ASNT NDT Handbook Volume 3 Infrared and Thermal Testing

involved pulsing the transducer to and was mapped. Tile teeth ·were
generate an ultrasonic pulse tl1at traveled numbered for reference.
through the structure to an aluminum
reflection plate and then back through The vibrothermograms of the entire
the structure to the transducer, which also seal, with tooth 1 at the top and with .
acted as the receiver. The received signal is excitation frequencies of 13 and 27 kHz
then compared in amplitude to a preset and temperature scales of 0.5 and 1.0 K
level. If the received amplitude is above (O.S and 1,0 oc; 1 and 2 °F} uncorrect<:d
this level, tile pen is instructed to write.
All the ultrasonic C-scans included in this for nonideal emissivity t, respectively, are
study are based on a good ultrasonic shown in Figs. 38a and 38b. The hotter
transmission zone being printed as black temperatures arc farther to the right on
or dark gray and a poor region as white or the color scales at the bottom of the
light gray. figures. Notice that in fig. 38a the regions
on the right of tooth 1 and the middle
Results upper portion of tooth 8 are !lot regions,
indicated by arrowheads. ln Fig. 38h the
The thennograms presented view the regions on the right of tooth 1 and the
same side of the seal as shown in Fig. 35, middle upper part of tooth 8 are hot
with the teeth numbered regions, indicated by arrmvheads. In
counterclockwise. If the entire seal is in Fig. 38b the region of tooth 7 on the right
the figure, then the topmost tooth close to the body and at the corner tip is
numbered is the point of reference. The hearing (see arrowhead). All of these
damage to the seal was observed optically sighted regions are marked in J.'ig. 35 as
discontinuities. However, in Fig. 38a, the
central body, or ring, has seven regularly
spaced hot spots along a circumference

FIGURE 38. Vibrothermograms of gate rotor: (a) 13 kHz excitation frequency, 0.5 K (0.5 "C =
0.9 oF) x emissivity E (on scale from 0 to 1.0) per color; (b) 27kHz excitation frequency, 1.0 K
(1.0 'C ~ 1.8 'f) x £per color; (c) teeth 1 to 3, 13 kHz excitation frequency, 0.5 K (0.5 'C ~
0.9 'f) x c per color; (d) teeth 1 to 3, 19.0 kHz excitation frequency, 0.5 K(0.5 'C ~ 0.9 'f) x
E per color.

(a) (c)

(b) (d)

336 Infrared and Thermal Testing

line. These zones probably are due to the bevel intersection with the top surface at
entire seal's resonating and are not the right base of the tooth, indicating
indicated as anomalous in Fig. 35. damage. This region corresponds well
with the visual observations shown in
Figures 3Hc and ~8d are thermograms Fig. 35 and also the vibrothermograms in
of teeth 1 to 4 at excitation frequencies of Fig. 38. \,Vhen used on tooth 5, this
13.2 and 19.8 kHz, respectively, with a technique detects an anomalous region
about three fourths out the length of the
temperature scale of 5 K (5 oc = 9 °F), tooth; this region was not seen visually
but was detected by vibrothermography.
uncorrected for the emissivity. In Fig. ~Sc,
regions on the lower right of teeth 1 and Figure 40 shows an X-radiograph of
2 are actively heating (where indicated by teeth 9 and 8, oriented with the underside
arrowheads). These regions correspond to up. Details of damage in the radiograph
a delamination, as indicated by the oil are difficult to detect. Again the beveled
staining; they are also hot in Fig. 38d. edges interfere with an evaluation
Also, regions around intersection of the technique because the changing thickness
bevels of the teeth and the central body interferes with locating damage on the
are hot. This intersection apparently acts bevel. A zinc iodide solution was used as
as a stress raiser, forming a semicircular an X-ray opaque penetrant agent in
hot spot. Fig. 40. Tetrabromoethane and gold
chloride solutions were also used with
An ultrasonic C-sccm made by scanning similar results. Apparently, delaminations
the seal twice, each time at a different have closed, preventing penetrants from
trigger level, is shown in Fig. 39. The entering open discontinuities. Because the
region in white indicates the worst discontinuities were created in service by
transmission and the dark gray indicated a complex failure mechanism, opening
good transmission of ultrasonic energy. the cracks to the penetrant by applying
The C-scan is useful in evaluating only similar loads was not possible.
half the width of each tooth because of
the two 45 degree beveled edges on each Frequencies of the excitation that
side of the teeth. These beveled edges caused hot spots to appear were 10, 11,
refract and reflect the ultrasonic beam 12, 13, 15.6, 18, 25, 25.5, 26 and 27kHz.
away from the transducer. Because of this To acquire the frequency response of the
effect, some interpretation is needed to seal, an optical dynamic distance
gain useful information from this C-scan. measuring device was used to measure
The observer needs to locate the line dynamic normal displacement. The signal
formed by the bevel where it intersects generated by the sensor was processed by
the top surface. This can be located by
passing a line between the outer tip of the FIGURE 40. X-radiograph of teeth 7 to 10 of
bevel and the root of the radius where the
body of the rotor meets the tooth. On the gate rotor; bottom side is up; zinc iodide
inside of this line the C-scan will provide penetrant was used.
valid data. Considering the top tooth,
number 1, note the irregularity of the

FIGURE 39. Ultrasonic C-scan of gate rotor;

dark gray, light gray, and white indicate

good, poor, and bad ultrasonic transmission,
...
respectively.
-.•.

..

•""';" ftii:\< ~.

Techniques of Infrared Thermography 337

a fast fourier signal analyzer to gen·erate pattern of a structural resonance at
the response spectra at a number of points 13 kHz. In this thermogram, there are
on the seal.83 Two of these spectra are seven hot zones arranged
presented in Figs. 41 and 42. The first of circumferentially on the body of the rotor.
these spectra was taken on back of the Because of the regular spacing of these
edge of tooth 9 and the second spectra hot zones, a resonance must be suspected.
was taken at a similar location on tooth 4. In Fig. 42 the response spectra on tooth 4
Notice that there are peaks at 11, 13 and confirmed that the rotor was resonating at
18 kHz and a small peak at slightly Jess 13kHz.
than 10 kHz in Fig. 41. In Fig. 42, the
major peak is at 13.2 kHz, \vith a wide X·radiography was limited because
peak at 15.25 kHz. The upper limit of the penetrants had failed to enhance the
signal analyzer ·was 25.2 kHz; hence, damaged areas that either had closed or
nothing can be said about the higher were not open to the surface in the
frequency peaks. However, these spectra beginning. To radiograph the body and
indicate that thermal activity at lower the area around the bevels, two different
frequencies must be activated by radiographs with different exposures had
structural resonances. Figure 38 provides to be taken. Ultrasonic C·scans could not
visual evidence through the thermal detect damage on the beveled teeth edges
and so could interrogate only half of each
FIGURE 41. Frequency response spectrum of point on gate tooth.
rotor.
Response spectra taken from various
:2 points on the gate rotor show that
vibrothermal peaks occur at frequencies
c corresponding to a structural resonance.
However, hot zones not caused by damage
~ were easily indicated by the symmetry.
Additionally, thermographic technique
g0 obtains field information on the part
being interrogated so an area of the part is
:.ee 25 tested rather than a point, as ·with many
other techniques.
~

"-~

c

2"m'

0 20
10

Frequency (kHz)

FiGURE 42. Frequency response spectrum of second point on
gate rotor.

