Light reflected from a moving object is subject to a change in frequency which depends on the object’s velocity (Doppler effect). From the frequency shift measured with an interferometer the vibrational motion of the probe is inferred.
If waves are emitted from an approaching (or moving away) source, successive wave crests reach the detector in smaller (larger) time intervals than they had been emitted. This phenomenon 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. The measured frequency shift Δfc of a laser with wavelength λc is for practical vibrometric applications to high accuracy proportional to the velocity v,
Δfc = 2 v/λc .
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 .
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) .
The variation in intensity is independent on whether the object is approaching or moving away from the vibrometer. This ambiguity is removed by heterodyning. When the frequency of the reference beam is shifted by a fixed amount fb , the interference of both beams for a non-moving probe results in a harmonic intensity variation with frequency fb . This carrier signal ∝ cos (2 π fb) is modulated by the motion ot the probe. Depending on the its direction of motion the frequency of the intensity is shifted towards larger or smaller frequencies.
The information on the motion of the object measured is obtained via demodulation from the intensities. After conversion into a digital signal, a performant signal processor determines displacement and velocity of the probe in real time. Demodulation (often also referred to as decoding) is done either for the velocity or the displacement.