Correction of laser Doppler vibrometry measurements affected by steering mirror vibration

The laser Doppler vibrometer (LDV) is now well-established as an effective non-contact alternative to traditional contacting vibration transducers. LDVs are technically well suited to general application but they offer special benefits in a variety of challenging measurement scenarios. A limitation in this respect is sensitivity to vibration of the instrument itself or of any steering optics used to orient the probe laser beam. Making use of a general vectorial framework for modelling the measured velocity, this paper will present a mathematical treatment of the velocity measured in the scenario where the laser beam direction is manipulated by a vibrating mirror. It will be shown that, by knowing the steering mirror vibration, it is possible to completely correct for the perturbation of the measured signal. A complementary experimental investigation is described. The LDV, the target and the mirror were relatively carefully aligned with respect to one another enabling three alternative angles of 90, 60 and 30 between the instrument and the target vibration direction. The vibrating target and the steering mirror assemblies were each instrumented with an accelerometer; the target measurement being the reference or "true" measurement while the mirror measurement is used to perform the required correction to the LDV measurement. Simultaneous measurements were taken with either the target or the mirror vibrating at "high" and "low" broadband levels; the LDV is shown to over-estimate in the mirror vibration only cases by over 22000 and 11000% respectively. Post-processing steps are presented which enabled the measurement to be corrected by circa 35dB.