Vibration Measurement Methods

If a wave is reflected by a moving object and detected by an instrument (as is the case with the LDV), the measured frequency shift of the wave can be described as:

f_D = 2· v/λ

where v is the object’s velocity and λ is the wavelength of the emitted wave. To be able to conversely determine the velocity of an object, the (Doppler) frequency shift has to be measured at a known wavelength. This is done in the LDV by using a laser interferometer.

The laser Doppler vibrometer works on the basis of optical interference, whereby essentially two coherent light beams, with their respective light intensities I₁ and I₂, are required to overlap. The total intensity of both beams is not just the sum of the single intensities, but is modulated according to the formula:

I_tot = I₁ + I₂ + 2 √(I₁ I₂) cos [2π(r₁ - r₂)/λ]

with a so-called “interference” term. This interference term relates to the path length difference between both beams. If this difference is an integer multiple of the light wavelength, the total intensity is four times a single intensity.

The image above shows how this physical law is exploited technically in the LDV.

The beam of a laser is split by a beam splitter (BS 1) into a reference beam and a measurement beam. After passing through a second beam splitter (BS 2), the measurement beam is focused onto the sample, which reflects it. This reflected beam is now deflected downwards by BS 2 (see figure), and is then merged with the reference beam onto the detector.

As the optical path of the reference beam is constant over time (r₂ = const.) (with the exception of negligible thermal effects on the interferometer), a movement of the sample (r₁ = r(t)) generates a light / dark pattern, typical of interferometry, on the detector. One complete light / dark cycle on the detector corresponds to an object displacement of exactly half of the wavelength of the light used. In the case of the helium neon laser often used for vibrometers, this corresponds to a displacement of 316 nm.

Changing the optical path length per unit of time manifests itself as the measurement beam’s Doppler frequency shift. In metrological terms, this means that the modulation frequency of the interferometer pattern determined is directly proportional to the velocity of the sample. As object movement away from the interferometer generates the same modulation pattern (and modulation frequencies) as object movement towards the interferometer, this set-up alone cannot unambiguously determine the direction the object is moving in. For this purpose, an acousto-optic modulator (Bragg cell) that typically shifts the light frequency by 40 MHz is placed in the reference beam (for comparison purposes, the laser light’s frequency is 4.74 · 10¹⁴ Hz). This generates a typical interference pattern modulation frequency of 40 MHz when the sample is at a standstill. If the object then moves towards the interferometer, this modulation frequency is increased, and if it moves away from the interferometer, the detector receives a frequency less than 40 MHz. This means that it is now possible to not only clearly detect the path length, but also the direction of movement too.

In principle, it is possible to directly measure displacements as well as velocities with the LDV. In this case, the Doppler frequency is not transformed into a voltage proportional to velocity; instead, the LDV counts the light / dark fringes on the detector. Using suitable interpolation techniques, Polytec’s vibrometers can thus attain a resolution of 2 nm, and with digital demodulation techniques this can even be extended as far down as the pm range. Displacement demodulation is better suited to low frequency measurements (in the sub Hz range), while velocity demodulation is better for higher frequencies, since the maximum amplitudes of harmonic vibrations can be expressed as follows:

v = 2π • f • s

As its frequency increases, a vibration generates a relatively high velocity at a very low displacement amplitude.