Restoring high accuracy to laser Doppler vibrometry measurements affected by vibration of beam steering optics

Laser Doppler vibrometers are now well-established as an effective non-contact alternative to traditional contacting transducers. Wide-ranging applications include those where beam steering optics are required to reach locations that are difficult to access but no attention has yet been given to measurement sensitivity to the vibration of those optics. In this paper, a thorough mathematical treatment of this sensitivity to steering optic vibration and its correction is set out. A very practical scheme requiring a single correction measurement, from the back-surface of the mirror at the incidence point and aligned with the mirror normal, delivers an error reduction typically in excess of 30 dB. After validation in the laboratory, the scheme is then applied to a genuinely challenging measurement scenario on a single cylinder racing motorcycle. Correction is theoretically perfect for translational mirror vibrations but angular mirror vibrations require an adapted scheme using a triplet of accelerometers arranged around a circular path on the mirror back-surface and this is set out theoretically.