Laser vibration sensing provides a sensitive non-contact means of measuring vibrations of objects. These measurements are used in industrial quality control and wear monitoring as well as the analysis of the vibrational characteristics of objects. In laser vibrometry, the surface motion is monitored by heterodyne laser Doppler velocimetry, and the received heterodyne signal is sampled to produce a time-series which is processed to obtain a vibrational spectrum of the object under test. Laser vibrometry data has been processed with a traditional FM discriminator approach and by spectrogram and time-frequency distribution processing techniques. The latter techniques have demonstrated improved performance over the FM discriminator method, but do not take full advantage of the prior knowledge one has about the signal of interest. We consider here a statistical signal processing approach to laser vibrometry data. In this approach the quantities of interest are the frequencies of vibration, while the phase and quadrature amplitudes are considered nuisance parameters. Because of the optimal use of prior knowledge about the laser vibrometry signal, the frequencies can be determined with much greater precision and greater noise immunity than using Fourier- or time-frequency-based approaches. Furthermore, the statistical approach is known to have superior performance when the data extends over a small number of vibrational periods. We illustrate the method with data from a fiber-optic laser Doppler velocimeter. Our results show that while the choice of processing method for determining the instantaneous velocity is relatively unimportant, the Bayesian method exhibits superior performance in determining the vibrational frequency.
