra of mixed signals with frequencies of ω1+ω2 and |ω1ω2|. (f) Time-domain plot of resampled signal with frequency 2ω2 after bandpass filtering.

    3. RESULTS

    A. Precision and Linearity

    To verify the measurement accuracy of the LFSC ranging system for noncooperative targets, an aluminum plate with a blackened surface due to oxidation was used as the measurement target, and 10 consecutive scanning cycles of the ECTL were considered as 10 measurements. The GAC was used to intercept the interference signal of the MZI with an equal tuning range for each scanning cycle, ensuring that the tuning range and sampling length of each measurement were consistent. The measurement results are presented in Fig. 7. The black surface-oxidized aluminum plate, which was approximately 16 m away from the emission point of the probe laser, was taken as the target to be measured. The standard deviation measured by the system was lower than 16 μm. Simultaneously, to test the measurement accuracy of the system for noncooperative targets on different noncooperative surfaces, 3D printed boards made of PLA, steel nut, cylindrical steel rod, paper, circuit board, sponge, carton, and plastic bottle were used as the measurement targets. The test results are presented in Fig. 8. The standard deviations of these target measurements were 33.62 μm, 49.86 μm, 25.41 μm, 44.32 μm, 41.82 μm, 53.92 μm, 66.75 μm, and 79.31 μm, respectively. To further test the accuracy and linearity of the measurement of noncooperative targets by the system, a surface-oxidized black aluminum plate was fixed as the measurement target on a precision displacement table (Newport, IMS400PP) with a positioning accuracy of 1 μm. During the testing process, the displacement table was placed approximately 7.3 m away from the ECTL, and a controller was used to drive the target on the displacement table in steps of 5 mm. Ten measurements were acquired at each position. The final measurement results are presented in Fig. 7(a). The maximum standard deviation during the step testing process did not exceed 23 μm. The measurement values at each step were fitted by taking the average of the measurement results obtained 10 times per step as the measurement value. The maximum residual was not greater than 7 μm. The results are shown in Fig. 7(b), corresponding to 1.4×104 linearity within 50 mm. The measurement accuracy decreased owing to the significant influence of the air disturbance on the laser transmission and influence of the optical path drift on the measurement results at longer distances. The same method was used to test the target at 15.5 m. The maximum standard deviation during the step testing process was not more than 68 μm, and the maximum residual was not more than 27 μm, corresponding to 5.4×104 linearity within 50 mm.

    Measured results. (a), (c) Standard deviation of step displacement at approximately 7.3 m and 15.5 m. (b), (d) Step linear fitting and residual error at approximately 7.3 m and 15.5 m.

    Figure 7.Measured results. (a), (c) Standard deviation of step displacement at approximately 7.3 m and 15.5 m. (b), (d) Step linear fitting and residual error at approximately 7.3 m and 15.5 m.

    Test results of different measured targets. (a) Surface-oxidized black aluminum plate; (b) 3D printed board made of PLA; (c) sponge; (d) steel nut; (e) cylindrical steel rod; (f) carton; (g) paper; (h) circuit board; (i) plastic bottle.

    Figure 8.Test results of different measured targets. (a) Surface-oxidized black aluminum plate; (b) 3D printed board made of PLA; (c) sponge; (d) steel nut; (e) cylindrical steel rod; (f) carton; (g) paper; (h) circuit board; (i) plastic bottle.

    B. Resolution

    In theory, the ranging resolution of a system depends on the sweeping bandwidth of the scanning laser source, which indicates the ability of the measurement system to distinguish nearby targets [2,35]. According to the formula for the ranging resolution, ΔL=c/2nB,where c is the speed of light, n is the refractive index of air, and B is the sweep bandwidth of the frequency-swept laser source. The sweeping bandwidth of the ECTL used in this system was 34 nm, and the theoretically calculated ranging resolution was 44.12 μm. In practical measurements, the full width at half maximum (FWHM) of the measurement spectrum can be used to evaluate the resolution of the ranging results of a system. As shown in Fig. 9, the FWHM of the spectrum corresponds to a distance of 0.126 mm. At the same time, in order to further test the measurement resolution of the system, a precision displacement table was used to move 600 μm, 500 μm, 400 μm, 300 μm, and 170 μm; 20 measurement points were taken at each moving position, and the average value was taken as the measurement value for that position as shown in Fig. 9(a). Until 170 μm, the system was still able to distinguish the moving distance of the precision displacement table, indicating that it has a measurement resolution of at least 170 μm. The actual resolution of the system deviates from the theoretical value to some extent because of the broadening of the spectrum caused by fiber dispersion, resulting in a decrease in the actual resolution [35].

    (a) Resolution step test. (b) Measurement results of the system with or without environmental disturbances. (c) Demodulation results of LFSC-AM and LFSC-FM. (d) Test results of the resolution.

    Figure 9.(a) Resolution step test. (b) Measurement results of the system with or without environmental disturbances. (c) Demodulation results of LFSC-AM and LFSC-FM. (d) Test results of the resolution.

    C. Comparison with FSI

    (a) Power spectrum of interference signals formed by LFSC and FSI. (b) Measurement results of oxidized black aluminum plate at a distance of 16 m for LFSC and FSI.

    Figure 10.(a) Power spectrum of interference signals formed by LFSC and FSI. (b) Measurement results of oxidized black aluminum plate at a distance of 16 m for LFSC and FSI.

    D. Ability to Resist Environmental Disturbances

    In order to demonstrate the robustness of the LFSC measurement system to factors such as air disturbances and temperature fluctuations in actual measurement environments, performance testing experiments were conducted. Simulate air turbulence and temperature fluctuations in actual scenarios using a warm air blower. The distance values of the system to noncooperative targets at a distance of 11 m were tested with and without disturbance, as shown in Fig. 9(b). The standard deviation of 20 measurements under undisturbed conditions was 49.64 μm, while under disturbed conditions it was 59.75 μm. It can be seen that the system can maintain its measurement accuracy under certain environmental disturbances.

    4. CONCLUSIONS

    This study proposed a resonant cavity enhanced LFSC ranging method. FSFI based on resonant cavity enhancement has higher precision and sensitivity for noncooperative targets than the conventional FSI, achieving a residual error of 27 μm for a distance of 15.5 m using a nanowatt-level feedback laser and simpler experimental setup. Furthermore, the LFSC permits the modulation of the interference signal to a higher laser frequency, which is an efficient way to detect relatively weak interference signals during long-distance measurements. In addition, EFRS overcomes the constraints of the Nyquist sampling theorem and uses a reference interferometer 1.5 m delay fiber to achieve a 16 m distance measurement, making the experimental setup more compact. At the same time, the higher sensitivity of the LFSC-FM demodulation technology than that of the conventional LFSC-AM demodulation provides a novel method for weak-signal detection of microwaves, gravitational wave detection, and other fields. In the future, the measurement precision and resolution can be improved by incorporating optical drift path compensation devices into this ranging system and ensuring a wider laser frequency-swept bandwidth. Alternative faster and more precise demodulation technologies, such as light-net computing and neural networks, also have the potential to improve demodulation, which can be explored in the future.

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    Weijin Meng, Junkang Guo, Kai Tian, Yuqi Yu, Zian Wang, Hu Peng, Zhigang Liu, "Resonant cavity enhanced laser frequency-swept carrier ranging method for noncooperative targets," Photonics Res. 13, 1767 (2025)
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