16

·cc
~

0

~

·.£"e 8

~

"·c~"

"m'

2

0 20
10

Frequency (kHz)

338 Infrared and Thermal Testing

PART 7. Thermoelastic Stress Analysis

Thermoelastic Coupling (19) pC-'JI ddTt -kV2T q

Despite numerical modeling of - a T0 dlJ
mechanical stresses in loaded structures,
experimental measurements are needed. --
Strain gages are widely recognized for
their unique properties: accuracy, dt
resolution and directivity. Because they
yield only localized measurements, the where p is density, Cp is specific heat, k is
thermoelastic effect is used for wider
spatial information. thermal conductivity, /1 is the sum of
principal stresses (first invariant of stress
Analogously to the adiabatic expansion tensor), a: is linear expansion coefficient
or compression of gases, a solid material, and T0 is the average temperature.
when submitted to tensile or compressive
stresses within the elastic range, Experimental Procedure
experiences reversible negative or positive
temperature changes (about 1 mK for The very small temperature variations of a
I MPa in mild steel). The theory of the sample under mechanical loading is
thermoelastic effect was introduced by measured with an infrared radiometer
VVeber84 and Kclvin85 and then extended (Fig. 43). Then a stress map (Fig. 44) is
by Biot86 and by Rocca and Bever,S7 calculated with an adequate model of the
within the framework of modern thermoelastic coupling.88 The
mechanical and thennodynamic theory. development of dedicated equipment
Thermoelastic coupling introduces a heat using noise rejection by the lockill
source term q into the heat diffusion technique has led to a wider diffusion of
equation: thermoelastic stress analysis.89-92 Progress
in infrared thermography devices,
fiGURE 43. Motor crank bar on fatigue especially in the acquisition hard\vare,
machine. permits use of standard infrared cameras
as well. To reach an adequate resolution
in terms of stress measurement; however,
noise rejection procedures are essential,
improving the thermal resolution from
some tens of mK to about 1 mK_93-97

These procedures integrate the
thermoelastic effect as long as the
mechanical loading is repeated, mostly
along harmonic cycles on a fatigue
machine, either synchronized or nol

FIGURE 44. Stress map of motor crank bar.

Techniques of Infrared Thermography 339

synchronized to the thermographic high loading frequencies or with poorly
equipment. conducting materials, it is much more
uncertain in most actual tests. In the case
Adiabatic Criterion of good conductors like metals, the heat
transfer attenuates the spatial temperature
Usually in thermoelastic stress analysis, gradients. J~igure 45 illustrates this
the hypothesis of adiabaticity is applied, smoothing effect for a hole in bar sample
neglecting the heat conduction within the under the same pure traction loading but
sample. In many real industrial tests, this at different excitation frequencies.
simplification fails because it is not
asserted by a relevant adiabatic criterion. 'JS Over the uniform stress region, at a
Under harmonic loading, the heat distance from the hole, the thermoelastic
diffusion equation becomes: temperature amplitude does not depend
on the excitation frequency because the
(20) - q(X,)') V2T(x,y) _ifi'_T(x,y) adiabatic hypothesis is always verified for
k u. uniform stress regions. On the other
hand, for the high contrast regions, on
rxToiro11(x,y) both sides of the hole, the thermoelastic
temperature amplitudes vary with
k excitation frequency.

where ro is tile angular frequency and Therefore, an adiabaticity criterion
a=- k·(pC })-1 the thermal diffusivity. linking the excitation frequency to the
spatial variations of the stress can he
If the beat conduction is negligible, the derived.
first term vanishes and the temperature
for a sample under harmonic loading,
distribution T(x,y) is proportional to the Eq. 20 can be written as:
stress distribution J1(x,y). If this is true at
(21) _!l

k

fiGURE 45. Thermoelastic maps of hole in bar at different where p is the so~called tltermal di(fusiou
excitation frequencies: (a) temperature calculated at
1000Hz, adiabatic conditions; (b) temperature calculated at length: -
20 Hz; (c) temperature calculated at 1 Hz. Temperatures are
differential and given in kelvin (K); 1.0 K = 1.0 'C = 1.8 'F. (22) fl 11n"f

(a)

The adiabaticity l1ypothesis supposes
the conduction fluxes to be neglected
with respect to the heating sources:

or
(b)

I I(24) lv2TI « k

Then:

lz; Iv~q(25) 112 «

and
(c)

(26) p «

Alternatively, the phase shift may also be
used as an adiabaticity criterion, because a
phase shift of -90 degrees is typically
observed under adiabatic conditions.

340 Infrared and Thermal Testing

High Emissivity Coatings FIGURE 46. Attenuation rate of thermoelastic signal across
paint layer.
\"'orking with low emissivity samples like
metals requires an increase in the infrared :t? 1.0 -- ~
emission with high emissivity coatings c
such as black paints. Unfortunately, these c"
coatings also insulate the samples from 0.8 \" ------ ----- ----- "-- "--
their environment. Consequently, the g
temperature at the coating surface differs :e '\
from the temperature at the sample ~ 0.6 \
coating interface (Fig. 46). This difference ' "\
depends not only on the coating 3 ' ' " "' ~
thickness but also on the excitation
frequency. The attenuation increases \Vith ~ "~
the coating thickness and the frequency
but is nearly zero for thin coatings .,c 0.4
(< 20 pm) in a large frequency domain
(< 100Hz). Thicker coating is of less .0
interest because it requires correction of ro
the signal (which is nevertheless possible). -~~-~
"c 0.2

~
0.0

0 20 40 60 80 100
(0.8) (1.6) (2.4) (3.1) (3.9)

Thickness, mm (in.)

