Download Laser Vibrometer Measurements of Objects Immersed

Application Note VIB-G-04
FIELD OF
APPLICATION
A Aerospace
B Audio & Acoustics
C Automotive Development
D Data Storage
G General Vibrometry
M Microstructure Testing
P Production Testing
S Scientific & Medical
T Structural Testing
U Ultrasonics
Laser Vibrometer Measurements
of Objects Immersed in Transparent Fluids
Laser Doppler Vibrometers are used for non-contact vibration measurements of solid objects
which move in transparent surrounding media. Most often, the surrounding medium is the
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.
Vibrometry through Fluids
Vibrometry on submerged objects is fundamentally not 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.
The figure shows the basic optical elements of a
simple interferometer configured as a vibrometer.
The laser beam is split into two beams: 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.
Polytec GmbH
Laser Measurement
Systems
Application Note
VIB-G-04
Nov 2005
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 double passes 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 times 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 a movement in air, the optical path difference is very close to the physical distance displaced (times 2) as the refractive index of air is
very close to unity. In water, the measured
result will be about 33% bigger, 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 the 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.
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Technical specifications are subject to change without notice. LM_AN_VIB-G-04_2005_11_E
Example Measurement
To demonstrate
the principles just
discussed, an
example measurement was
taken (see photographs on the title
page and to the
right). A metal
beam with two
attached side
pieces has been
immersed in a
water basin such
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 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 such that the first side piece is immersed.
The simultaneous measurement is then repeated. The vibrometer that measures the immersed piece shows, as expected, a larger result. When dividing the values of the two simultaneously acquired results, we thereby find an
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estimate for the refractive index of the medium.
In order to avoid structural resonances, we
move the test piece sinusoidally at very low
frequency of 1Hz. In this simple setup, an index
of refraction for water was calculated as 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 index of the
surrounding fluid.
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