Fig. 1. The quantity of papers and times cited of FMCW from 2006 to 2021

Fig. 2. Schematic of absolute distance measurement by laser frequency scanning interference^[7]

Fig. 3. Triangular frequency-modulated laser and echo from stationary objects^[8]

Fig. 4. Influence of FM nonlinearity on ranging results. (a) Time-frequency graph of the FMCW signal; (b) Time-frequency graph of the fluctuant beat signal; (c) A broadened distance spectrum obtained by FFT on the ranging signal without nonlinear calibration^[15]

Fig. 5. (a) Experimental setup for broadband optical frequency chirp linearization using the self-heterodyne technique; (b) Top: range peak centers for 40 consecutive measurements. The standard deviation of the errors is 86 nm. Bottom: relative range measured as the target was manually moved over 100 μm in 10 μm increments^[17]

Fig. 6. (a) Optoelectronic feedback loop for the generation of accurate broadband linear chirps; (b) Measured spectrogram of the output of the loop photodetector when the loop is in lock, corresponding to an optical sweep rate of 100 GHz/ms; (c) Fourier transform of the photodetector output measured over a 1 ms duration^[18]

Fig. 7. (a) Detailed block diagram of the EO-PLL with gated ramp switching; (b) Photograph of experimental setup for ranging; (c) Schematic of experimental setup for ranging^[20]

Fig. 8. Schematic of the experimental setup.

AOFS: acousto-optic frequency shifter; FUT: fiber under test; SMF: single-mode fiber; PMC: polarization-maintaining coupler;

PC: polarization controller; PMF: polarization-maintaining fiber; PD: photo detector;

DPFD: digital phase frequency detector; VCO: voltage controlled oscillator^[21]

Fig. 9. Schematic of distance measurement with equal optical frequency interval resampling

Fig. 10. Schematic diagram of the dual interferometry FMCW laser ranging system^[31]

Fig. 11. (a) Normalized range peak in decibels obtained by different methods; (b) Comparison of MSE obtained by different methods^[32]

Fig. 12. Schematic of the FMCW laser ranging system with two auxiliary interferometers^[33]

Fig. 13. A new hardware structure for correcting FM nonlinearity with only a single detection channel.

TLS: tunable laser source; PC: polarization controller; FOC: fiber optic coupler; CIR: circulator;

FUT: fiber under test; BPD: balanced photo detector^[38]

Fig. 14. (a) Experimental setup. A MEMS-based ECL is swept sinusoidally over 1 THz with a 1 ms period. The system simultaneously records the ladar heterodyne signal and the instantaneous ECL frequency, as measured against a free-running frequency comb; (b) Sonogram of the measured ladar signal. The peak amplitude corresponds to f_FMCW(t); (c) Instantaneous ECL frequency, v_ECL(t)−v₀; (d) Range signal to the brushed Al surface for a single 0.5 ms long sweep and ~10 nW~100 nW return power; (e) Expanded view illustrating the unapodized, bandwidth-limited resolution of ΔR = 0.9c/(2B) = 130 μm, despite the sweep rate of up to 3400 THz/s^[45]

Fig. 15. (a) Photograph of an Al-step block with the NIST logo imprinted and a quarter located on the lower left corner; (b) False colored, 3D surface image of the step block, along with a quarter on the bottom left, measured by our FMCW LADAR system at a stand-off of z₀= 4.760 m; (c) The FMCW LADAR image (green trace) is compared to an average of 12 measurement points taken with a CMM (blue crosses). The error (red crosses) has a standard deviation below 2 μm^[46]

Fig. 16. (a) Measurement schematic diagram of instantaneous frequency calibration with narrow bandpass filter; (b) Illustration of frequency positions of the sweeping laser, comb lines, and the bandpass filter.

PC: polarization controller; FC: fiber coupler; RR: retro-reflector; PD1 and PD2: photodiodes; OF: optical filter; PBS: polarized beam

splitter; f_c: central frequency of the narrow bandpass filter; f_r: repetition rate of the femtosecond laser (comb line spacing)^[47]

Fig. 17. (a) Schematic of the experimental setup; (b) Time-frequency graph of the interference signal between FMCW laser and soliton comb; (c) Time-domain graph of the ranging signal and calibration peak^[15]

Fig. 18. (a) Spectral of the soliton comb after filtering; (b) Time-domain graph of the ranging signal and auxiliary signal; (c) Extraction of calibration peak positions in the auxiliary signal. The figure contains the original auxiliary signal and the complex envelope signal through Hilbert transform (HT), as well as the waveform processed by low-pass filtering and envelope fitting for the complex envelope signal^[15]

Fig. 19. A diagram of two Fizeau interferometers connected to two lasers and one gas absorption cell^[52]

Fig. 20. (a) Multiple scans of a measurement interferometer with the target on a linear motion stage; (b) Single scan at fastest linear motion stage speed; (c) Zoom in of (a) with a straight line fit; (d) Residual to the straight line fit in (c)^[52]

Fig. 21. (a) The residual of the fit to the long range test data; (b) The relative residual of the (a)^[52]

Fig. 22. Schematic diagram of the phase noise compensation in PNC-OFDR^[53]

Fig. 23. Schematic of PNC-OFDR configuration^[53]

Fig. 24. (a) Schematic diagram of FMCW ranging system based on amplitude modulation; (b) The mixing signal of the amplitude modulation system^[56]

Fig. 25. Schematic of ILC pre-distortion of laser frequency sweep linearization. (a) Block diagram of the ILC process; (b) Detailed setup for laser frequency sweep measurement^[58]

Fig. 26. Experimental results of laser frequency sweep linearization of VCSEL by ILC. (a) Residual nonlinearity versus the number of iterations; (b) Laser frequency sweep and the corresponding drive voltage waveforms at the 256th iteration. The ROI is labeled by red color; (c), (d) The down- and up-ramp laser frequency sweeps and residual errors in the ROIs of the 256th iteration; (e), (f) The down- and up-ramp laser frequency sweeps and residual errors of the 1st iteration for comparison^[58]

Fig. 27. (a) The sketch diagram of the proposed FMCW-based LiDAR system. AWG: arbitrary waveform generator; DFB: distributed feedback laser; PC: polarization controller; MZM: Mach-Zehnder modulator; BPD: balanced photodetector; DAQ: data acquisition card. Solid line means light path and dash line means electronic path; (b) The optical spectra of the master laser after optical modulation (red), the slave laser without the optical injection (black), and the slave laser after the injection-locked (blue)^[59]

Fig. 28. Solid-state 3D imaging architecture^[6]

Fig. 29. (a) Point clouds of stacked cardboard boxes at 54 m; (b) Point clouds of exterior wall at 75 m. Distance to the target is indicated by color in (a) and (b)^[6]

Fig. 30. FMCW LiDAR ranging system based on HCN gas cell