legend

--=1Hz
---- =10Hz
-·-·---=30Hz
--=100Hz

Techniques of Infrared Thermography 341

PART 8. Thermomechanical Couplings in Solids

Thermomechanical coupling effects in Occurrence, Measurement
engineering materials and structural and Modeling of Damage
components have traditionally been
neglected in thermal stress analyses. The In fatigue1 for example, the term damage
temperature field and the deformation commonly describes
induced by thermal dilation and (1) crack initiation, fatigue lifetime and
mechanical loads were solved separately. the early microcracking stages of crack
growth and (2) fatigue damage associated
However, this effect could become ·with macroscopic fatigue crack extension.
significant when mass inertia is not
negligible because of the flux of heat Nevertheless1 the main question
generated tluough the boundary of the remains: \-\'hat is damage'! Several types
body or when the material is loaded have been identified without leading to a
beyond its stable reversible limit. The practical quantitative characterization:
relevance of coupled thermomechanical
analysis has been demonstrated for a 1. persistent slip bands characterized by
variety of problems, such as fault analysis extrusion shape and height; roughness
of nuclear reactors, damping of stress profile of extrusion; microcracks
wave propagation, deformation formed at interfaces between
localization after bifurcation and strength persistent slip bands and matrix; and
softening of material because of heat microcracks formed in valleys of
generated by repeated plastic surface roughness of persistent slip
deformations. Internal energy dissipation band surface profile;
has been recognized by a number of well
known :;;cientists.99-1°8 Carrying out 2. surface roughness originating from
random reversible slip within persistent
experiments on the cyclic twisting of slip bands and in planar slip materials
cylindrical bars, Dillon lOY identified the without persistent slip hands;
work done to the system by plastic
deformation as the major contribution to 3. fatigue damage in the form of slip step
the heat effect and proposed an internal formations at grain boundaries; and
dissipation rate :D related to plastic strain. grain boundary cracks at persistent slip
The thermal effect due to bands.
thermomechanical coupling at the tip of a
moving crack has been investigatedll0 Jvfany attempts have been made to
within the framework of measure loc.:al plastic strains within
thermodynamics, taking into account individual grains using the following.
stress and strain singularities. \.Yell
developed empirical theories of plastic 1. Thin mica flakes have been used as
deformation in metal have allowed reference gages to determine surface
engineers to predict the behavior of a displacements over 20 pm
variety of structures and machine (8 x JQ-4 ln.) gage lengths.
elements loaded beyond the elastic limit
for purposes of design. 2. X-ray line broadening studies and
stress analyses have been used to
This text emphasizes the application of characterize quantitatively the fatigue
infrared thermography to detect the induced lattice deformation and
macrostructural aspects of change in residual stress before crack
thennoplasticity,Ill that describe the initiation.
ocmrrence and the £'1'olution of damage in
engineering materials and structures 3. Small angle neutron scattering
under monotonous loading, in metallic measurements have yielded void
products subject to fatigue testing and in nucleation rates and individual void
geomaterials withstanding vibratory growth rates as functions of loading
excitations. parameters.

4. Oxide films have served as
quantitative sensors of metal fatigue.

5. Decrease in load at constant strain
amplitude has been chosen as a
damage parameter.

342 Infrared and Thermal Testing

6. Small surface cracks randomly introducing the concept of fracturing
distributed over unnotched smooth stress or fracturing strain. The elastic
surfaces often initiate, grow and plastic fracturing model combines the
coalesce and have been statistically elastic plastic Jaw and the elastic brittle
analyzed. law.I16 Taking into account the most
fundamental aspects of inelastic
7. The sliding-off process has been deformation and neglecting details at the
related to the crack tip opening microstructural level, Mrozl17 has
displacement.
developed phenomenological constitutive
8. A microhardness technique has been models that are widely applied in
used to determine the plastic zone's engineering applications.
dimensions, its form, its contour and
the distribution of plastic strain in it. Micromechanics

9. Plastic deformations have been The micromechanical approach aims to
measured by intcrferential contrast, provide a comprehensive understanding
interferometry and microhardness of the damage mechanism at the
techniques. macroscale. A random macrostructure is
generated by computation from the
A 1982 meeting that resulted in Special known behavior of microstructures, each
Technical Publication 811 of the American microstructure being characterized hy a
Society for Testing and lvfaterials finite number of parameters.IJR On the
concluded that fatigue damage can he basis of microscale and macroscale
defined as either (1) a chemical physical relationships, Dang-Van 119 proposed a
process whereby irreversible degradation multiaxial fatigue criterion with a realistic
of a specific property results from the physical interpretation of fatigue
application of cyclic stress and strain or phenomena. During a polycyclic fatigue
(2) a physical separation of the material test, the stress at the macroscopic scale
(cracks, cavitation ctc.).112 remains elastic. However, at the
microscopic scale, the metal is neither
More significant advances in isotropic nor homogeneous. It is
understanding fatigue damage must make constituted of randomly oriented crystals.
clear distinctions among: the physical This induces local fluctuations of the
damage, the process of damage and the microscopic stress and defines the
manifestation ofdamage. macroscopic stress. Thus the local
microscopic stress can locally exceed the
Continuum mechanics assumes that yield strength in certain unfavorably
the initiation and growth of microcracks oriented grains, whereas the macroscopic
and microcavities induce damage. stress remains elastic. If the cyclic plastic
Damage theories usually rely on assumed response of the grain to the solicitation is
discontinuous phenomena at the not clastic shakedown, some microcracks
microscopic scale. 1B Damage parameters, will appear. These microcracks coalesce to
considered as internal variables, ·are form a crack of detectable size.
introduced according to the following Papadopoulos12o and Deperrois121 have
main approaches. recently extended this formulation for a
better fit with experimental results.
Effective Stress
The present discussion proposes
To develop the concept of an effective differential infrared thermography to
stress, Kachanov 114 introduced a quantitatively evaluate the evolution of
continuous variable D related to the scalar temperature generated by the specimen
density of discontinuities. The elastic under applied reversed stresses. Infrared
body is assumed to contain many cracks. thermography has been succe~sfully used
The empty phase comprising the cracks as an experimental technique to detect
has zero volume fraction. It has been the plastic deformation of a steel plate
thought that the stiffness reduction under monotonic Joading110 or as a
produced by the cracks is due to the stress laboratory technique for investigating
singularities at the crack tips. As a result damage, fatigue and failure mechanisms
of this, the stress energy for the prescribed occurring in engineering materials.IZZ-127
surface fractions is increased by a finite
amount relative to the stress energy of a Plastic deformation is not homogeneous
crack free body. Thus the cracks increase and the stress acting on a plastic
the compliances and decrease the heterogeneity embedded in an elastic
stiffnesses. This has been the starting surrounding is a funliion of its plastic
point of damage theories developed for strain, diminishing with increasing strain.
analyzing creep, fatigue in metals and the llecm.1se of the thermomechanical
interaction of creep and fatiguc. 115 coupling, the generated plastic dissipation
is readily detect<..d by infrared
Plasticity Formalism thermography.

The approach of plasticity formalism
describes the inelastic behavior of
progressively fracturing solids by

Techniques of Infrared Thermography 343

Thermomechanical ±(31) E ~ (vxrLix-l)
Couplings in Solids
The superposed dot indicates the material
The development of the time derivative. The continuity equation
thermoelastic-plasticity equations requires and the balance of angular momentum
three types of basic are implicitly satisfied in the fundamental
assumptions.99, Jos, Io9, t2H·J :w equations.

