Fig. 1. Illustration of the principle of the proposed phase unwrapping algorithm. (a) Traditional phase unwrapping algorithm based on group delay estimation. (b) The proposed phase unwrapping algorithm based on discrete frequency sampling. PSD, power spectral density. In (a) P1, P2, and P3 are the frequency points chosen by the traditional phase unwrapping algorithm. In (b) P1, P3, and P5 are the frequency points selected by the proposed phase unwrapping algorithm. P4 is obtained by linearly fitting P1 and P3. (c) Flowchart of the proposed OTD measurement process.

Fig. 2. Relationships between the number of frequency points and (a) the required phase accuracy and (b) the peak-to-average power ratio (PAPR).

Fig. 3. Two implementations of the single-shot OTD measurement system. (a) OTD measurement with electrical path reference. (b) OTD measurement with optical path reference. LD, laser diode; MZM, Mach–Zehnder modulator; DPMZM, dual-parallel Mach–Zehnder modulator; OC, optical coupler; RF, radio frequency; PD, photodetector; ADC, analog-to-digital converter; DSP, digital signal processor.

Fig. 4. The relationship between sampling time and two key variables: (a) phase variance and (b) short-term frequency stability.

Fig. 5. (a) Modeling of the third-order intermodulation distortion in the frequency and time domains. (b) The effect of third-order intermodulation distortion of the received signal. (c) The magnitude of the 3 kHz periodic phase jitter induced by the third-order intermodulation distortion interference. The power of frequency points f1 and f2 is kept at 15 dBm, and f3 is kept at 10 dBm, while the frequency point f4 varies from 0 dBm to 15 dBm. (d) The magnitude ratio of the periodic phase jitter relationship between f2 and f3. (e)–(h) Phase detection results of f1 to f4 within 1 ms when the modulated signal powers of f1 to f4 are 15, 15, 10, 15 dBm.

Fig. 6. (a) Experimental results of the system stability over 20 minutes. (b) The measured delay of the motorized delay line from 10 ps to 1 ps. (c) The deviation of the measured delay line. (d) Schematic diagram of distributed coherent aperture experiment with OTD measurement and compensation. G is the gain of coherent aperture synthesis. (e) Power gain of the coherent synthetic with different OTD differences. (f) Detailed power gain of the coherent synthetic with compensated OTD.

Fig. 7. (a) Verification experiment of the measurement speed and measurement range. Blue dot: 20 km fiber link. Red dot: 10 km fiber link. (b) Comparison with other optical delay measurement and ranging methods [20,23,26,29,31–38" target="_self" style="display: inline;">–38].