FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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by the detector, the detected signal in the case of the heterodyne probe can
be written (the speckles add up incoherently) (18):
l D = sß Isp cos f 2irf ßt + (?i -t2).t(t) + * (t)] (3)
where fjj is the shifting frequency kj and k2 are the wavevectors of the 2
beams, (ki - k2>.ô = 4n sin 6 (sin a 6x + cos a 6z)/A, a being the angle
between k^ - k2 and the normal to the surface, ôx and Sz being respectively
the in-plane and out-of-plane displacements. As seen above, this expression
gives a carrier signal at fß and two sidebands, which enables easy
calibration. In-plane and out-of-plane displacements can be detected, but
this probe is particularly useful to detect displacements parallel to the
surface (in this case ki-&2 is perpendicular to the surface and a = TT/2).
When both sidebands are detected, it can be shown that the signal-to-noise
ratio is given by (it is indépendant of the number of speckles):
is/iN = (?i -k2).t \/n Isp/(2 B h v) (4)
Eq. 4 also shows that, in order to improve the signal-to-noise ratio,
ISpShould be maximized, which means that the speckle size should be of the
order of the detection aperture and consequently that this aperture should be
large enough to collect a large part of the scattered light. This means, in
turn, very sharp focusing. When typical numerical values are used, a
detection limit of the same order as the one found before is obtained.
Therefore, this probe has the same drawback as the one described in the
previous section. Furthermore, it tends to be more bulky since 0 cannot be
too small for a reasonable detection limit.
IV THE MICHELSON VELOCITY INTERFEROMETER
A typical setup is sketched in fig. 4. We will note the main difference
between this setup and the one of fig. 2: here the interferometer does not
make use of the surface as a mirror, but views the light scattered by it.
This type of system has been used in shock wave research (25) and has been
also considered for the detection of ultrasound (26). The detected intensity
for a given direction 6 of an incident ray is:
ID = Ai + A2 cos (2TT V/AV + $) (5)
where A, B and are constant, the free spectral range Av = 1/T =c/2Ad(8),
(T is the delay time, Ad(8) is the difference of arms lengths for the incident
ray inclined by 6. As sketched in the boxed diagram of fig. 4, which plots
the spectral response given by eq. 5, frequency discrimination is obtained
when the laser frequency (a single frequency laser source is necessary) is
tuned to a zero crossing 2ir v/Av + = +_ IT/2 + 2mir, m being an integer). The
surface being rough and irregular acts as an incoherent source, so the fringes
are only observed at infinity (24) or at the focus of a lens. It can be
readily shown that Ad(6) = Ad cos 6, where Ad is the path difference for the
ray perpendicular to the mirrors. The fringes are then concentric rings, and