Laser Doppler vibrometers are used for non-contact vibration measurements of solid objects which move in a transparent surrounding media. Most often, the surrounding medium is ambient air, with a refractive index which is very close to unity. However, vibrometer measurements are not limited to object movements in air. With a little care it is possible to accurately measure the vibrations of submerged objects in water or any other transparent fluid.
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Vibrometry through Fluids
Vibrometry on submerged objects is not fundamentally different from vibrometry in air. In air, the object must be visible; in a fluid, the probing laser must also "see" the object and return enough light from the object to make an accurate measurement. In air, the index of refraction is close to one, the same as in a vacuum, and can be neglected. In a fluid, the index is much greater and must be taken into account by dividing the measured value by this factor. For example, a velocity measured from an object submerged in water has to be manually divided by n = 1.333, the refractive index of water.
The central optical element of a vibrometer is an interferometer with one arm utilizing the reflected light from the object being measured. By considering the working principle of such an interferometer, it becomes obvious that the refractive index of the medium surrounding the measured object must be considered.
Figure 1: Basic optical elements of a simple interferometer configured as a vibrometer.
The laser beam is split in two: the reference beam travels inside the vibrometer housing and is directed to the detector; the probe beam is directed to the measured object and retro-diffused light from the object is collected, collimated and aligned with the reference beam on the detector. The reference and probe beams interfere on the detector. The output signal from the detector depends on the optical path difference between the two beams.
If the optical path difference is an integer multiple of the laser wavelength then the two beams interfere constructively. If the path difference is exactly in-between these values, then the beams interfere destructively. Constructive interference results in high intensity on the photodetector, destructive interference in low intensity. Since the light reflecting from the object passes twice the distance to the object, a displacement that matches an optical path length of half the laser wavelength leads to a full wave of change and causes the interference to go from a maximum through a minimum to the next maximum.
The optical path length is defined as the physical distance traveled by the light multiplied by the refractive index of the medium. This is the important quantity and not the measured distance. This path length difference is a result of the fact that the wavelength of light in a medium is shorter than in a vacuum and can be calculated by dividing the vacuum wavelength by the index.
What happens when a measurement is made on an object that moves by the same fixed distance inside and outside of a fluid like water? For movement in air, the optical path difference is very close to the physical distance displaced (times two) as the refractive index of air is very close to unity. In water, the measured result will be about 33% greater, as the optical path difference is d times 1.33, the refractive index of water. The resulting measurement must be divided by the refractive index to obtain the physical displacement.
Two side remarks:
1. Only the medium in which object movement takes place has to be considered, as only the optical path length inside this medium changes. If an object is placed in a glass basin filled with water and the vibrometer is outside the basin in air, neither the index of air nor that of glass has to be considered, only the index of the water that surrounds the object and in which the optical path change actually takes place.
2. If only a thin film of a liquid is applied of the object surface (e.g. oil on a technical surface) no refractive index correction has to be applied. The reason is that the thin liquid film moves together with the surface and no optical path change in this medium takes place.
Example Measurement
To demonstrate the principles just discussed, an example measurement i taken (see Figure 2). A metal beam with two attached side pieces has been immersed in a basin so that the first side piece is under water while the other remains above the water level. The movement of the two side pieces is measured simultaneously by two fiber-optic vibrometers.
Prior to filling the tank with water and covering the lowest side piece, the output was checked to show that both interferometers measured the same signal. Next, the tank is filled with water so that the first side piece is immersed. The simultaneous measurement is then repeated. The vibrometer that measures the immersed piece shows a greater result, as expected. When dividing the values of the two simultaneously acquired results, we thereby find an estimate for the refractive index of the medium. In order to avoid structural resonances, we move the test piece sinusoidally at 1Hz. In this simple setup, an index of refraction for water was calculated at n = 1.329, which is in very good agreement with the published value for pure water of n = 1.333.
In conclusion, measuring an object immersed in a fluid that is optically transparent is simple and straight forward. The true physical displacement and velocity can be derived by dividing by the measured values by the refractive index of the surrounding fluid.
Figure 2: Experimental setup. Left, two OFV-5000 Vibrometer Controllers and Fiber-Optic Interferometers. Right: metal beam submerged in water.
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