MATERIALS CHARACTERIZATION USING RECONSTRUCTED
THERMOGRAPHIC DATA
S.M. Shepard, J.R. Lhota, B.A. Rubadeux, D. Wang, and T. Ahmed
Thermal Wave Imaging, Inc., 845 Livernois, Femdale, MI 48220 USA
ABSTRACT. Pulsed thermography has generally been used to identify, and in some cases, measure the
depth of subsurface defects. In general, quantitative analysis of pulsed thermographic data has required
the presence of a reference sample or region in the field of view, which is not practical for a majority of
real inspection situations. Recently, we have developed a new approach to processing pulsed
thermographic data, Thermographic Signal Reconstruction (TSR), which allows quantitative
characterization without the use of a reference region.
INTRODUCTION
In active thermography, the front surface of a solid sample is heated either
instantaneously or continuously while an IR camera monitors changes in the surface
temperature. Surface areas located directly above buried features that obstruct the flow of
heat into the sample will temporarily appear hotter than intact areas, which cool to
equilibrium more rapidly. Near surface flaws with large aspect ratios may be detected
using a simple heating apparatus (e.g. a hot-air gun or heat lamp) and visual observation of
the IR camera video display. However, instantaneous heating using optical flashlamps
(Fig. 1), commonly referred to as Pulsed Thermography (PT), has become the preferred
implementation for many NDE applications in the aerospace, power generation and
automotive industries, as it offers significantly better repeatability and sensitivity than
continuous heating approaches.
•defect
flashlamp
sample
FIGURE 1. Schematic of the pulsed thermography process. The sample surface is heated with a pulse of
electromagnetic radiation from a flashlamp. Heat from the surface diffuses into the sample, and is obstructed
by the presence of a subsurface defect. The accumulated heat energy at the defect causes a transient
nonuniformity in the infrared radiation from the sample surface, which is detected by the IR camera.
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/$20.00
1270
Analysis of PT data is performed on either a local or global scale. In local analysis
methods, which are simpler and more widely used, individual images taken from the
cooling time sequence are examined to find anomalous "hot spots" that are indicative of
subsurface defects [1]. Increased signal to noise performance is obtained by viewing a
"gate", which is the average of several consecutive frames (the amount of signal to noise
improvement is equal to the square root of the number of frames in the gate). Contrast
between defective regions and the intact background may be enhanced by subtraction of
later gates from earlier ones, or by viewing the time derivative each pixel in the gate.
Conventional image processing methods may also be used to further enhance image
contrast. However, there is a cost associated with the use of time gating for signal to noise
improvement. Heat deposited at the sample surface diffuses in both normal and lateral
directions (with respect to the sample surface). Although the normal diffusion component
allows interrogation of deeper features as time elapses, the lateral components give rise to
blurring of subsurface features in PT images that grows more severe as time elapses. Thus,
as more frames are added to the gate to improve S/N, these include later frames in the time
sequence, which have suffered the effects of diffusion blurring. Consequently, there is a
trade-off between signal to noise improvement and spatial resolution that must be
considered when applying local methods.
In global analysis methods, the time response of each pixel in the field of view is
considered over the entire duration of the heating event and subsequent cooling period.
The time evolution of the difference between the amplitude of a point on the sample and
that of a defect free reference point, usually referred to as a contrast curve, has been widely
used to quantitatively characterize dynamic response to pulsed heating. For every frame in
the data sequence, the amplitude of the reference point (or the mean amplitude of the
reference region) is subtracted from the amplitude of every pixel in the image. In principle,
points which lie over defect free areas will behave nearly identically to the reference and
yield flat contrast curves with near-zero amplitude, while points that lie over defect areas
will display contrast maxima that are correlated to feature depth. The peak, early time and
inflection point, integral and moment of the contrast curve have been investigated as a
means of defect characterization [2]. Defect depth maps may be created by generating a
contrast curve for every pixel in the image and identifying a characteristic (e.g. peak slope
time, peak contrast time) that can be correlated to subsurface depth. Contrast curve
methods are not widely implemented as they are relatively insensitive to small or deep
defects and their reproducibility is poor, due to the strong dependence on the position of the
reference point.
