Singular spectrum analysis for extracting low amplitude vibrations in femtosecond laser time-of-flight distance measurements

Abstract

We utilize singular spectrum analysis (SSA) for post-processing distance measurement data obtained by a dual-comb femtosecond laser rangefinder. Signal denoising technique based on SSA allows detection of low amplitude vibrations from time series of distance data with limited signal-to-noise ratio (SNR). Various one-dimensional vibrations, including harmonic, amplitude modulated harmonic, and sinc-function vibrations, with micrometer amplitude comparable with measurement uncertainty of laser rangefinder, have been imposed on the target mirror by a piezo positioner. These vibrations have been extracted by SSA and the obtained vibration amplitudes agree with that imposed on the target very well. A commercial interferometer is used to evaluate the accuracy of SSA. Standard deviations of residuals between the SSA extractions and interferometer measurements are smaller than 0.6 μm. This technique is promising for complex moving pattern detection in object tracking and remote sensing.