Singular spectrum analysis for precision improvement in dual-comb laser ranging
Cao Hui, Song You-Jian, Yu Jia-He, Shi Hao-Sen, Hu Ming-Lie, Wang Qing-Yue
Key Laboratory of Opto-electronic Information Technology, Ministry of Education(Tianjin University), School of Precision Instrument and Opto-electronics Engineering, Tianjin University, Tianjin 300072, China
Optical methods in distance measurement, which are categorized by interferometry and time-of-flight (TOF) detection, have received widespread attention in recent years. However, interferometry cannot provide absolute distance and traditional TOF measurement cannot obtain a high precision measurement result either. The TOF ranging by femtosecond lasers, a novel precise measurement approach, enabling a sub-micrometer precision for long distance absolute ranging, can solve the problems above and has a wide application prospect in aerospace, remote sensing and surface profilometry. Particularly, a dual-comb ranging approach has attracted great attention due to high update rate (~kHz) and a simple system structure (i.e., working with free running mode-locked laser system). However, the quantum limited timing jitter of mode-locked lasers will inevitably introduce uncertainty into TOF estimation due to the equivalent sampling nature of a dual-comb scheme. As a result, the distance measurement precision is significantly degraded. Even though a simple multiple averaging can be used to alleviate this problem, the measurement speed is limited to a very low level, which is unacceptable to many applications. Moreover, multiple averaging fails in the presence of more complex noise sources. Singular spectrum analysis (SSA), known as a non-parametric spectral estimation technique, has been widely used in dynamic systems to distinguish complex patterns in signals without a priori knowledge of the dynamical model. In this paper, for the first time, we apply SSA to extract distance information from a noisy time series generated by a high update rate dual-comb ranging system. Numerical simulation shows that the SSA is a powerful tool for separating distance series into signal and random noise regardless its color. Specifically, we extract a one-dimensional step profile with high precision in the presence of violet noise (density proportional to f2). In experiment, a dual-comb ranging system is built based on two home-built polarization maintaining mode-locked fiber lasers by using carbon nanotube as saturable absorber. Their repetition rates are both about 74 MHz, their difference being about 2 kHz. We measure the distance of a moving target placed at ~0.5 m away from the range finder and use the SSA for signal extraction. The direct measurement precision is 1.9968 μm rms at 200 Hz update rate. The SSA successfully separates the quantum noise from the ranging time series, resulting in 0.1522 μm rms ranging precision, corresponding to about 13 times ranging precision improvement. This method can be further extended to high dimension, enabling high precision and high speed profilometry for complex surfaces based on femtosecond laser ranging.