RECONSTRUCTION OF THERMOGRAPHIC IMAGE SEQUENCES
Recently, significant improvements in signal to noise performance as well as
sensitivity to smaller and deeper defects have been reported using a Thermographic Signal
Reconstruction (TSR) approach to global PT sequence analysis [3-4]. The method exploits
the well known observation that in a thick solid sample the surface temperature response to
instantaneous uniform heating is described by the 1-dimensional heat diffusion equation
f£-!^=o,
dz2 a dt
CD
with the solution
r= 2
1271
(2)
where Q is the input energy and e is the thermal effusivity (the square root of the product of
density, heat capacity and thermal conductivity).
The 1 -dimensional approximation
recognizes that heat diffuses in all directions, but assumes that the lateral diffusion
components more or less cancel in a defect free sample. However, in the presence of an
adiabatic subsurface boundary such as a void or a wall, the incident heat flow from the
sample surface is impeded, and the 1 -dimensional description no longer applies locally. In
effect, defect detection in pulsed thermography can be thought of as identification of areas
where the 1 -dimensional assumption breaks down. In principle, the separation between
normal (1 -dimensional) and anomalous cooling should be simple, and in fact, this is the
case for large or very near surface cases (the same type of cases that can be readily imaged
with an IR camera and heat gun excitation). However, as one attempts to detect smaller,
deeper defects, or detect the presence of walls, where no deeper reference area exists, the
effects of IR camera noise and instability, as well as the random structure (e.g. fibers,
porosity, granularity) found in many samples, significantly complicate and limit the ability
to discriminate between intact areas and boundaries.
Additional insight into the surface temperature response to pulsed heating is gained
by considering the time evolution of the surface temperature in the logarithmic domain [5]
(Fig. 2). In this case, the solution to the ideal 1 -dimensional heat flow behavior expressed
in Eq. 2 becomes
which is significant in several respects:
1. For a defect- free sample, Eq. 3 describes a straight line with slope = -0.5.
2. Time dependence has been separated from input energy and material properties.
3. The linear and fixed slope behaviors are invariant with respect to sample material,
input energy or IR camera calibration. Only the scale of the response will change
as these parameters vary.
4. The predictable slope and straight-line behavior allows identification of a defect
point without a reference point.
5. Both intact and defect points are "well-behaved", i.e. they do not undergo sudden
deviations from quasi-linear behavior.
In practice, logarithmic data may vary from ideal 1 -dimensional behavior for a
variety of reasons (e.g. nonlinear camera response, background radiation or convective
heating contributions). Nevertheless, the logarithmic behavior of the time evolution
exhibits remarkable consistency, in that pixels representing defect free areas are nearly
linear, and pixels corresponding to subsurface defects depart from the near-straight-line
behavior at a particular time that is correlated to the depth of the defect (this time is
essentially the peak slope time that is detected in time domain contrast curves). We can
approximate the logarithmic time dependence of a pixel by a function, or set of orthogonal
functions. In most cases, a polynomial (Eq. 4) provides an excellent fit to experimental
data.
ln(T(t)) - a0 + ailn(t) + a2[ln(t)]2 + a3[ln(t)]3 + a4[ln(t)]4
1272
(4)
17000
8.5
17000
16000
8.0
16000
7.5
15000 -
14000
14000 -
ln T
amplitude
15000
13000
13000 12000
7.0
6.5
12000 11000
6.0
1100010000
5.5
5.0
10000
9000
9000-10
90
190
290
90time (frame
190number)290
0
390
1
2
3
4
5
ln t
390
time (frame number)
FIGURE 2. Comparison of linear and logarithmic temperature time plots for a points on a steel flat bottom
FIGURE
2. In
Comparison
time plots
for a pointswith
on aan
steel
flat region.
bottom
hole
sample.
the linear of
plotlinear
(left)and
thelogarithmic
defect can temperature
only be identified
by comparison
intact
hole sample.
In the
linear
plotbehave
(left) the
defect can
only
be slope
identified
comparison
withuntil
an intact
region.
However,
the log
plots
(right)
as straight
lines
with
–0.5 by
(solid
black line)
a subsurface
However,
the log plots
as from
straight
lines
with slope -0.5 (solid black line) until a subsurface
defect
is encountered
and(right)
the plotbehave
deviates
linear
behavior.
defect is encountered and the plot deviates from linear behavior.