The basic thermomechanical quantities The constitutive assumptions
describing thermodynamic processes with describing the material response and
time: body force b per unit mass, elastic ensuring the compatibility of the
strain tensor P', inelastic strain tensor E1, constitutive equations with the
heat flux vector q per unit area, heat fundamental equations of mechanics.
supply r, the second Piela-Kirchhoff stress
tensorS, specific entropy s, absolute The basic constitutive kinematic
temperature T, motion x, a set a 1 of assumption regards the additive
internal state variables characterizing the decomposition of the total strain tensor
material, the mass density p and the into elastic and plastic parts:
Helmholtz free energy'¥· All these
quantities are functions of the reference (32) E ~ E' + E1 + p(T- 1!,)
position vector X and of time t.
where pis the coefficient of the thermal
The fundamental equations of
mechanics postulating for the balance expansion matrix and TH the reference
laws of linear momentum, angular temperature.
momentum, mass and energy, as well as
the second law of thermodynamics The requirement of the second law of
expressed in the above variables. thermodynamics has three consequences.

The balance oflinear momentum is 1. The response functions S~ 'V and s are
described by the following fundamental independent of the temperature
equation: gradient VT.

where V' is the gradient operator, FT is the 2. Response function 'V determines both
the stress tensor and the specific
transposed transformation gradient and X entropy throu_gh Eqs. 33 and 34.
is acceleration. The conservation of
3. The values w, E1 and q obey the general
angular momentum is expressed by the
symmetry of the stress tensor. inequality expressed in Eq. 35.

The balance ofe11e1g)' is described by the (33) s ihj!
follo-wing fundamental equation: p JE'

(28) pe P(o/ + sT +d) (34) s

S:E - 'V·q + pr

where the inner product of two tensors is (s -(35) p J1J1 ) : £'
expressed by the following: JE'

(29) S:E 3 The above thermodynamic restrictions

L,s;; E·;; may now be applied to the equation of
energy conservation, yielding:
i,j=l

The balance laws are assumed not to p((36) EC Jo£1J11 - T~)·E1
change from those in thermoelasticity. JTJ£1 .
The second Jaw of thermodynamics
expresses the entropy production T~oT:E'- o02T1'Jif
inequality:

- pT + S·"T
·P

S:£1 - divq + pr

where p (kg-m-:~) is the mass unit in the where EC is a place holder expressing the
identity of values in Eq. 36, where Eq. 37
reference configuration, e is the specific defines response function 'V and where

internal energy and Eis the

Green-Lagrange strain tensor:

344 Infrared and Thermal Testing

Eq. 38 expresses the fourier heat from external heating (sometimes referred
conduction Jaw: to as passive heating) where local
differences in thermal conductivity cause
(37) ljl ~ variations on isothermal patterns, or from
internally generated heat referred to as
- C . T i n ( J1.R: . . - 1 ) active heating. 135
I
Thermal Conduction
(38) q ~ - K gradT
The second term on the right hand side of
\-\'hen restricting the analysis to the thermomechanical equation governs
perfectly viscoelastiC plastic material, this the transference of heat by thermal
leads to the follo·wing coupled conduction in which the heat passes
thennomechanical equation: through the material leading to a uniform
specimen temperature. The second~order
(39) pC,.T pr + div(KgractT) tensorial nature of the thermal
conductivity k may sometimes be used for
- (P:D:E'') T +S:E1 the detection of anisotropy of heavily
loaded materials.
where ~ denotes the coefficient of the
thermal expansion matrix, Cv0·kg-1·K-I) is The variances in thermal conductivity
specific heat at constant deformation, Dis may arise because of local heterogeneities
the fourth~order elastic stiffness tensor, e or discontinuities in the material. 136
is specific internal energy and k is thermal \•Vhere an unsteady state exists, the
conductivity (\-\'·nrl.K-1). thermal behavior is governed not only by
its thermal conductivity but also by its
The volumetric heat capacity C = p C\. heat capacity. The ratio of these two
of the material is the energy required to properties is termed thermal diffusivity a.
raise the teniperature of unit volume by 1 = k·C-1 (m2·s-1), which becomes the
K (I "C ~ 1.8 "F). governing parameter in such a state. A
high value of the thermal diffusivity
\Vhen using internal state variables implies a capability for rapid and
that describe structural changes of considerable changes in temperature. It is
material, the right hand side member will important to bear in mind that two
be completed by others terms materials may have very dissimilar
representing cross coupling effects.131 thermal conductivities but, at the same
These effects influence the evolution of time, they may have very similar
temperature through the second order diffusivities. A pulsed heat flux has been
terms when compared ·with the internal used to characterize a delamination
dissipation term. Their contribution to within a composite by the break caused in
internal heating during the adiabatic the temperature time history. 137
process is small. These terms arc
sometimes neglected. Thermoelasticity

This coupled thennomechanical The third term illustrates the
equation suggests the potential thermoelastic coupling effect. Within the
applications of the infrared scanning elastic range and vvhen subjected to
technique in diverse engineering tensile or compressive stresses, a material
domains: detection of fluid leakage,132 experiences a reversible conversion
nondestructive testing using thermal between mechanical and thermal energy
conduction phenomena, elastic stress causing temperature change. Provided
measurements and localization of adiabatic conditions are maintained the
dissipative phenomena. 133 Thus the relationship between the change in the
detected temperature change, resulting sum of principal stresses and the
from four quite different phenomena, corresponding change in temperature is
must be correctly discriminated by linear and independent of loading
particular test conditions and/or specific frequency. It is the reversible portion of
data reduction. This is the principal the mechanical energy generated. This
difficulty when interpreting the thermal thermoelastic coupling term may be
images obtained from experiments under significant in cases of isotropic loading. A
the usual conditions. stress analysis technique known as .stress
pattern analysis by thermal emissions
Heat Sources {SPATE) measures the temperature due to
the thermoelastic heating and cooling of a
The first term is related to the existence of body under cyclic loading. DR
sources or sinks of heat in the scanning
field. J:H Surface heat patterns displayed on Intrinsic Dissipation
the scanned specimen may result either
The last term defines the energy
dissipation, generated by plasticity and/or

