从含噪数据中提取信号从而提升数据采集系统精度是极为重要的问题.奇异谱分析（singular spectrum analysis，SSA）作为一种无参数频谱估计技术，广泛用于区分系统模型未知情况下的动态系统信号的复杂成分.本文应用SSA方法提取双光梳飞秒激光测距系统中的含噪时间序列的距离信息，数值仿真显示SSA方法可以从含有有色噪声的信号中提取距离信号.实验中，SSA方法成功地从含有量子噪声的测距信号中提取出激光与目标之间的距离信息，提取后的信号有13倍的精度提升.这种方法同样适用于高维信号，如基于飞秒激光测距的高精度、高速率表面形貌测量的图像提取.
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.
Project supported by by the National Natural Science Foundation of China (Grant Nos. 61675150, 11527808, 61535009).
- 曹辉, 宋有建, 于佳禾, 师浩森, 胡明列, 王清月. 奇异谱分析用于提升双光梳激光测距精度[J]. 物理学报, 2018, 67(1): 010601.
- Cao Hui, Song You-Jian, Yu Jia-He, Shi Hao-Sen, Hu Ming-Lie, Wang Qing-Yue. Singular spectrum analysis for precision improvement in dual-comb laser ranging[J]. Acta Phys. Sin., 2018, 67(1): 010601.