High-Resolution Optical Frequency Rapid Measurement Method Based on the Hilbert Transform for Extracting Instantaneous Frequency

Coherent spectroscopy provides a high optical frequency resolution; however, as the measurement speed increases, the number of cycles in the chirped signal generated by the interference between the local oscillator (LO) and the signal under test (SUT) decreases. This study addresses this issue by focusing on frequency changes within the chirped signal. By relying on instantaneous frequency variations of the interference signal instead of its amplitude variations, the proposed method allows for faster scanning speeds. A high-resolution rapid-frequency analysis of the SUT was achieved by extracting the low-frequency components of the chirped signal and applying the Hilbert transform to obtain the instantaneous frequency, which was combined with the power characteristics of the signal. This study demonstrates that, at a measurement speed of 40.3 nm/s, this method can achieve an optical frequency resolution of 3 MHz (approximately 24 fm near 1550 nm). Therefore, the proposed method demonstrates its significant practicality and broad application potential for high-precision optical frequency detection in dynamic environments.