FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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function is approximated by a Gaussian distribution then it is multiplied by the relative pressure
amplitude function to produce the expected frequency spectrum of a signal reflected from a void.
The expected frequency spectra so calculated have both amplitude and phase components making it
possible to obtain the real time signals and the magnitude frequency spectra expected. However, only
relative amplitudes of the time signals and magnitude spectra can be determined since the exact
pressure at the focus is not known. Shape comparisons between measured and calculated signals and
spectra are possible and are shown below.
III. EXPERIMENTS
Figure 1 shows the experimental set-up used. The commercial focussed immersion transducer has a
piezo-electric ceramic element and is labelled as 25 MHz resonant frequency. It has a 6.2 mm element
and a focal length of 25 mm in water making it a F/4 class. Signals reflected from the sample are
picked-up by the same transducer and routed to the amplifier and gating electronics; they are then
passed to an oscilloscope and a spectrum analyzer. First, the samples were scanned ultrasonically to
pinpoint the defects. Then the transducer was positioned and refocussed to yield the maximum signal
from the void on the oscilloscope and the trace was recorded photographically. A frequency spectrum
was made of the returned signals by means of a spectrum analyzer and this was also photographed;
however, noise from the gating electronics obscured the spectrum of signals from small bubbles
pointing to the need of improved gating circuitry, to improve the signal-to-noise ratio. Oscilloscope
trace photographs for select voids were enlarged and digitized on a graphics tablet so that they could
be Fourier transformed by computer to obtain frequency spectra without interfering noise. From
these spectra, frequency measurements could be made accurately. Figure 2 shows the typical signal
reflected from the flat surface of the samples and its corresponding frequency spectrum. The shape of
this spectrum was theoretically approximated by a Gaussian distribution with a centre frequency of
30 MHz and a full width at half maximum of 16 MHz (Figure 3) for use in the calculations.
IV. RESULTS
Figure 4 a-d is representative of the voids examined. Shown in (a) is a photograph of the void giving
the major pnd minor cross-sectional dimensions; in (b) the signal trace of the void from the
oscilloscope; in (c) a photograph of the spectrum analyzer trace, and in (d) a plot of the frequency
spectrum as calculated from the Fourier transform of the digitization of the oscilloscope trace. (Note
the absence of noise on this trace). The shape of the signals and spectra, changes with void
dimensions. In order to quantify these changes, the frequency at maximum amplitude and frequency
full width at half maximum (FWHM) were measured.
Figures 5 and 6, a and b are measured and calculated frequency spectra for void diameters of 49 urn
and 132 urn. The calculated spectra have been determined for a shock pulse and glass matrix
parameters ct = 5660 ms 1 and C|/cr = 1.67, which are average values for crown glass. Rather than
a one to one comparison of measured to calculated frequency spectra, repeated calculations have been
performed to generate plots of frequency at maximum amplitude versus void diameter (Figure 7a)
and frequency FWHM versus void diameter (Figure 7bl