
- Photonics Research
- Vol. 13, Issue 6, 1767 (2025)
Abstract
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 [6–8]. 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) [18–20].
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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
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
Taking the laser emission point as the initial position, owing to the distance from the target to be measured, there is a time delay
The probe and feedback lasers oscillate in the laser resonant cavity comprising
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
Owing to the extremely high propagation speed of the laser, the time
By substituting Eq. (5) into Eq. (3), the interference signal intensity can be expressed as
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
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
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
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:
Because
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
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]:
When the feedback laser is reflected by an external object and reenters the laser cavity, its round-trip phase change satisfies
For phase matching conditions, the feedback laser round-trip phase difference can be described as
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
Simulation Parameter Settings
Parameter | Symbol | Value |
---|---|---|
Center wavelength | 1550 nm | |
Bandwidth | 40 nm | |
Period | 1 s | |
Sampling rate | 20 MHz | |
Quadratic coefficient | ||
Cubic coefficient | ||
Reference fiber length | 5 m | |
Target distance | 30 m | |
Resampling factor | 10 |
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:
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
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.
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.
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
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
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
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.
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,
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
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.
References
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[27] Y. Wang, Z. Hua, J. Shi. Laser feedback frequency-modulated continuous-wave LiDAR and 3-D imaging. IEEE Trans. Instrum. Meas., 72(2023).

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