SAMPE Journal - May/June 2020 - 48

FEATURE / NONDESTRUCTIVE INSPECTION
py and in-plane (x-y) anisotropy can exist, altering
the rates at which heat flows through the blocking
and leakage surfaces, and increasing the minimum
detectable flaw size from what is required in a geometrically equivalent, isotropic material6. Additionally, defect size with relation to the clutter due
to the fabric must be considered, as variation presented by the clutter of the fabric can overshadow
any contrast presented by a small defect7.
Thermographic Signal Reconstruction
In many cases, qualitative detection of large aspect
ratio flaws that involve a significant thermal discontinuity (such as voids or trapped water) can be
performed by direct viewing of the infrared image
of the surface cooling response. However, in recent
years, considerable emphasis has been placed on
signal processing methods to enhance quantitative analysis and detection of smaller, more subtle
flaws8. The thermographic signal reconstruction
(TSR) technique is a popular processing approach
in composite NDT applications where high sensitivity or automation is required, and it has been
adapted to pulsed, step and modulated excitation9-11. The technique builds on the simplicity of
the behavior of the logarithmic temperature versus
time plot and amplifies anomalous deviations from
linearity.
The behavior of an ideal, infinitely thick solid
that has been uniformly and instantaneously heated at the surface, is fully described by one-dimensional thermal diffusion. The one-dimensional
thermal diffusion equation for surface temperature change relative to the pre-flash temperature
in a flaw-free, infinitely thick sample heated by an
instantaneous, uniform source is as follows.
[2]
The logarithmic temperature time response is
a straight line with slope (first derivative) -0.5 and
second derivative 0. The presence of a subsurface
discontinuity, whether spatially extended (such as
a wall or substrate) or constrained (such as a void,
delamination or inclusion), will result in deviation
from the straight-line temperature and constant
derivative behavior of the ideal case. The first and
second derivatives initially follow ideal one-dimensional behavior, with constant values of -0.5
and 0, respectively. However, as time evolves, the
presence of the adiabatic interface results in a deviation from one-dimensional behavior to a state
where diffusion is terminated, and the first derivative converges to 0. The solution for the surface
temperature change relative to the pre-flash tem-

SAMPE JOURNAL

perature in an adiabatic, flaw-free sample with
thickness, L, heated by an instantaneous, uniform
source is shown using Equation 312.

[3]
In TSR, the logarithmic temperature response
of each pixel is fit to a simple function (for example, a low order polynomial), using a least-squares
fit algorithm. The resulting equation is a replica
of the original data that is free of temporal noise,
enabling further processing without generation of
additional noise. The derivatives of the logarithmic
signal, calculated with respect to logarithmic time
are extremely useful for identifying and amplifying
deviations from normal thermal diffusion.
Self-Referenced Evaluation of Flaw Contrast
When viewing a flash thermography image sequence, spatially discrete subsurface defects appear as localized hot (or cold) regions, indicating
high (or low) thermal effusivity defects, with respect to the host sample material. Quantitative
evaluation of defect contrast requires that a reference "sound" area is defined, either globally, or for
each detected indication. Numerous schemes for
sound zone definition have been proposed and implemented, with the understanding that the choice
of sound zone can significantly affect the measured
contrast, complicating evaluation of system performance or comparison of results from different
samples, experiments or systems.
A Self-Referenced (SR) approach to contrast
measurement, introduced in 1999 by one of the
authors, eliminates the need for sound zone placement and treats all pixels in an equivalent manner to facilitate comparative analysis13. In this
approach, the an NxN pixel area surrounding the
center pixel is blurred by applying a mean filter K
times. The blurring kernel size is on the order of the
size of the defect or larger, and the number of iterations is sufficient to significantly reduce the amplitude of the feature. The SR Contrast (SRC) is the
difference between the unblurred center pixel and
the blurred kernel.

M AY/J U N E 2 0 2 0

[4]

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SAMPE Journal - May/June 2020

Table of Contents for the Digital Edition of SAMPE Journal - May/June 2020