Techniques of Infrared Thermography 345

viscosity. UY Internal energy dissipation changes in thermal emission caused hy
has been recognized by many scientists. 140 small and slow crack tip advances.
The work done to the system by plastic
deformation is identified as the major Experimental evidence shows that only
contribution to he_at effect. In part of the input plastic deformation
thermoelastic plasticity, there exists a power cr;/tP;i is expended to the change of
general acceptance that not all the material's microstructurei the other
mechanical work produced by the plastic part is dissipated in the form of heat
deformation can be converted to the (Table 1).
thermal energy in the solid. A significant
portion of the work is believed to have In materials testing under industrial
been spent in the change of material environment, thermal noise often
microscopic structure. The work done in generated by gripping systems may
plastic deformation per unit volume can sometimes obscure the intrinsic
be evaluated by integrating the material dissipation of the tested specimen. 143 This
stress~strain curve. This internal difficulty can be overcome using thermal
dissipation term constitutes an important image subtraction or differential
part of the nonlinear coupled thermugmplly as shown for instance in
thermomechanical analysis. Hg. 47 in the case of a direct hardening,
nonalloy steel specimen (French AFNOR
The quantification of this intrinsic A35-552 grade XCSS, corresponding to
dissipation for engineering materials is an ASTM A576-I055) 144 subject to rotating
extremely difficult task if infrared bending fatigue testing. This procedure of
thermography is not used.141 thermal image processing provides the
fatigue limit of steel materials within a
Infrared thermography is mainly few hours instead of the several months
concerned with differences in temperature required when using the standard
(or thermal gradients) that exist in the staircase technique.
material rather than with the absolute
values of temperature. It conveniently Closing
detects the dissipation regime of the
material under loading. This text has demonstrated that material
dissipativity can be considered and used
Ignoring the significance of the as a highly sensitive and accurate
coupled thermomechanical equation, an manifestation of damage, owing to the
unsuccessful attempt has been made by thermomechanical couplings.
Leaity and Smith142 to monitor thermal
emissions during fatigue crack Infrared thermography provides a
propagation tests. The technique used was nondestructive, real time and noncontact
unable to quantitatively detect the

TABLE 1. Thermomechanical coupling models reported in literature.

Reference Postulates and Stored Energy Internal Energy Heat to
Internal Variable (IV) at Microlevel Dissipation Rate ~ Plasticity
0
Dillon, 1963109 IV E~ responsible for T' 0 G;j£·p,1= G~' f;'; 0
IV E~ plastic power Tx·(ilA)/(ilX)
lee, 1969100 IV=- w; tS(1- y)a,1 ,(0.9<y<l.O) y Gq E~
T(iJn)·(ilT)- 1
Nied and r. = dislocation energy; A cr;; EfJ where A = (stored (1 - A}cr;; ff;
Battermann, . ·P energy) + (expended T(iln)·(iJT)- 1
1972101 XW:::: G)j €ij inelastic energy) =0
0
Raniecki and IV= work hardening K; X(K,T)i>
Sawczuk, 1975102 w =integrating factor;
CJ;; €· P; j - II ·•
Mroz and Raniecki, k = w (a;;,1) a,1tf;
1976103 K
IV= work hardening K; K = crqt-~

Lehmann, 1979104 IV=- K;

~ =experimental constant;
K = (1-S) o,1 £~

" = dissipation rate y =variable factor of A =- function of T; O.f = deviator stress
dissipation measure of ratio of
IV = internal variable stored energy to X = dislocation energy
T =temperature s' = work hardening plastic energy (0 =- integrating factor
··p = experimental constant
€ ij =deviator plastic strain Gij = stress
n =conjugate of IV
rate

346 Infrared and Thermal Testing

FIGURE 47. Intrinsic dissipation due to 3000 technique to observe the physical
load cycles of rotating bending fatigue processes of degradation and to detect the
testing at 380MPa (5.5 x 104 lbrin.-2): occurrence of intrinsic dissipat~on in
(a) thermal image at reference time tref·; engineering materials and structures.
(b) thermal image at time !3000 after 3000
load cycles; (c) heat change between trel It highlights the advantages of infrared
and tJooo obtained by heat image thermography, used for the detection and
subtraction of image in Fig. 47b from image the discrimination of diverse physical
in Fig. 47a. (resting conditions are assumed phenomena involved in these nonlinear
stationary between trel an'd t3000; coupled thermomechanical effects within
temperature values are given in degree the framework of a consistent theoretical
celsius.) background.

(a)

(b)

(c)

Techniques of Infrared Thermography 347

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Techniques of Infrared Thermography 357



CHAPTER

Data Processing and
Modeling for Infrared and

Thermal Testing

Xavier P.V. Maldague, University Laval, Quebec,
Quebec, Canada (Parts 2 and 4)
Abdelhakim Bendada, Industrial Materials Institute,
National Research Council of Canada, Boucherville,
Province of Quebec, Canada (Part 3)
Mario Bertolotti, National Institute for the Physics of
Matter (INFM) and the University of Rome, Rome, Italy
(Part 5)
Grigore L. Liakhou, National Institute for the Physics of
Matter (INFM), Rome, Italy, and the Technical
University of Moldavia, Kishinau, Moldavia (Part 5)
Roberto Li Voti, National Institute for the Physics of
Matter (INFM) and the University of Rome, Rome, Italy
(Part 5)
Stefano Paoloni, National Institute for the Physics of
Matter (INFM) and the University of Rome, Rome, Italy
(Part 5)
Yuri A. Plotnikov, General Electric Research &
Development, Niskayuna, New York (Part 1)
Concita Sibilia, National Institute for the Physics of
Matter (INFM) and the University of Rome, Rome, Italy
(Part 5)

Portions of Parts 2 and Part 4 adapted from Nondestructiw Emluation o{A-faterials by Infrared Thermography.
©Copyright 1993, Springer-Verlag, London, United Kingdom. Reprinted with permission.

PART 1 • Signal Acqu.d~ition and Processing

The overview of system setups for Memory/Computer Industry Association
thermographic nondestructive testing is (PC'tvfCIA) card that can store from 50 to
given elsewhere. This chapter desrribes 300 images ·with 12~bit resolution.
thermal data processing in general.
Systems for thermal data collection and
Data Acquisition System analysis have become simpler and more
accurate since their appearance in the
A block diagram of a typical setup for early 1980s. The common components in
thermal data collection and processing is the past, such as a liquid nitrogen
presented in Fig. 1. An active container, frame grabher for real time
thermographic system with external digitization of a video signal and photo
thermal stimulation and a single side camera for screen photography, are nnw
access to the evaluated component is rarely in use. Significant advances were
shown. If a discontinuity causes made during in the 1990s in both infrared
temperature variations on the observed technology (sensors and instrumentation)
surface - variations strong enough to be and computers. As a result, digital image
resolved by the thermal imager - analysis coupled with the quantitative
advanced image processing techniques approach is preferred in thermographic
can be applied to t11e thermal response to nondestructive testing.
obtain additional information about the
discontinuity. The components typically used in a
thermal evaluation system are the
A tvw-sided test system has the same specimen holder, thermal stimulation
hardware componentsi however, the source, thermal imager, video monitor,
thermal excitation and observation occur video tape recorder and processing unit
on opposite sides of the workpiece- an (computer and peripherals).
arrangement called the transmission
mode. A data acquisition system for Specimen Holder
passive thermal testing has similar
components yet without the external For the part to be evaluated, the holder
thermal excitation of the evaluated part. A provides a position convenient for the
system for passive thermal testing can be heat absorption and thermal response
as simple as a hand carried infrared acquisition. In some cases it may include
camera equipped with a power supply the thermal stimulation supply. For
block and an image storage device. The instance, systems for turbine blade
storage device can be a floppy disk drive classification ·with heating and cooling
or a Personal Computer cycle stimulation use the built~in water
(or air) hose connections. 1·3 Switching the
control valves generates in the blade the
thermal flow required for testing.