A low order expansion is applied intentionally in order to serve as low pass filter
A low order
appliedresponse,
intentionally
in order
to serve
as low passnoise
filter
that preserves
the expansion
essential is
thermal
while
rejecting
non-thermal
that
preserves
the
essential
thermal
response,
while
rejecting
non-thermal
noise
contributions. In the logarithmic domain, the inclusion of higher orders only replicates
contributions.
In the
logarithmic
thedata.
inclusion
orders only
replicates
noise
that appears
in the
later, low domain,
amplitude
Once of
thehigher
time evolution
of each
pixel
noise
that
appears
in
the
later,
low
amplitude
data.
Once
the
time
evolution
of
each
pixel
has been approximated by Eq. 4, or a similar function, we can reconstruct the original
has
been
approximated
by
Eq.
4,
or
a
similar
function,
we
can
reconstruct
the
original
data, since
data, since
T(t) = exp[a0 + a1ln(t) + a2[ln(t)]22+ a3[ln(t)]33+ a4[ln(t)]44]
(5)
T(t) - exp[a0 + ailn(t) + a2[ln(t)] + a3[ln(t)] + a4[ln(t)] ]
(5)
nd
The reconstructed time sequence in Eq. 5 is readily differentiable, so that 1stst, 2->nd
n or
The
reconstructed
time
sequence
in
Eq.
5
is
readily
differentiable,
so
that
1
,
2
~ or
higher order time derivative images can be created (Fig. 3). If the entire sequence of TSR
higher
order
time
derivative
images
can
be
created
(Fig.
3).
If
the
entire
sequence
of
TSR
images is to be stored, it is only necessary to save the polynomial coefficients, regardless of
images
is to
is only necessary
the polynomial
of
the
length
of be
thestored,
imageitsequence.
Images to
(orsave
derivative
images) coefficients,
representing regardless
any point in
the length
theduration
image sequence.
Images
derivative
images)using
representing
any point
time
duringofthe
of acquisition
are (or
created
on demand
Eq. 5 (creation
of in
a
timex during
the duration
acquisition
are created
on
demand using
Eq.
5on(creation
of a
320
240 image
from a 6thof
order
polynomial
requires
approximately
0.1
sec
a
700
MHz
320 x 240PC).
imageAs
from
6th order
requires
approximately
0.1 sec
on a 700
MHz
Pentium
a aresult,
thepolynomial
TSR method
provides
a significant
degree
of data
Pentium
PC).
As
a
result,
the
TSR
method
provides
a
significant
degree
of
data
compression. For example, a 500 frame, 320 x 240 pixel, 16-bit image sequence normally
compression.
For
example,
a
500
frame,
320
x
240
pixel,
16-bit
image
sequence
normally
occupies 78.8 MB or RAM, while the corresponding data set comprising the coefficients of
MB or RAM,
while
dataspace.
set comprising the coefficients of
aoccupies
6ththorder78.8
polynomial
requires
less the
thancorresponding
5 MB of storage
a 6 order polynomial requires less than 5 MB of storage space.
FIGURE 3. Raw (left) and TSR 1st stderivative (right) PT images of a steel plate at 550 msec after flash
FIGURE
3. sample
Raw (left)
TSR 1 derivative
images
of a steel
plate at0.125”
550 msec
flash
heating.
The
has and
3 horizontal
sets of flat(right)
bottomPT
holes
at depths
of 0.200”,
and after
0.050”,
from
heating.
The sample
has 3 horizontal
sets of
flat bottom
holes
at depths
of 0.200",contrast
0.125" and
top
to bottom,
respectively.
The derivative
image
has higher
signal
to background
and 0.050",
great from
top to bottom,
derivative
sensitivity
to therespectively.
deepest set ofThe
holes
(top). image has higher signal to background contrast and great
sensitivity to the deepest set of holes (top).
