Time-Delay Measurement Method Based on the Frequency-Spectrum Distribution of Laser Intensity or Phase Noise Signal

The frequency-domain measurement method of time delay based on laser intensity or phase noise as multifrequency signal source is proposed. The frequency-spectrum distribution of noise signal caused by the time delay is analyzed to extract the characteristic frequencies to derive the time delay. The experimental results with intensity noise source show that for the time-delay fiber ranging from 0.5 to 15 km in length, the measurement deviation compared to optical time-domain reflectometer (OTDR) results ranges from −0.0514% to 0.0949%, demonstrating good measurement accuracy. For multiple measurements of 5-km-long time-delay fiber, the measurement deviation range with intensity noise source is from 0.0417% to 0.0689%, with a characteristic frequency fluctuation of 11 Hz, corresponding to time-delay measurement resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6.69\times 10^{-{9}}$ </tex-math></inline-formula> s. The deviation range of the measurement with phase noise source is from −0.2437% to 0.1257%, with a characteristic frequency fluctuation of 150 Hz, corresponding to time-delay measurement resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9.11\times 10^{-{8}}$ </tex-math></inline-formula> s. Therefore, the time-delay measurement resolution for the two noise sources is lower than the minimum interval of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times 10^{-{6}}$ </tex-math></inline-formula> s, corresponding to a sample rate of 500 kHz. It also meets the precision requirements of shifting discrete-signal timing needed for common-mode suppression on phase or intensity noise in optical fiber sensor arrays.