FIGURE 1. Block diagram of typical thermal data acquisition system.

Subsurface TI1ermal
flaw stimulation

Video Computer
output Data storage

Digital output

Specimen
holder

360 Infrared and Thermal Testing

In many cases the specimen holder is is needed when advanced image
designed to make possible the scanning of processing is performed on the thermal
the tested componrnt. If the test is a part images to avoid signal degradation caused
of a production flow, the holder has to by multiple digital-to-analog and
provide automated capture and motion of analog-to-d_igital conversions.
the tested part in front of the stationary
heater and thermal imager. Video Monitor

Thermal Stimulation Source The video monitor (often incorporated as
an integral part of the camera in the form
A choice of a thermal stimulation source of a visor or liquid crystal display) helps
depends on parameters of the tested to adjust the camera position relative to
component (thermal diffusivity and the target and provides real time thermal
thickness), test flow {stationary or imaging. It is also necessary for the
moving, one-sided or two-sided access) manual adjustment of the focus of the
and expected discontinuity parameters camera's optical system.
(size, depth, thermal resistance and
position in relation to the surface). An During the infrared survey ·with a hand
important requirement for the thermal carried unit the viewing of thermal
stimulation source is the ability to images in real time is important to locate
produce uniformly distributed heat flow an abnormal component. The thermal
of a required duration with high imager converts the illuminated infrared
repeatability. 1•2 Noncontact thermal signal to a video format output for
stimulations (quartz lamps, flash lamps, viewing the observing area. Looking at
lasers, air jets and others) are used to the video monitor, an operator can pick
exploit the advantages of remote out a suspicious part from a wide range of
nondestructive testing. objects.

The majority of known systems use Video Tape Recorder
heat to produce the necessary thermal
contrast on the observed surface above an Even though the modern thermographic
abnormality. Hmvever, cooling is also test stations are oriented toward
applied for this purpose when it is processing of the thermal signal in the
inconvenient or uneconomical to add digital form, analog recording of the
extra heat to the evaluated component.I.2 signal in a video format for later analysis
is still useful. At present, tape recording is
Mobile configuration with continuous used mostly for surveillance, ·when it is
line heating (for testing of a large area) required to record hundreds of images at
and static configuration ,..,,ith flash area different locations before they have to be
heating, such as the box car structure, 1·2 processed (such as for electrical line and
(for area-by-area testing) are among the buried pipeline surveillance and building
most attractive for thermography. 1'2 To inspection). After the end of the
detect the discontinuities located acquisition routine the recorded images
perpendicular to the surface, the line can be viewed with a video monitor in
pulsed heating in static configuration is different modes {playback, pause, slow
applied. 4 ln this case the locally generated speed or fast speed) or digitized and
heat flow crosses the discontinuity transferred to a computer for advanced
causing the noticeable thermal gradient processing.
above the discontinuity.
\'\7ith an inexpensive video recorder,
Thermal Imager signals must be recorded with caution
because the video format and equipment
Most systems for thermographic limit the range of thermal images suitable
nondestructive testing use the infrared for recording.l,2 The limited dynamic
camera for remote monitoring of the range of the video recorder (typical value
surface temperature of a structure under is 40 dB) makes unfeasible correct
test. This is a very important and often recording of the high resolution thermal
the most expensive part of the signal. For instance, many infrared
thermographic system. The advantages of cameras provide 12-bit resolution that
infrared imagers are remote sensing, requires the dynamic range of 72 dB.
spatial visualization of temperature Another problem comes from the limited
distribution and temporal separation of bandwidth of regular video equipment.
the images. Most infrared cameras are This could be an issue for a fast frame rate
equipped with both analog video and or a large size (for instance 512 x 512
digital outputs. The video format is used pixels or more) of the image. Automatic
for the real time observation of the tested gain control incorporated in video
object. After an invisible temperature recorders causes the loss of the direct level
distribution has been converted to a color in a frame. This loss is important for
image, visual testing is used to search for processing of the thermal signal in the
suspicious areas. The digital format output time domain.

Data Processing and Modeling for Infrared and Thermal Testing 361

Processing Unit (Computer and dimension of L x M x N (Fig. 2). Single
thermal images as well as time t'Volution
Peripherals) functions for a particular pixel with
coordinates (i,j) are used for analysis. This
Heplacing analog video equipment, the represents the three-dimensional nature of
computer is the dominant tool for digital the thermal signal, which can be
processing of thermal images. Most narrowed to a two-dimensional or
infrared cameras provide a digital output one-dimensional analysis in a particular
to computer and peripherals for image application.
display and processing. The digital format
of the thermograms is very convenient for Tile most important parameters used in
image processing, wire transmission of the characterizing thermal response arc as
images, printing hard copies and long follows.
term storage.
1. The term temperature signal T (kelvin)
Thermal image processing provides a applies to temperature measurements
solid basis for thermogram analysis, and mathematical simulations and is
interpretation and measurements. In the applied also to a sensor voltage signal
1980s and early 1990s personal computers and thermogram level of brightness.
were used to control the data collection
process. Postprocessing was executed on 2. Temperature difference LlT is measured
more powerful computers. 1'2 Modern between the observed and reference
personal computers with the processor (discontinuity free) points.
speed of 300 to 700 MHz and random
access memory of 32 to 256 megabytes or 3. Thermal contrast Cis the temperature
greater can accomplish both tasks. difference normalized by the
temperature in the reference area. This
If a thermal imager has the digital parameter may be defined in different
output, a data acquisition board provides ways.l,z,.s,6
an interface between the camera and
personal computer. It is commonly an Data Processing
internal plug-in board for a personal
computer. A software driver (provided by The thermal response, obtained via an
an imager vendor) is necessary to control infrared imager in form of the series of
the data transmission bet\veen the imager, digitized images (Fig. 2), is degraded
board and computer. Some boards allow because of several factors. Uneven
real time image processing during the heating, variations of emissivity on the
data collection (summation or subtraction observed surface, optical distortions and
of frames). If there is not enough time for noises of multiple nature significantly
the real time operations (data acquisition decrease the quality of the obtained
is performed with a fast frame rate) the thermal images. These factors limit the
images are placed into the board's or potential sensitivity of the method. The
personal computer's video buffer. At the
end of the measurement the data can be FIGURE 2. Signal collected by thermal inspection system:
transferred into the computer random series of N images with size L x M pixels.
access memory or written to the hard
/
drive.
Additional computer equipment /
(i,;,n)
(external data storage, network
connection, printer) makes the work with
thermal data more convenient. General
application, inexpensive computer
components are suitable for the thermal
test system.

