FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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rod. After time and frequency measurements were taken, the transducer was
rotated about the x-axis to a different orientation and was Y-scanned to
optimize the signal.
THEORY
T .e geometrical theory of diffraction assumes that in addition to reflected,
refracted and incident rays, diffracted rays are produced when a ray hits an
edge [91. The incident ray produces an infinite number of diffracted rays,
traveling in directions determined by the law of diffraction. This law stateo
that each diffracted ray which lies in the same medium as the incident ray
makes the same angle with the edge as the incident ray. Furthermore, the incident
and diffracted rays lie on opposite sides of the plane normal to the
edge at the point of diffraction. However, the diffracted ray need not lie
in the same plane as the incident ray and the edge. Therefore the diffracted
rays form the surface of a cone with its vertex at the point of diffraction.
When a plane wave generated by a transducer is incident on a circular scatterer
at an angle, the only sound wavelets diffracted back into the transducer
originate from two opposite edges of the scatterer (Fig. 3). The wavelets are
coherent sources that interfere at the face of transducer. Because these
wavelets contain a broad range of frequencies, the condition of constructive
interference will always be satisfied by some frequencies. From geometrical
consideration, the frequencies of the wavelets that interfere constructively
at the center of the transducer may be expressed as [10]
f =
n
nv
dsine + [D + Dd sin 9 + ^ à r' - [D - Dd sin 6 + d ] 1 /? (1)
where n is an integer
v = velocity of sound in the medium
d = diameter of the circular scatterer
D = distance of the circular scatterer from the center of the
transducer
9 = orientation of the axis of the transducer with respect to the
axis of the circular rod.
In the far field, d«D, Eq. (1) reduces to
nv
f n = 2dsine
Let e = 8 + y
where ß is the orientation of the axis of the transducer with respect to
the vertical and can be measured and y is the orientation of the axis of
the circular scatterer with respect to the vertical and is an unknown.
Substituting Eq. (3) into Eq. (2) and rearranging terms
2 _n cos S
n
= d cos y tan 6 + à sin
(2)
(3)