Laser Doppler vibrometers (LDVs) measure vibrations in ways that other sensors can't. From large aircraft structures to microscopic MEMS sensors, and vacuum enclosures to red-hot mills, LDVs measure both vibrational velocity and displacement with linear response and 30-MHz bandwidth. Because they don't introduce any mass loading, they don't affect dynamics.

The Doppler effect

So how do LDVs work? Everyone has experienced the Doppler effect, when a moving vehicle's acoustical tone changes as it passes on the road. Well, the propagation of light is similarly affected by motion, and the same physical principles apply.

If light is reflected by a moving object and then captured, the measured frequency shift of the light is:

where v = Object's velocity and λ = Wavelength of the incident laser light.

To determine the velocity of an object, the frequency shift of the Doppler effect must be measured. This is done in LDVs with a laser interferometer.

Interferometry

Inferometers work by optical interference (overlapping) of two coherent light beams with intensities I₁ and I₂. The resulting intensity is not just the sum of the individual intensities, but is modulated with a so-called interference term relating to the path-length difference of the beams:

If the intensities are equal and the path-length difference is an integer, then overall intensity is four times a single intensity; overall intensity is zero if the two beams have a path length difference of half of one wavelength. In the former case, the two beams interfere constructively; in the latter, it is destructive interference.

The interferometer modulation frequency is directly proportional to object velocity. But because objects moving away from an interferometer generate the same interference pattern (and frequency shift) as objects approaching an interferometer, these alone cannot determine motion direction.

Vibration maxima - click for full image

Displacement as well

For that added functionality, an acousto-optic modulator (or Bragg cell) can be placed in the reference beam. Say the laser light frequency is 4.74 × 10¹⁴ Hz and a setup with a Bragg cell modulates fringe pattern frequency at 40 MHz when the object is at rest. If an object moves towards the interferometer, modulation frequency is reduced; movement away, and the detector collects a frequency higher than 40 MHz. In this way, it's possible to not only detect the amplitude of movement, but its direction as well.

Besides reporting velocity, LDVs can also measure displacement. Here, the Doppler frequency is not transformed into a voltage proportional to velocity. Instead, the LDV circuitry counts the bright/dark fringes on the detector. With interpolation programming, resolution can reach 2 nm, and with digital demodulation techniques, it can reach the picometer range. Note that displacement demodulation is better suited for low-frequency measurements, and velocity demodulation is better for higher frequencies, because the maximum amplitude of harmonic vibration is: