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High-precision time interval measurement is widely used in time synchronization, satellite navigation, laser ranging, and nuclear electronics. The resolution and accuracy of the currently used time counter are about 25 and 100 ps, respectively. A new time interval measurement method, in which the signal under test is used to trigger a sampler and the phase of the reference sinusoid signal is sampled to record the time stamp of the test signal, was put forward. Then, the sampled reference sine signal's phase is estimated by the interpolated fast Fourier transform (FFT), and 1-ps resolution and accuracy can theoretically be achieved. The test experiment of the prototype instrument shows that a 10-ps accuracy has been reached. If the hardware prototype is improved to reduce trigger jitter and sampling clock jitter, the measurement instrument may reach 1-ps accuracy. The measurement system is used not only for time interval measurement but also for period measurement and even modulation domain analysis.