# Measurement Principle - Laser Vibrometry

Light reflected from a moving object is subject to a change in frequency proportional to the object’s velocity (Doppler effect). Measuring this frequency shift with an interferometer allows the precise determination of the vibrational motion of the object.

## Doppler Effect

If waves are emitted from an approaching (or receding) source, successive wave crests reach the detector in smaller (larger) time intervals than they had been emitted. This phenomenon is observed as a shift in frequency is known as Doppler effect. An acoustic example is the apparent change in tone pitch of a siren of an ambulance passing by a pedestrian. The measured frequency shift Δfc of a laser with wavelength λc is for practical vibration applications to high accuracy proportional to the velocity v,

Δfc = 2 v/λc

## Vibrometry

The detected frequency shift is used to derive the velocity v(t) of the surface from which the laser light is reflected, as well as the displacement d(t) and acceleration a(t). In the case of a harmonic vibration with frequency f and displacement d(t) = D sin(2π f t), the amplitudes of displacement, velocity, and acceleration related through

A = 2π f V = 4π² f² D .

## Interferometer

The changes in frequency are by means of a Mach-Zehnder-interferometer converted into a time-series in intensity, whose frequency domain is accessible to further electronic processing. Within the interferometer the laser beam is split into a reference beam and a measurement beam. The light reflected from the probe is brought to interference with the reference beam. The intensity recorded in a photodetector contains, apart from the intensities of the reference beam Ic, and the reflected light Iv, a contribution which depends on the difference in optical path Δz,

I(t) = Ic + Iv + 2 (Ic Iv)1/2 cos (2 π Δz(t)/λ) .