1273
COMPARISON OF CONVENTIONAL AND RECONSTRUCTED SEQUENCES
COMPARISON OF CONVENTIONAL AND RECONSTRUCTED SEQUENCES
Raw and reconstructed thermographic sequences were created for a 0.5" thick steel
Rawhole
and target,
reconstructed
thermographic
were created
a 0.5”
thick
steel
flat bottom
with sets
of 5 holes at sequences
depths of 0.050",
0.125"forand
0.200"
beneath
flat
bottom
hole
target,
with
sets
of
5
holes
at
depths
of
0.050”,
0.125”
and
0.200”
beneath
the sample surface. The diameter of the holes was 1", 0.75", 0.50", 0.25", 0.125". The
the sample
The diameter
of thewith
holes
was 1”, 0.75”,
The
front
surfacesurface.
of the sample
was coated
a washable
black0.50”,
poster0.25”,
paint 0.125”.
to enhance
IR
front surface of the sample was coated with a washable black poster paint to enhance IR
emissivity and light absorption. A commercial pulsed thermography system (EchoTherm®,

emissivity and light absorption. A commercial pulsed thermography system (EchoTherm ,
Thermal
Wave Imaging, Inc.) was used for flash excitation, data acquisition and
Thermal Wave Imaging, Inc.) was used for flash excitation, data acquisition and
reconstruction of the data sets. The system uses an IR camera with an InSb detector
reconstruction of the data sets. The system uses an IR camera with an InSb detector
operating at 60 Hz, and 2 linear xenon flashtubes, each driven by a 5 kJ power supply,
operating at 60 Hz, and 2 linear xenon flashtubes, each driven by a 5 kJ power supply,
yielding a flash pulse with a 2 msec duration. Digital data was acquired directly from the
yielding a flash pulse with a 2 msec duration. Digital data was acquired directly from the
IR camera immediately prior to flash heating, and continued for 3 seconds (180 frames).
IR camera immediately prior to flash heating, and continued for 3 seconds (180 frames).
Viewed
on a frame-by-frame basis, the raw and reconstructed images appear to be
Viewed on a frame-by-frame basis, the raw and reconstructed images appear to be
nearly
identical,
although there is less granular noise in a reconstructed image than in the
nearly identical, although there is less granular noise in a reconstructed image than in the
corresponding
raw
The effects
effects of
of the
the reconstruction
reconstruction process
process are
are somewhat
somewhatmore
more
corresponding raw image.
image. The
evident
as aa movie,
movie, as
as noise
noise in
in the
the original
original sequence
sequencevaries
variesinin
evident when
when the
the sequence
sequence is
is viewed
viewed as
time,
variations in
in the
the reconstructed
reconstructed image
image are
are extremely
extremely
time, while
while small
small pixel-to
pixel-to pixel
pixel spatial
spatial variations
stable
over
the
period
of
the
entire
sequence.
The
effect
of
the
reconstruction
process
on
stable over the period of the entire sequence. The effect of the reconstruction process on
temporal
noise
is
illustrated
in
Figure
4,
where
reconstructed
and
raw
data
sequences
on
temporal noise is illustrated in Figure 4, where reconstructed and raw data sequences on aa
single
The statistical
statistical correlation
correlation between
between the
the 22 180-frame
ISO-frame
single pixel
pixel are
are compared
compared directly.
directly. The
sequences
in the
the figure
figure shows
shows the
the significant
significant reduction
reductioninintemporal
temporal
sequences is
is 0.99942,
0.99942, and
and the
the inset
inset in
noise
over
a
50-frame
interval.
However,
it
is
also
instructive
to
consider
the
effect
that
noise over a 50-frame interval. However, it is also instructive to consider the effect that
TSR
has
on
spatial
noise
performance
as
a
function
of
time.
As
an
example,
we
consider
TSR has on spatial noise performance as a function of time. As an example, we consider
the
15 xx 15
15 pixel
pixel region
region surrounding
surrounding the
the single
single pixel
pixelconsidered
considered
the standard
standard deviation
deviation of
of aa 15
previously
(Fig.
4,
right).
In
the
raw
data,
the
standard
deviation
exhibits
considerable
previously (Fig. 4, right). In the raw data, the standard deviation exhibits considerable
frame-to-frame
However, the
the reconstructed
reconstructed data
data exhibits
exhibits very
very little
little frame-toframe-toframe-to-frame variation.
variation. However,
frame
first few
few frames
frames during
during and
and after
after flash
flash heating,
heating,when
whenthe
the
frame variation,
variation, except
except for
for the
the first
camera
is
driven
beyond
the
limits
of
its
calibration.
