Extraction of nanometer-scale displacements from noisy signals at frequencies down to 1 mHz obtained by differential laser Doppler vibrometry

Abstract

A method is presented by which very small, slow, anharmonic signals can be extracted from measurement data overlaid with noise that is orders of magnitude larger than the signal of interest. To this end, a multi-step filtering process is applied to a time signal containing the time-dependent displacement of the surface of a sample, which is determined with a contactless measurement method, differential laser Doppler vibrometry (D-LDV), at elevated temperatures. The time signal contains the phase difference of the measurement and reference laser beams of the D-LDV, already greatly reducing noise from, e.g., length fluctuations, heat haze, and mechanical vibrations. In postprocessing of the data, anharmonic signal contributions are identified and extracted to show the accurate displacement originating from thickness changes of thin films and related sample bending. The approach is demonstrated on a Pr0.1Ce0.9O2−δ (PCO) thin film deposited on a single-crystalline ZrO2-based substrate. The displacement extracted from the data is ca. 38 % larger and the uncertainty ca. 35 % lower than those calculated directly from the D-LDV spectrum.