Fig. 1. Physical model of pulse interference in the Z domain.

Fig. 2. Distance between cavity phase points.

Fig. 3. (a) Four vectors (green or orange) are chosen randomly to extract the most likely cavity phase. The theoretical cavity phase (red) is 0 rad. (b) Histogram of all cavity phase candidates. The phase interval is 1.0°.

Fig. 4. Simulation results. The probe pulse train consists of 41 pulses. The cavity phase calculation needs 40 iterations. (a) Pure system without noise. (b) Actual system with 1.0% power level noise.

Fig. 5. Scanning the theoretical cavity phase over one cycle and extracting the most likely cavity phase accordingly. (a) Pure system without noise. (b) Actual system with 1.0% power level noise.

Fig. 6. Errors of extracted cavity phases in a three-cavity system. (a) Cavity phase error is 0.7° (RMS) in the first cavity. (b) Cavity phase error is 0.8° (RMS) in the second cavity. (c) Cavity phase error is 0.9° (RMS) in the third cavity.