The
relative
stability
of
the
TSR
camera is driven beyond the limits of its calibration. The relative stability of the TSR
standard
to the
the raw
raw data
data suggests
suggests that
that temporal
temporal noise
noise has
has been
been
standard deviation
deviation compared
compared to
effectively
from the
the reconstructed
reconstructed sequence.
sequence.
effectively removed from
3000
25
25
450
2500
20
20
400
350
stdev
amplitude
2000
1500
300
50
1000
60 70
80 90 100
15
15
10 10
55 -
500
0
0
0
50
100
150
150
200
00
50
50
100
100
150
150
200
200
time(f(frame)
time
rame)
(frame)
time (f
rame)
FIGURE 4. Comparison of raw
FIGURE
raw and
and reconstructed
reconstructed sequences.
sequences. (Left)
(Left) The
Theraw
rawand
andreconstructed
reconstructed(gray
(grayline)
line)
time evolution
evolution curves for a single pixel over
time
over an
an intact
intact region
region have
have aa statistical
statisticalcorrelation
correlationofof 0.99942.
0.99942. The
The
inset shows
shows the
the detailed
detailed behavior
behavior over
inset
over aa 50
50 frame
frame interval.
interval. (Right)
(Right) The
Theraw
rawand
andTSR
TSRstandard
standarddeviation
deviationofofa a
15 xx 15
15 pixel
pixel region
region surrounding
15
surrounding the
the intact
intact point
point isis plotted
plotted as
as aa function
function ofoftime.
time. The
Thereconstructed
reconstructedcurve
curve
shows little
little frame-to-frame
frame-to-frame variation
shows
variation and
and isissignificantly
significantlylower
lowerthan
thanthe
theraw
rawcurve.
curve.
1274
STATISTICAL CONTRAST ANALYSIS
contrast
Contrast curves have been widely used for quantitative analysis of pulsed
thermographic data. A contrast curve is formed
formed by subtracting the time history of aa
designated reference pixel (or the mean of a group of reference pixels), corresponding
corresponding to
to aa
defect
from the time history of the pixel under consideration.
defect free
free region of the sample, from
Unlike the raw
raw time history,
history, which is monotonically decreasing, the contrast curve of a
defect
defect free
free point is (ideally) flat), while the contrast curve representing a defect has aa
distinct peak, indicating the time at which maximum defect-background contrast occurs.
Various investigations have used the peak contrast, peak contrast time, or the time at which
the ascending slope of the contrast curve is maximized to characterize subsurface defects.
In practice, implementation of contrast curve analysis methods is complicated by the fact
that results are highly dependent on the placement of the reference point, and
and the
the
dominance of noise as deeper or more subtle defects are encountered. Comparison of
of
raw and
and reconstructed data (Fig. 5) from
from the steel flat
flat bottom hole
contrast curves for raw
sample show that the overall behavior is identical, but the TSR contrast curve is almost
completely free of temporal noise.
As alternative
alternative to
to contrast
As
contrast analysis
analysis using
using aa reference
reference point,
point, the
the time
time evolution
evolution of
of the
the
standard deviation
deviation in
in aa region
region surrounding
surrounding the
may also
be studied.
standard
the defect
defect may
also be
studied. Best
Best results
results are
are
achieved when the sampling region is approximately the side of the
the defect under
under
consideration, but
but covering
covering only
only half
half the
consideration,
the defect
defect area,
area, so
so that
that the
the region
region contained
contained roughly
roughly
an equal
equal amount
amount of
of defective
an
defective and
and intact
intact pixels.
pixels. Comparison
Comparison of
of standard
standard deviations
deviations for
for raw
raw
and reconstructed
reconstructed data
data (Fig.
(Fig. 6,
left) show
show the
the frame-to-frame
frame-to-frame consistency
consistency of
and
6, left)
of the
the standard
standard
deviation, compared
compared to
to the
the raw
raw data,
data, although
although the
the amplitudes
amplitudes are
are nearly
nearly the
deviation,
the same.
same.
However, the
the standard
standard deviation
deviation of
background region
However,
of aa 25
25 xx 25
25 pixel
pixel background
region over
over aa defect
defect free
free are
are
is significantly
significantly reduced
result. This
is
reduced in
in the
the TSR
TSR result.
