As a cutting-edge spectral technology with characteristics including high resolution, broadband spectral range and fast measurement, dual comb spectroscopy has shown great potential in many applications in modern optical research. The premise of high resolution spectral measurement with dual comb spectroscopy is that the dual-comb system has a high degree of mutual coherence. Therefore, how to improve the mutual coherence of the dual-comb system has been a key challenge restricting its performance improvement and wide applications. At present, the traditional methods such as active coherent control have problems of high complexity and high cost, the passive coherent control method has problems of limited measurement bandwidth and poor tunability, and the self-reference error correction method involves complex algorithms and models. Focusing on this problem, this paper takes the radio-frequency-locked dual-comb system as the research platform and proposes a self-reference correction algorithm for dual comb spectroscopy based on an innovation-based adaptive extended Kalman filter, which corrects the distortion of the interference signal in the time domain and recovers the mutual coherence.

In order to solve the problem of frequency drift caused by noise interference in dual-comb system with low mutual coherence, the spectral self-reference error correction algorithm of the dual-comb system based on an innovation-based adaptive extended Kalman filter is used to extract and compensate the noise information accurately, and gradually restore the mutual coherence of the dual-comb system. Because of the nonlinearity of the dual-comb system, the extended Kalman filter is chosen as the research algorithm, and the noise matrix is calculated by the innovation-based adaptive method to reduce the dependence on the prior knowledge of the noise matrix. First, the continuous dual-comb interference signal sequence is segmented in time domain according to the repetition period to separate the interference signal frame by frame. In the process of correction, one frame is taken as the reference frame, and the time jitter, center frequency jitter and carrier envelope phase jitter of other frames relative to the reference frame are calculated. Then, Hilbert transform is used to extract the envelope of the time domain interference signal, and the time jitter is calculated by the distance between the envelope peaks, so as to reflect the jitter of the relative repetition frequency of the dual-comb system. Subsequently, the carrier frequency and carrier envelope phase of the interference signal are selected as the state variables, and the state space model of the interference signal is established. Based on the innovation-based adaptive extended Kalman filter, the carrier frequency and carrier envelope phase of each frame are optimally estimated, and the frequency and phase jitter values are calculated. Finally, according to the extracted jitter information, the numerical operations such as translation and phase rotation of the interference signal are carried out to realize the correction of dual comb spectroscopy and restore its mutual coherence.

To fully verify the effect of the self-reference correction algorithm based on the innovation-based adaptive extended Kalman filter for the dual-comb system with low mutual coherence, the research work is carried out from two perspectives of simulation and experiment, and the effectiveness of the algorithm is verified from the aspects of extracted jitter error, spectral resolution and mutual coherence. Simulation and experimental results show that this method can first accurately extract and compensate the jitter signal of the dual-comb system, and then realize the error correction of the signal. The experimental results show that before correction, due to the existence of various noises, the mutual coherence of the dual-comb system is seriously affected. This results in the distortion of the interference signal, and significant broadening of the longitudinal modes in the radio frequency domain, with the linewidth of the longitudinal mode being far greater than the 1 kHz repetition frequency difference. After correction, within 1 s acquisition time, the longitudinal mode linewidth in the radio frequency domain is reduced from far more than 1 kHz to 1 Hz, and the spectral resolution is significantly improved. The signal-to-noise ratio after the interference signal coherence average is increased from 382 to 16446, which is about 40 times higher. These results prove that the method can effectively improve the spectral quality and restore the mutual coherence of the dual-comb system.

In this paper, a self-reference correction algorithm for dual comb spectroscopy based on an innovation-based adaptive extended Kalman filter is proposed by using the radio-frequency-locked dual-comb system and the simulation model of dual-comb system. This method can effectively restore the coherence in the dual-comb sources, reduce the longitudinal mode linewidth in the radio frequency domain from the original greater than 1 kHz to 1 Hz within 1 s acquisition time, significantly improve the spectral resolution, and at the same time, the signal-to-noise ratio after the interference signal coherence average is increased by about 40 times. Compared with those of the traditional extended Kalman filter algorithm, the model complexity is reduced, and the calculation process does not require the number of combs, which can solve the problem that the traditional method has difficulty in calculating for large mode-locked lasers.