Geoscience Reference
In-Depth Information
subjected to acoustic vibration. The frequency of the shifted beam is changed by an
amount proportional to the frequency of the acoustic wave,
f
bragg
. As a result, when
the beams cross, the fringe pattern will appear moving with the shift frequency.
Detected frequencies smaller than
f
bragg
will result in negative velocities (Fig.
5
).
LDA measurements are not exempt of error. The Doppler burst may be hidden
by noise associated to the instrumentation (electric noise due to poor insulation,
noise introduced by the photodetector, noise introduced by the laser generation). In
general, these sources of noise are uncorrelated and produce white noise.
Errors introduced by seeding and signal amplification include (1) signal spiking
or absent counts due to scarce seeding, (2) signal canceling due to excess seeding,
and (3) saturation and bias to small frequencies due to too many particles in the
measurement volume and high amplification. The latter two are not common as
they require a high concentration of seeding particles.
Poor beam focus due to lens aberration causes spatial gradients in the fringe
pattern (Fig.
6
), resulting in poor estimates of the frequency
f
. Errors due to
positioning are frequent, especially in 3D arrangements where the user is required
to match the measuring volumes of two different probes. Working in coincidence
mode, for which a passing particle must generate a burst recognizable by the
detectors associated to each of the three wavelengths, may drastically reduce the
frequency count if the measurement volumes are not perfectly aligned.
Since LDA velocity measurements are actually particle velocities, errors are
introduced, especially in turbulent flows, because particles do not follow the fluid
exactly. The equation that describes particle motion in a viscous fluid was derived
and solved by Crowe et al. (
1998
) and Hjemfelt and Mockros (
1996
). The leading
f
f
max
f
bragg
Fig. 5 Eliminating signal
ambiguity through frequency
shifting (Bragg cell principle)
f
min
u
min
u
max
u
Fig. 6 Crossing of laser beams.
Left
: correct crossing with parallel fringe pattern.
Right
: incorrect
crossing due to lens aberration (Fringe model from http://www.nat.vu.nl/environmentalphysics/
REAL%20Experiments/LDA%20exp/LDA.html)
