Laser triangulation, according to its low cost and simple implementation, is nowadays the most widespread technology on the market. Its applications spans from the biomedical area, for example for monitoring the cardiovascular system, to industrial applications, where needed non-contact measure and the other sensors, like accelerometers, does not work, for example in hot environments.
The main advantages of laser triangulation sensors are:
- non-contact and non-invasive measurements;
- good resolution and accuracy (with a trade-off on working distance)
- can measure on small targets since spot size of laser beam is very small
The disadvantages of this technique are:
- the limited achievable range of working distance;
- the moderate frequency response, typically limited to below 1kHz
- it can be negatively affected by ambient light
- it is difficult to measure on irregular and mirror-like surfaces
From a basic point if view, a laser-triangulation system consists of a laser source with a lens that focalizes or collimates the laser beam on the target, and a CCD (or C-MOS) sensor or a PSD (Position Sensitive Detector), a second lens used to generate the laser spot image onto detector.
The idea behind this technique is very simple: the laser beam is aimed onto the target under test and the back-scattered light is focalised onto the PSD. The PSD is an optical position sensor that can measure the position of a light spot in one or two dimensions. By changing the target position, the laser spot imaged on the PSD moves.
The target position can be retrieved as:
The displacement or vibration measurements can be easily derived, by looking at the time-varying output signal from the sensor. When the distance changes by an amount s, also the position of the spot on PSD (or CCD) changes by x. The vibration/displacement can thus be obtained as:
For small displacements, last equation can be linearized and the displacement s and the position x on the PSD can be write respectively as:
s = s0 + ∆s (where s0 is the target position at rest)
x = x0 + ∆x (where x0 corresponds to the position at rest projected onto the PSD surface)
With ∆s << s0 and ∆x << x0 we have:
s0+ ∆s = DF/(x0+ ∆x)= (DF (x0- ∆x)) / (x0^2 - ∆x^2 )
Considering that ∆x << x0 the denominator term can be simplified obtaining:
s0+ ∆s ≈ DF/x0 - DF/ (x0^2 ∆x)
∆s= - DF/ x0^2 ∆x