Part of this project deals with the option to acquire not only one point but
the full-received trace in order to extract more information and
finds solutions to the problem caused by the factor 1000 increase
in data flow.. (For more information about this see
signal processing article)
The received image can be analyzed in several ways,
either in Spatial Domain or in the frequency domain. By far the most common
way of analyzing is in the Spatial Domain.
Spatial domain analysis is the classical way of analyzing ultrasonic
C-scan images in the aerospace industry. An image is acquired
and a simple rejection criterion is established. If a reading
exceeds a certain level the pixel is "marked", if too
many (adjacent) markings are recorded the part is rejected. Generally
a 6 dB criterion is used because, under the assumption that a
delamination has an infinite attenuation, the current position would indicate the center of the transducer on a straight and infinitely long delamination.
An example of a 6 dB rejection analysis of a fatigue induced delamination in Glare
can be seen in the image below.
Image with a 6dB rejection criterion active
One of the problems, specially for Fibre Metal Laminates, is to find
a suitable reference from which the (6 dB) criterion is to be
established. Because small changes in stiffness or thickness can
make a enormous difference in the amount of interference, this
can create indications with an attenuation higher than 6dB without the material having any damage or change in quality. Because of the value of the rejected
laminates even low rejection rates are not acceptable.
Another problem with this method is that it can not
be used for subtle evaluation of material quality. Only "large"
defects that cause a sufficiently high attenuation can be detected.
This can exclude large collections of relatively small voids
that have a substantial impact on mechanical performance of the
examined laminate.
A way to avoid some of these problems is to statistically
evaluate the distribution of the attenuation over a certain area
of the image. This makes a more sensitive evaluation possible
without increasing the chance on false alerts. Two of the most
useful parameters of this so called histogram analysis are the average attenuation
and the standard deviation. The average attenuation indicates
the global effect caused by general stiffness or thickness changes.
The standard deviation is an indicator of the lack of homogeneity
in the material and is not sensitive to general effect such as
a global decrease in material stiffness or a slightly different
layer thickness. A disadvantage of this statistical analysis is it's
inability to detect localized problems or damage.
Changes in cure-cycle can cause a drastic change
in the spread of ultrasonic readings. This has been tested for
Fibre Metal Laminates as well as for thermoplastic composites (2) for which
more than 260 different cure-cycles have been evaluated. The figure
below show a small fraction of the results.
Consolidation Vs C-scan Standard deviation
It clearly indicates the
strong correlation between the standard deviation and cure-cycle.
Other research confirmed the effect of the cure-cycle on the mechanical
properties of the materials.
By using criteria for both average as well as standard
deviation the Probability Of Detection can be increased. An even better way can be
the combination of parameters (dimensions).
Both average as well as standard deviation correlate
strongly with the quality of the material. By combining the two
a higher degree of distinction can be made. By expanding
the number of independent variables this could be further increased.
Hyper-plane criteria can then be used to increase the chance
of detection for small defects or small global deterioration of
the material without increasing the number of false alarm situations.
Apart from the classical method of analyzing an
image directly it is also possible to analyze an image in the
frequency domain. To do this the image has to be transformed from
Spatial Domain into the Spatial Frequency Domain (SDF).
This process can be rather time-consuming specially
since the number of Fourier transforms increases dramatically
with the size of the image. The number of Fourier transforms for
an images size m x n is equal to m + n and because images are relatively
large the one dimensional transform lenghts are very large. The time for one trace is lineair with n2. This results in very long calculation times.To compensate for this problem a Fast Fourier Transform (FFT) algorithm is generally
used. This algorithm reduces the necessary calculation time to N.log(N).
The result of this calculation is an image of which
the 1st and 3rd and the 2nd
and 4th quadrant are identical. By swapping these quadrants
an image results where the 0-Hertz component, which is equal to
the average, is in the center of the image and the highest frequencies
are furthest away from the center. The scale is linear in terms
of spatial frequency i.e. twice the distance from the center is
twice the frequency. Frequency is expressed in terms of mm-1
instead of the more familiar sec-1.
Both the Spatial Domain images as well as its Spatial Frequency Domain spectrum are compared in the images at the right:
An example of this transformation is the following image of a honeycomb Nomex structure
inspected with a 5MHz probe. The spatial domain image is very noisy and it is very hard to recognize
individual cells or to measure cell size and orientation.
| 
C-scan Image of honeycomb structure
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In the Spatial Frequency Domain representation six dots can be observed.
These indicate the six repetitive directions of the honeycomb.
The distance of these dots from the center of the image indicate
the size of the honeycomb cells. The angle between the dots and
the vertical axis indicate the angle of the honeycomb with the
scanning direction. The above mentioned information can be used
to accurately evaluate the orientation of the core after cure with
the main load directions of the panel in a more accurate way than
could be achieved with the original (spatial) C-scan image.
| 
SFD Image of honeycomb structure
|
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An even more useful application of this analysis is the
determination of the ratio in which the unidirectional layers
of the laminate have been laid in a certain direction. This is
important because the unidirectional layers have an extreme degree
of anisotropy. Changing the ratio of layers per direction directly
changes the mechanical performance of the material as a function
of loading direction.
This analysis is performed by integrating the amount
of energy present in a certain angular section of the Spatial Frequency Domain spectrumand plotting this energy against the angle (see image on the bottom-right).
The relative height
of the peaks indicate the ratio of the fibre directions. This can be clearly observed
in the image below
Angle versus energy in SFD, peaks at 47 and 137 degrees (2:1)
| 
Glare 4 C-scan image
Glare 4 SFD image
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In the next section we will demonstrate methods to
use this information to process images for improved evaluation in the spatial
domain.