This apparent
apparent reduction
reduction in
in background
background spatial
spatial
noise, as
as aa consequence
consequence of
noise,
of temporal
temporal noise,
noise, yields
yields aa small
small increase
increase in
in detectability
detectability in
in the
the
TSR images.
images. Comparison
TSR
Comparison of
of conventional
conventional contrast
contrast and
and TSR
TSR standard
standard deviation
deviation data
data (Fig.
(Fig.
right) shows
nearly identical
66 right)
shows nearly
identical peak
peak behavior.
behavior. However,
However, the
the standard
standard deviation
deviation decays
decays
more slowly
slowly than
the raw
raw contrast,
defect retains
more
than the
contrast, since
since the
the area
area above
above the
the defect
retains heat
heat in
in aa
nonuniform distribution
distribution for
nonuniform
for some
some time
time after
after peak
peak contrast
contrast has
has occurred.
occurred.
450
400
350
300
250
200
150
100
50
0
0.75", 0.125"
0.50", 0.125"
0.50", 0.200"
0
100
200
200
time
time (frames)
(frames)
300
300
400
400
FIGURE 5.
bottom holes
holes in
FIGURE
5. Comparison
Comparison of
of raw
raw and
and TSR
TSR contrast
contrast for
for 33 flat
flat bottom
in aa steel
steel plate
plate sample.
sample. Behavior
Behavior of
of
the raw
raw and
and TSR
TSR curves
curves is
is nearly
nearly identical,
but temporal
temporal noise
the
identical, but
noise is
is significantly
significantly reduced
reduced in
in the
the TSR
TSR data.
data. The
The
deepest hole
hole exhibits
exhibits negative
negative contrast
deepest
contrast later
later in
in the
the sequence,
sequence, as
as aa consequence
consequence of
of placement
placement of
of the
the reference
reference
region.
region.
1275
500
150
0.75", 0.125"
125
stdev
100
0.75", 0.125"
400
300
0.50", 0.125"
75
200
50
100
0.50", 0.125"
25
0
reference
0
0
0
0
50
50
100
150
100
150
time
time (frames)
(frames)
200
200
250
250
50
100
150
200
250
-100
time (frames)
time
(frames)
FIGURE
for raw
raw and
and TSR
TSR (gray)
(gray) data,
data. (right)
(right) Comparison
Comparison
FIGURE6.6. (left)
(left) Comparison
Comparison of
of local
local standard
standard deviation
deviation for
of
time histories
histories for
for 0.50"
0.50” and
and 0.75"
0.75”diameter
diameterholes
holeslocated
located0.125"
0.125”
ofraw
rawcontrast
contrast and
and TSR
TSR standard
standard deviation
deviation time
beneath
to allow
allow comparison
comparison with
with the
the contrast
contrast data.
data.
beneaththe
the surface.
surface. Standard
Standard deviation
deviation has
has been
been scaled
scaled to
CONCLUSION
CONCLUSION
The
reduces the
the temporal
temporal noise
noise content
content of
of the
the
The reconstruction
reconstruction process
process significantly
significantly reduces
time
image sequence,
sequence, while
while providing
providing an
an
time response
response of
of each
each pixel
pixel in
in aa thermographic
thermographic image
excellent
representation
of
the
true
thermal
nature
of
the
data.
However,
the
reduction
excellent representation of the true thermal nature of the data. However, the reduction inin
temporal
in temporal
temporal noise,
noise, which
which isis essentially
essentially aa linear
linear
temporal noise
noise also
also yields
yields aa reduction
reduction in
combination
and aa snapshot
snapshot of
of the
the instantaneous
instantaneous temporal
temporal
combination of
of the
the focal
focal plane
plane nonuniformity
nonuniformity and
noise.
to characterize
characterize subsurface
subsurface defects
defects demonstrates
demonstrates
noise. The
The use
use of
of the
the standard
standard deviation
deviation to
the
performance of
of the
the reference
reference region.
region.
the spatial
spatial noise
noise reduction, particularly in the performance
Standard
those of
of the
the contrast
contrast curve,
curve, but
but no
no
Standard deviation
deviation peak
peak characteristics
characteristics are similar to those
arbitraryreference
reference region
region isis required.
required.
arbitrary
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