Fig. 1. Ultrafast ranging system and schematic diagram based on dispersion-controlled dual-swept laser. (a) Ranging system with a mode-locked laser. Panel I represents the amplification and stretching section of the light source. A beam of light is separated using beamsplitter 1 (BS1) for temporal reference and is ultimately detected by photodetector 1 (PD1). Panel II denotes the generation of ultrafast pulsed laser. The dissipative soliton (DS) laser system used in the experiment is configured as shown in the diagram, and primarily consists of a 15-m erbium-doped fiber (EDF, Nufern, EDFC-980-HP), a 2.7-m single-mode fiber (SMF), an optical coupler (OC), a wavelength division multiplexer (WDM), a polarization-independent optical isolator (ISO), a polarization controller (PC), and a saturable absorber (SA) made from single-walled carbon nanotubes. Due to its low saturation power characteristics, this laser system can operate stably with a relatively low pump power of 35 mW. The DS laser generates pulses with a duration of approximately 25 ps and a repetition rate of around 7.75 MHz. The output is a rectangular spectral pulse centered at 1565 nm with a spectral bandwidth of 11.6 nm. Panel III represents the measurement system based on a Michelson interferometer, with the interferometric signal ultimately detected by photodetector 2 (PD2). EDFA, erbium-doped fiber amplifier; DCF, dispersion compensated fiber; BS, beamsplitter; Cir, circulator; Col, collimator lens; Oscope, oscilloscope. (b) Principle of dual-sweep frequency laser ranging. By adjusting the position of the mirror M using a motorized linear translation stage, we can vary the measurement distance L. This adjustment results in the sweep frequency signal moving horizontally from left to right.

Fig. 2. Dispersion controlling process of the dual-sweep frequency ranging system. (a) The temporal evolution of the measurement arm’s signal optical pulse as it propagates through the 7400-m-long DCF1. (b) The temporal evolution of the reference arm’s signal optical pulse as it propagates through the 7400-m-long DCF1 and the 105-m-long DCF2. (c) The pulse shapes of the two interferometric arms’ optical signals after dispersion control. (d) The interferometric signals and the sweep frequency curves of the two interferometric arms’ optical signals when the measured distance is zero.

Fig. 3. The precise determination process of the ZPOs. (a) The interference signals near the ZPO acquired by the oscilloscope, with the corresponding target distances of 4 mm, 10 mm, and 16 mm. (b) The AC components obtained after filtering and envelope detection of the interference spectra. (c) Apply the Hilbert transform to the obtained AC components to determine the phase. (d) Perform phase unwrapping on the obtained phase. (e) Fit a polynomial to the phase curve and differentiate to determine the precise location of the ZPOs.

Fig. 4. Results and analysis of the simulation experiments. (a) Interference signal at a target distance of −20  mm, with introduced random noise. (b) ZPO’s time-distance curve. (c) Computed results of target distances and the corresponding fitting curves. (d) Reproducibility results under varying signal-to-noise ratios. (e) Fluctuations in target distance measurement error under varying signal-to-noise ratios.

Fig. 5. Characterization of the experimental light source and partial interference signals acquired. (a) Spectrum of the light source before stretching. (b) Spectrum of the light source after stretching. (c) Temporal pulse of the light source before stretching. (d) Temporal pulse of the light source after stretching. (e) The five sets of interference signals corresponding to variations in target distance. The red dots indicate the position of the ZPOs. (f) The eye diagram of the interference signals collected from 3070 sets of reproducibility experiments at a distance of 1136 mm.

Fig. 6. The results of the static targets distance measurement using DCDSL. (a) During the measurement process at different distances with an interval of 1 mm, the upper figure illustrates the correlation between the measured distance and the corresponding time of the ZPOs, along with the measurement results. The lower figure displays the measurement deviations at different positions. (b) The upper figure presents the measurement results and corresponding standard deviations at a distance interval of 20 μm, while the lower figure illustrates the fluctuation patterns. (c) Deviation of the 3070 sets of measurement results at a distance of 1136 mm. (d) Statistical analysis of the DCDSL measurement values reveals that the 1σ value is 4.227 μm. (e) The repeatability of the proposed method is represented by the Allan deviation, indicating that the measurement repeatability of DCDSL is 4.25 nm over an average duration of 4 ms.

Fig. 7. Results of dynamic displacement measurements using DCDSL. (a) A total of 30,700 sets of interference signals were collected during the dynamic displacement measurement process, where the blue dashed line represents the drift trajectory of the ZPOs. (b) Dynamic displacement measurement results of approximately 100 μm. (c) Displacement-time measurement curve and determination of the average velocity for target. (d), (e) Repeated velocity measurement results and their distribution, suggesting a maximum error ±0.14  mm/s and an STD 0.09 mm/s.

Fig. 8. The effects of Doppler shift phenomenon on the measurement results for the proposed method. (a) Interference signals randomly acquired. (b) Interference signals after envelope removal. (c) Results of 300 velocity measurement experiments. (d) Phase curves under two different conditions.