Fig. 1. Working model of the laser frequency-shifted feedback system. (a) Working process of the LFFI. ML, microchip laser; M1,M2, resonator mirrors of the ML; FS, frequency-shifter; T, target; Ein, light field reflected by M2; Eext, backscattered light field from the target. (b) Schematic diagram of the phase amplification process of returned light in the LFFI. Eback, light field returned to the laser cavity from the target with the phase change of Δφ; Eout, re-output light field after phase amplification of N times (here, N=11) by the FIHG effect.

Fig. 2. Frequency spectra of the output laser after feedback interference under different external optical loss states (different κ) with external modulation frequency shift of 1 MHz. (a) κ<10−12. (b) κ=9×10−12. (c) κ=2.5×10−7.

Fig. 3. Schematic diagram of the experimental setup. BS, 7:3 (transmittance:reflectivity) beam splitter; L, convex lens; AOM1, 2, acoustic-optic modulators to provide frequency shift Ω of external light; f0, laser frequency; AP, aperture; T, target; PD, photodiode.

Fig. 4. Flowchart showing the signal processing process of obtaining amplified phase change through lock-in amplifier. Mixer, frequency mixer; LPF, low-pass filter; I, in-phase component; Q, quadrature component; A, θ, amplitude and phase of the signal, respectively; NΔφ, phase output after N-fold amplification.

Fig. 5. Corresponding frequency spectra of different harmonics in laser cavity, with corresponding SNR of each spectral peak marked in each sub-figure. (a) Fundamental wave. (b)–(k) Second through eleventh harmonics.

Fig. 6. Schematic diagram of phase amplification result and measurement values. (a) Result of the original phase change and quadrupling phase change without unwrapping. (b) Actual value of the phase change in each cycle after amplification and the average phase change value.

Fig. 7. Comparison of the original unwrapped phase change with two, four, eight, and eleven times amplified unwrapped phase change. (a) Two times amplification. (b) Four times amplification. (c) Eight times amplification. (d) Eleven times amplification.

Fig. 8. Theoretical standard phase values corresponding to different OPDs (0.5 μm, 1 μm, 1.5 μm, 2 μm) at different magnifications.

Fig. 9. Errors between measured values and standard phase values corresponding to different OPDs (0.5 μm, 1 μm, 1.5 μm, 2 μm) at different magnifications. (a) Two times amplification. (b) Four times amplification. (c) Eight times amplification. (d) Eleven times amplification.

Fig. 10. Physical device of the long-distance experiment and the results of phase amplification. (a) Diagram of the experimental system and the target (aluminum block) in the corridor; inside the red frame is the overall schematic diagram of this long-distance experiment. (b) Diagram of the mirror used to turn the light path, which makes distance from the target to the LFFI reach 130 m. (c) Result of the phase amplified by two times and four times.

Fig. 11. Corresponding frequency spectrum of the 20th harmonic in laser cavity.

Fig. 12. Schematic diagram of the circular LFFI with adding optical amplifier to get greater phase amplification. ML, microchip laser; L, lens; NPBS1–3, non-polarizing beam splitters with ratios of transmittance to reflectivity of 5:5, 7:3, 5:5, respectively; ISO, optical isolator; M1, 2, mirrors; OA, optical amplifier; AOM1, 2, acoustic-optic modulators to provide frequency shift of external light; T, target; PD, photodiode.