1. Introduction
 Fibre Metal Laminate Fatigue Crack bridging 
Part of this project deals with the option to acquire not only one point but the fullreceived 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.
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 curecycle 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 curecycles have been evaluated. The figure
below show a small fraction of the results.
Consolidation Vs Cscan Standard deviation
It clearly indicates the
strong correlation between the standard deviation and curecycle.
Other research confirmed the effect of the curecycle 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.
Hyperplane 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.
This process can be rather timeconsuming 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 n^{2}. 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 1^{st} and 3^{rd} and the 2^{nd}
and 4^{th} quadrant are identical. By swapping these quadrants
an image results where the 0Hertz 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.  Cscan Image of honeycomb structure 
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) Cscan image. 
SFD Image of honeycomb structure 
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 bottomright).

Glare 4 Cscan image

In the next section we will demonstrate methods to
use this information to process images for improved evaluation in the spatial
domain.
There are many ways to process images but all
of them share the danger of discarding the information that was originally
sought. In this article only frequency domain filters will be discussed.
In a frequency domain filter an image is:
The frequency domain filters have been split into
two sections, each of which are subdivided into the two following subsections:
Because measurement equipment does not have ideal
properties, noise is introduced into the measurements. This can
consist of electronic noise due to external sources, imperfect
instruments or noise caused by inherent characteristics of the test equipment.
Some deviations linked to the transducer spot size (See deconvolution).
Some degree of correction for these effects can be achieved by filtering images in the frequency domain.
 Noise
Because of the limited spatial bandwidth of the transducer high frequency changes can be eliminated
To illustrate this effect the following example is given.
Assume an inspection system with a transducer with a spot size of 1 mm and
a measurement resolution of 0.1 mm. When this system takes a series of measurements at the highest resolution, this would still mean that even
if the transducer was moving onto an infinite attenuator only
a small (low frequency) change in amplitude would be registered. Because only a slightly larger section of the beam is attenuated or reflected.
Since electronic noise is not correlated with the material under investigation
and changes fast it is therefore now possible to correct for this noise
by applying a lowpass filter. This filter can be applied in
the Spatial Frequency Domain and has the form of a circle where the distance to the
center indicates the cutoff frequency.
This cutoff frequency has to be determined for every
transducer. If high levels of noise and large changes in amplitude
are present within the image, ringing may occur due to this filtering.
To counteract this problem windowing functions have to be applied
at the cutoff zone. The effect of applying a Hanning window is
illustrated in the figure below.
Left side: no windowing function Right side" Hanning window
The shape of the Hanning window function can be seen in the graph below.
The shape of the windowing function
For some curved object accurate evaluation can be severely hindered by the effect of angle of incidence of the ultrasound beam onto the material. Even if these effects are small they can significantly change the statistical evaluation parameters of the laminate.
To illustrate this effect the following example has
been selected.
A slightly curved Fibre Metal Laminates platewith fibre layers in 0 and
in 90 degree angles has been inspected. The curvature results in a low frequency
change of attenuation from left to right over the plate. If this low frequency component is removed in the Spatial Frequency Domain and the section is transformed back to Spatial Domain the effects
of the curvature are gone but the effect of the small fibre bundles
can still be observed. This is illustrated in the image below
where the filter has only been applied to the bottom section of
the image. The main fibre directions are still clearly visible
but the homogeneity indicator (standard deviation) has decreased with 40% to a level normal for this kind of material.
Curved FML panel
It may sometimes be necessary to remove significant
information because this information hides the effects under evaluation.
For the honeycomb this could mean that the six dots representing
the repetitive directions of the material in the Spatial Frequency Domain would be
removed. This would decrease the honeycomb noise effect inside the image
and deviations could be more clearly visible.
In case of the demonstrated Glare laminate the main
67% fibre direction could be removed to study the 33% directon
or both could be removed to enhance the contrast of the fatigue
damage against the background laminate.
To Eliminate of the dominant fibre direction the follwoing filter has been applied.
All the yellow parts have been set to zero in the SFD.
When this image section is transformed back to the spatial domain the following image results:
On the left side, the effect of the filter can be clearly observed
Rolf Diederichs 01. Jan 1997, info@ndt.net