Fig. 1. Experimental setup. ECDL, external cavity diode laser; AOM, acousto-optic modulator; EOM, electro-optic modulator; EDFA, Er-doped fiber amplifier; MRR, microresonator; TEC, temperature controller; PD, photodetector; LPF, low-pass filter; PBS, polarization beam splitter; BS, beam splitter; FBG, fiber Bragg grating; OSA, optical spectrum analyzer; ESA, electrical spectrum analyzer; PNA, phase noise analyzer; OSC, oscilloscope; SG, signal generator; Servo, moku lab; OTF, optical bandpass filter; $\lambda /2$, half-wave plate; Col, collimator; $\lambda /4$, quarter-wave plate; LI, laser interferometer; Sg, sliding guide.

Fig. 2. Experimental results. (a) Optical spectrum of the single soliton. The spectrum of a ${\mathrm{sech}}^2$ shape with about 100 nm optical band can be found. (b) Electrical spectrum of the free-running repetition frequency [blue, measured with 1 kHz resolution bandwidth (RBW)] and the locked repetition frequency (red, measured with 30 Hz RBW). (c) SSB phase noise of the free-running repetition frequency (blue) and the locked repetition frequency (red). The noise floor is shown as the black line. (d) The long-term measurement of the locked repetition frequency. The gate time of the frequency counter is 1 s. (e) Relative Allan deviation of the free-running repetition frequency (green), the locked repetition frequency (red), and the signal generator at 49 GHz (black). (f) The letters XIOPM obtained by programming the locked repetition frequency. (g) Linear modulation of the locked repetition frequency.

Fig. 3. Experimental results. (a) Electrical spectrum of the in-loop beat frequency between the pump laser and the fiber comb. The signal-to-noise ratio is better than 35 dB with 1 kHz RBW. (b) Electrical spectrum of the out-loop beat frequency between the pump laser and the additional fiber comb. The signal-to-noise ratio is 35 dB with 1 kHz RBW. (c) SSB phase noises of the free-running pump laser (red), the free-running 20th comb tooth (blue), the locked pump laser (green), and the locked 20th comb tooth (yellow). The noise floor is shown as the black line. (d) The long-term measurement of the locked pump laser with 1 s gate time. (e) The long-term measurement of the locked 20th comb tooth with 1 s gate time. (f) Relative Allan deviation of the free-running pump laser (black), the free-running 20th comb tooth (red), the locked pump laser (green), the locked 20th comb tooth (pink), and the hydrogen maser (blue).

Fig. 4. Experimental results. (a) Interferograms of the hybrid-comb interferometry. (b) Fourier transform of the interferograms. (c) Ranging results at a standoff distance of 0.5 m. The red points indicate the results when the measuring time for the single measurement is $4\mu \mathrm{s}$, and the blue line represents the results with $40\mu \mathrm{s}$ averaging time. (d) Results of the distance measurement. (e) Allan deviation measured at the distance of 0.5 m. (f) Measured surface profile of the disk. The black points show the measurement results and the red lines are the results measured by CMM.

Fig. 5. The interferometry characteristics of different types of dual-comb sources. (a) Time-domain description of dual-fiber-comb interferometry. The difference between the repetition frequencies of the signal source (SS) and LO is often at the kilohertz level, implying that the update of the distance measurement is at the kilohertz level. The advantage of this system is that it is relatively easy to develop two fully stabilized fiber combs. (b) Time-domain description of hybrid-comb interferometry. The $f_{\mathrm{rep}}$ of the microcomb is usually high at the gigahertz level, or even at the terahertz level, and in contrast, the fiber comb often holds tens or hundreds of megahertz repetition frequency. In spite of this highly different repetition frequency, hybrid-comb interferometry can occur. With the aid of the self-referenced fiber comb, the microcomb can be fully stabilized. In addition, the update rate can reach hundreds of kilohertz, or even megahertz, which is capable of rapid measurement. (c) Time-domain description of dual-microcomb interferometry. Since the high $f_{\mathrm{rep}}$, the detuning between the repetition frequencies of SS and LO can easily reach tens of megahertz. Consequently, the update rate can also achieve tens of megahertz, showing the capability of ultrafast measurement. However, it is rather challenging to fully stabilize two microcombs without the help of the self-referenced fiber comb. (d) Frequency-domain description of dual-fiber-comb interferometry. Because of the (relatively) small repetition frequency and the broad optical band, the optical band pass filter is generally required to circumvent the spectrum aliasing. The beat notes should be smaller than $f_{\mathrm{rep}}/2$, with a frequency separation of $\mathrm{\Delta }f$. $\mathrm{\Delta }f$ is the difference between the repetition frequencies. (e) Frequency-domain description of hybrid-comb interferometry. Interestingly, the beat components are composed of a series of groups with different center frequencies. An electrical filter can be used to select the different groups of the beat notes, whose phases can be used to calculate the distances. (f) Frequency-domain description of dual-microcomb interferometry. Similar to dual-fiber-comb interferometry, the beat notes are located with the separation of $\mathrm{\Delta }f$. The optical bandpass filter is not strictly required since the repetition frequency of microcomb is large.

Table 1. Comparison with other dual-comb ranging methods.