Thermal Signal Parameters n
t,
A wide variety of thermal responses can
be obtained using different thermographic 0
nondestructive testing techniques and 0
configurations. A typical signal obtained
with the active thermal test system legend
(related to the scheme shown in Fig. 1) is i,j = pixe!
a series of N two-dimensional N =total numller of Images
thennograms collected with a rate l·(Llt)-1, n "'given image
where Llt is the time interval between two I= time
sequential thermal images. If each image
has L x M elements (or pixels), the result
of an observation is a three-dimensional
array of thermal response values having a

362 Infrared and Thermal Testing

goal of data processing is to reduce the Because at least one image has to be
amount of noise in thermal images and present in each zone, it is necessary to
local storage requirements while check if the first time zone is long enough
improving the discontinuity visibility. The compared to the acquisition time
various signal conditioning operations interval 8t:
make the work on interpretation of
thermal images by an operator more (3)
effective and improve capabilities of the
automatic discontinuity detection and The appropriate adjustrnents are made for
visualization. the parameters t.v and Nz to satisfy this
condition.
Different techniques of data processing
in the space and time domain can be The length of the time zones increases
performed during the data acquisition or exponentially. The number of images
postprocessing time to improve visibility falling into each time zone (only whole
of hidden discontinuities and to numbers are considered) gro-ws
characterize them. exponentially as ·well. The images are
averaged in every zone and the resulting
Real Time Processing image is associated with the time t~.:

It is advantageous to perform the first (4)
phase of data processing during the
acquisition process to avoid the storage of where 11;.; is the number of images in time
a large number of images. Another reason zone k and t1 is the time corresponding to
for using real time processing is the the image number I in zone k,l,Z
online monitoring and control of
manufacturing operations. In this case the The logarithmic time scale makes it
final decision based on an inverse possible to increase the processed time
problem solution or a pattern recognition interval. In addition, averaging of the
technique must be made promptly to go images in the latest time intervals
with the production flow. improves the signal·to·noise ratio. This
improvement in ratio happens because
Real time averaging of successive the thermal events evolve slowly at later
frames is commonly used to upgrade the times and provide a consistent
collected thermal images and save the contribution to a number of sequential
space on the computer media for data frames as time passes. The thermal
storage. It reduces the random noise by contrast in a single image becomes weaker
3 dB for each two frames averaged because of three·dimcnsional diffusion.
together7 but could accumulate the
instrumental distortions. Because the To improve discontinuity visibility
most rapid changes in the thermal during data collection, another simple
evolution curve happen at the time technique is temporal reference
interval immediately followed by the thermogram enhancement. It entails
thermal excitation it is beneficial to recording the background thermogram to
record the thermal images using a a buffer memory. The image T(i,j,O)
logarithmic time scale. (I:ig. 2) is acquired with the thermal
imager before the thermal excitation
The images can be grouped into an hegins. Subtraction of this background
uncomplicated logarithmic sequence.1.2 during the acquisition time eliminates
The observation time from the moment t1 parasitic reflections and optical distortions
after the thermal perturbation starts to t,v if they have a constant contribution to
at the end of the experiment (Fig. 2) is the thennograms during data acquisition.
divided into NL time zones. The upper
limit of the time zone for the logarithmic The speed of data transmission from
time scale is defined based on the closing the imager output to the data acquisition
time of the previous time zone: board and the speed of digital image
operations for this board limit possibilities
where f1 is the constant defining the for real time data proce~sing. For example,
length of the time zones. For initially evaluation of thin 1 to 2 mm (0.04 to
given values of t 11 tN and NZI this 0.08 in.} aluminum panels requires a fast
parameter can be computed: I,Z {hundreds of framt's per second) thermal
data collection rate after a flash heating.
In this case the time interval M between
the subsequent images is too \hort to
accomplish any real time processing
procedures. On the other hand, for 10 to

Data Processing and Modeling for Infrared and Thermal Testing 363

20 mm (0.4 to 0.8 in.) thick low False color coding is a \Videly used
conductive plastic the frame rate may be technique to enhance a contrast in
10 Hz or slmvcr and it is possible to apply thermal images. Because the human eye
several kinds of real time image can resolve thousands Of colors, it is
processing routines to enhance beneficial to add color to thermograms.
discontinuity visibility. Initially, the signal from a thermal imager
has only amplitude resolved information.
An example of a sophisticated real time Using a color map (also called a color
processing procedure is a thermal palette) the green, blue and red color
tomography technique applied to values are given to each pixel of a gray
composite panels.8 The processing scale image from the corresponding
technique consists of an extraction of lookup tables. 9 Values obtained in such a
thermal difference evolution curves on a way are transmitted to the red, green and
pixel-by-pixel basis. Each curve, obtained blue inputs of a color monitor (Fig. 3).
by subtraction of the time evolution at a The pseudo coloring gives more natural
reference point, is smoothed and the peak and pleasant persistence and provides the
time of the curve is determined. The resolution of smaller differences of the
pseudo image of peak times and the temperature variations that are
collection of greatest values of the unresolvable in the gray scale images.
thermal difference evolutions are stored in
a buffer of the real time processor. The The infrared camera vendors supply a
tomographic image is obtained by number of colw palettes available in real
converting the peak times to the depths. time imaging or for postprocessing.
The reported routine can produce the Observing the same temperature
tomographic and peak thermal difference distribution in different color palettes
images of 512 x 480 elements gives a better .sense of the character of an
simultaneously at the sampling rate up abnormality present in the image. Color
to 10Hz. does not add new information but may
help distinguish the background and
Image Postprocessing reduce visibility of the noise.

After the thermal response from an The run time observation of many
evaluated component has been put into successive thermal images recorded after a
the data acquisition board for temporary thermal excitation is especially effective in
storage or has been recorded on the color for the discontinuity and reference
computer hard drive or other medium, areas localization. This technique was the
postprocessing can be performed. only possibility in thermographic
Sophisticated algorithms requiring nondestructive testing before 1980 and is
millions of computations could be applied still useful to obtain a sense of
to the digitized thermal signal. The discontinuity shape and depth.
processing time at this stage is not as
critical as in real time processing. Even so, Different sizes and types of filters can
it is always desirable to reduce the be applied to a single image to improve
computational time. discontinuity visibility, reduce random
noise and define the discontinuity's
Some goals of this stage are obtaining borders. One-dimensional low pass filters
higher signal-to-noise ratio and are applied to each line to reduce the
determination of the shape and depth of a noise in the images and enhance the
subsurface discontinuity in the tested defect appearance. Two~dimensional
component. Regular digital image image filtration sometimes provides a
processing techniques combined with unidirectional feature not available ·with
special algorithms based on heat line-by-line one-dimensional filtration.
conduction theory can be applied to each
scan stored in the computer memory. Often, the median fitter yields a better
Generally, the techniques used for real result than does the averaging spatial
time processing arc applicable to the filter when applied to the thermal images.
stored images as well. Continuing This filter effectively removes s!Jot noise
progress in computer processors and (the single pixel abnormal amplitude)
hardware components aiiO'WS while preventing good definition of the
implementation of sophisticated image discontinuity edges. 1·2 The filter assigns to
processing techniques in real time. each pixel a new value equal to the
median of its neighbors instead of their
Spatial Processing averaged value.7

