Calibration of laser Doppler vibrometer exploiting Bessel functions of the first kind

Abstract

Laser Doppler vibrometers (LDVs) both in a bulk optics and fibre optic format have been available for more than 30 years. Calibration of the vibrometer at fixed frequencies varies from counting fringes at low frequencies to measuring the displacement from the Doppler velocity. The proposed method for calibration exploits the properties of the optical vibration spectrum which can be described by Bessel functions of the first kind making it intrinsic to the vibrometer itself and not requiring any additional optical equipment. Calibration was achieved using an electric shaker to generate the vibration signal over a range of frequencies. Ideally the shaker should be calibrated but this is not required in the proposed system. This approach enables the maximum vibration amplitude and the minimum amplitude to be determined. In addition, an example of the calibration of a LDV is presented in which a minimum displacement of 1.6 nm at 4 kHz was achieved.