FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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As the probed surface is not polished to a mirror like finish, the scattered
light shows the well known speckle phenomenon. It can also be shown that the
best signal-to-noise ratio is obtained when one speckle is detected (18) and
when the speckle size is of the order of the incident beam size, which can be
obtained by focusing on the surface with diffraction limited optics (19).
Then, if the beam diameter on the lens is noted a and if the focusing distance
between the lens and the surface is noted D, the solid angle of one speckle is
" (a/D) . Assuming isotropic scattering and neglecting the losses produced by
various optics, we then find that S » (a/2D) 2 . Taking IL = 5 mW, a = 4 mm,
D = 15 cm a detection limit of = 1.5 Â is found for a bandwidth of 10 MHz. A
detection limit of the order mentionned above has been observed with our
system on nearly isotropic scattering surfaces (18). This limit can be
lowered by using a higher laser power (the detection limit scale as l/^/T^),
or a closer working distance D (the detection limit scales as 1/D) (20, 21),
but closer focusing produces a smaller spot size and a shorter depth of
focus. These results are consistant, as shown below, with the antenna theorem
for heterodyne detection (22) which states that the étendue of the receiving
system (i.e. its light gathering efficiency, exactly the product of the viewed
area by the solid angle of the system aperture from the surface) is X at
most. The maximum received power is obtained for the minimum spot size on the
surface and is then equal, to II X /TT WQ , where WQ is the focal spot
radius. Since WQ - XD/a we retrieve equation 5.
Since the displacement Michelson interferometer probe produces a useful
detection limit only for sharp focusing and close working range, its
usefulness for industrial NDT applications is rather limited. However, it
should be noted that it does not require a single frequency laser and as far
as the path lengths in the interferometer are compensated, it can use a rather
broad band laser. It can be very useful for ultrasonic field mapping and
ultrasonic transducer characterization, since, in this case the signal being
repetitive, the signal-to-noise ratio can be greatly increased by simple
averaging. This probe measures most easily displacements normal to the
surface, but it can also be used when inclined to measure in-plane motion
(17).
In conclusion, this type of optical receiver which is rather simple to realize
has however a small étendue (its figure of merit) of the order of X . We will
see below that velocity probes can be made with a much larger étendue.
Ill THE DIFFERENTIAL DISPLACEMENT PROBE
(OR OPTICAL GRATING DISPLACEMENT PROBE):
As seen in fig. 3, this probe is made by having two beams issued from the same
laser and separated by an angle 26 focused at the same location on the surface
(18, 23). A grating is then produced on the surface and a part of the speckle
field scattered from the surface is viewed by a detector. The grating is
fixed when the frequency of the 2 beams is the same (homodyne probe) and
moving when it is heterodyne. If N speckles of mean intensity Isp are seen