Fig. 1. Schematic illustration of the pulse-modulated frequency-shifted LFI. An AOM is used as an extracavity pulse modulator. T, Doppler cycle; Δt, time delay.

Fig. 2. Exploration of the ToF dynamics characteristics in the pulsed LFI system. (a) Schematic illustration of extracavity frequency shift; (b) time-domain waveform envelopes and according Doppler spectra at different pulse overlapping time windows; (c), (d) variation of the velocity signal intensity with pulse overlapping time interval and RF modulation voltage, respectively; (e), (f) minimum feedback photon number of the successfully attained pulsed LFI signal under different overlapping time intervals and modulation voltages, respectively. Here, pulse overlapping time refers to the overlapped time interval between the feedback light signal pulse and the original light pulse, namely, the time window for effective LFI interference occurrence within the pulse modulation period. FWHM, full width at half-maximum; SNR, signal-to-noise ratio. The minimum feedback photon number is defined as the number of feedback photons per Doppler cycle, satisfying the condition of SNR=1, which corresponds to the achievable sensitivity of the system under different modulation parameters.

Fig. 3. Performance characterization of pulsed LFI system at different extracavity velocities. (a) Doppler frequency spectra at different velocities; (b) repeatability test of the sensor in the initial status by five repeated measurements; the target’s velocity is varied from 73.5 to 612.6 mm/s. (c) Mapping of Doppler frequency spectra, under the external distance of 2.0 km; (d) dependence curves of the measured velocity on the actual velocity, under the external distance of 2.0 km. The SNR of the Doppler frequency signal is decreased by 5 dB as the velocity increases.

Fig. 4. Observations of the pulsed LFI velocity signal characteristics under different extracavity distances. (a) Variation curve of the velocity signal intensity via different distances; (b) dependence of measured distance versus the actual distance; (c) Doppler frequency spectra at different distances; (d) temporal waveform envelopes of the pulsed LFI velocity signals at different distances. Noticeably, the SMF acts as the long-distance transmission platform for the feedback light to carry the effective motion information of the moving target. In the experiment, the length of the SMF is adjusted to measure the target’s velocity at various distances.

Fig. 5. Various LFI velocity signals with respect to different extracavity distances. (a) Simultaneous measurement of distance and velocity in the range of 73.5−612.6  mm/s, and the distance ranges from 2.0 to 25.5 km. The horizontal and vertical error bars indicate the SD of the distance and velocity measurements, respectively. (b) Distance measurements at different velocities, under the external distance of 5.0 km; (c) velocity measurements with the external distances when the turntable velocity was set to 245 mm/s.

Fig. 6. Experimental system for the pulsed LFI sensor for simultaneous velocity and distance measurement. WDM, wavelength division multiplexer; AOM1,2, acousto-optic modulators; CIR1,2, circulators; PD, photodetector; SMF, single-mode fiber.

Fig. 7. Schematic of the all-fiber pulsed LFI theoretical model for simultaneous sensing of velocity and distance based on the extracavity frequency-shifted optical feedback effect under pulse modulation. (a) Equivalent three-mirror F-P cavity model of the DFB fiber laser; (b) variation curve of system gain factor with the frequency shift of the external cavity under different normalized pumping coefficients; (c) theoretical attainable maximum attainable gain factor of the LFI system as a function of the normalized pumping coefficient.

Fig. 8. Numerical simulation results of simultaneous measurement for the external velocity and distance (ν=0.03  m/s, θ=60°). (a) Without frequency shift of the external cavity; (b) frequency shift amount of fAOM=60  kHz, (c) fAOM=120  kHz, and (d) fAOM=180  kHz; (e) applied external pulse modulation level; (f) without adding the external sensing fiber, (g) with the sensing fiber length of ΔLext=5  km, and (h) ΔLext=10  km.

Fig. 9. Spectra and speckle envelopes of the pulsed LFI velocity signals. (a), (b) Spectrum and temporal waveform of the initial LFI velocity signal, respectively; (c), (d) spectrum and temporal waveform of the LFI velocity signal when the Doppler frequency signal moves to the laser relaxation oscillation peak, respectively; (e), (f) spectrum and time-domain waveform of the LFI velocity signal under pulse modulation, respectively.

Fig. 10. Spectrum and time-domain waveform of the LFI velocity signal under 2.0 km delay fiber. (a) Pulse-modulated reference level signal; (b) frequency spectrum of the LFI velocity signal; (c) temporal waveform envelope of the pulsed LFI velocity signal; (d) partial enlargement of signal waveform diagram of (c).