This kind of processing is performed with fiGURE 3. Coloring of thermal image.
thermograms in a space domain. lt is
possible to work with a single thermal ,-----,"E~;L,,,,, r;::c==~
image, time averaged image or the result
of a more complicated procedure. Thermal Color map Blue , Color
irnage (palette) (;~;:;,;;-·~·"" monitor

V•>;~o;c"·.-c;;-">

364 Infrared and Thermal Testing

A frequency domain transform, such as processing for discontinuity size
the discrete fourier transform, could be determination and temporal processing
applied for periodical noise reduction.?
The inverse transformed image has an for discontinuity depth or thermal
attenuated noise. resistance estimation helps to separate the

Temporal Processing discontinuity parameters while solving
the inverse task of discontinuity
An important feature of active characterization. I, 12
thermographic nondestructive testing is
the time evolution of the thermal
response. It enhances the importance of
analysis of acquired data in the time
domain. To improve the probability of
detecting discontinuities in the material, a
spatial reference technique can be
applied. 1'2 A reference thermal response is
obtained by an independent measurement
on a sample knuwn to have no
discontinuities. An image~to-image
comparison for each moment of time
enhances differences between the
reference specimen and the part being
tested. The absolute difference between
two images has effectively reduced
influence of parasitic factors that are
changed with the temperature but
repeated from one measurement to
another (that is, heating unevenness and
optical distortions). This approach
requires that measurement conditions be
exactly matched. Therefore this technique
is suited only for testing of identical
components under identical test
conditions.

A much more common practice is to
select a region of the evaluated
component considered from prior
experience to be free of significant
discontinuities and use this region to
determine the reference response. The
next step is a pixel-by-pixel computation
of time evolution functions of the
thermal difference LlT(t) or thermal
contrast C(t). These functions are used for
determination of the discontinuity's
parameters. For instance, to estimate a
discontinuity's depth, inverse algorithms
typically parameterize the discontinuity
depth in terms of a specified point on the
thermal contrast curve10 or a divergence
point between two temperature evolution
curves above a sound, and a tested area. 11
The result of a temporal analysis may be a
new image very different from raw
infrared camera output. An example of
such an image is a timegram, which
shows the value of characteristic time for
each pixel.

Combined Temporal and Spatial
Processing

The most powerful approach is based on
processing of a three-dimensional data set
rather than analyzing the separate
thermal images or time evolution curves.
For example, an application of spatial

Data Processing and Modeling for Infrared and Thermal Testing 365

PART 2. Automatic Discontinuity Detec:::tion2

To detect subsurface discontinuities 1. Stricter requirements for quality
infrared nondestructive testing typically dictate quality control implementation
entails submitting the tested work piece to during production.
a thermal pulse. The temporal
temperature response of the work piece 2. Labor costs, especially in developed
surface is analyzed to discover an eventual countries, make operator independent
anomaly linked to subsurface automated test systems affordable if
discontinuities. The optimum time of not essential.
observation is proportional to the square
of the depth Zctef for the considered 3. Human operators cannot sustain fast
discontinuity. Thermal nondestructive production rates. Humans are limited
testing is especially sensitive to relatively to about two or three decisions per
lnrge size discontinuities (with respect to second at best and cannot maintain
the discontinuity depth). The discussion such a rate over long periods of tirne.
below focuses on the classical
experimental techniques and on the 4. In the penguin phenomenon, a company
image processing techniques needed for is forced to follow its competitors who
discontinuity detection and localization have acquired state-of-the-art
based on this principle, generally using technology. State-of-the-art technology
thermal sources external to the material. is a marketing tool.
Actual algorithms have been published
elsewhere. 2 5. The cost of computers, sensors and
related hardware has gone down.
Images have always been an efficient
means for representing a large quantity of lvlany reported applications of
information. Electronic images play an automatic testing are primitive and often
essential role in the society as a vehicle on a gu/na-so basis, at least when
for knowledge transmission - for compared to reported research activities,
example, multimedia applications and despite the advantages of automatic
computer assisted learning. testing. In fact, automatic test techniques
are advantageous for the following
As often mentioned in previous reasons: 15•10
chapters, recorded thermal nondestructive
testing images are often corrupted by 1. Automatic testing is accurate.
various sources of noise. ~vforeover, in the 2. Automatic testing offers consistency in
case of active approach, signals are of
small amplitudes and are further degraded accept/reject dCcisions and
by temperature spreading due to the repeatability in test results.
tridimensional diffusion of the thermal 3. In-depth teaching and training of
front under the surface. Considering this, employees is not required.
special processing is needed to enhance Performance is not degraded by a
thermal nondestructive testing image monotonous repetitive job.
contrasts either for the quantitative 4. The task may be performed in
characterization, for the traditional dangerous and uncomfortable
operator assisted procedure {for example, environments.
to present images in a more 5. Measurements can be compiled
comprehensive format) or for automated automatically and used to compile
testing. statistics on the production process.

Automatic versus Manual In this respect, some image processing
Inspection techniques are well suited for automatic
thermal nondestructive testing.
In its first 30 years of evolution since
1960, numerical image processing and False Color Image Coding
automatic testing were slow to find
application by industry.IJ,I.J However this One of the simplest image processing
situation has been changing since 1995 technique to enhance contrasts is to
for the fo11mving reasons: display images in false colors rather than
in gray leve1s. 17,JH This method is based
on the fact the human eye can distinguish
only a few lens of gray levels whereas it
Glll resolve thousands of different colors.
In the hum<Jn eye, etKh color sensitive
cone cell is connected to its own nerve
whereas intensity sensitive rod cells are

366 Infrared and Thermal Testing

connected as a group to optical nerves, For instance, in the case of bonded
thus reducing the amount of detail aluminum foam laminates, the threshold
discernible by these receptors.l9 for detection, 0.2 K (0.2 oc ~ 0.36 °F),
corresponds to a radius-to-depth ratio on
The simple technique of false color the order of 40. Detected discontinuities
display is useful but limited. Although have a ratio on the order of this value.
sometime it gives good results, it can be This is at the limit of detectability for
very annoying in some instances, thermal nondestructive testing. In the
particularly when infrared images are case of these aluminum foam
taken from visible structures (for example, components, discontinuities that
a human face or a tree) and have to be absolutely must be detected in ~ervice
compared somehow with corresponding have a much greater ratio. Typical
visible images. In the case of subsurface discontinuity sizes are on the order of
discontinuity images, no visible equivaln1t 300 x 300 mm (1 ft2) with a
exists. Therefore, false color coding is a corresponding radius-to-depth ratio of
useful presentation tool that moreover -150. Undetected discontinuities of this
makes it possible to reduce the noise size can be dangerous because of reduced
effect, especially if a limited number of mechanical properties for the damaged
colors are displayed (noise is integrated in component. Thermal nondestructive
the various color bands). testing is thus particularly well suited as a
test technique for this kind of material.
General Considerations
Discontinuity Detection
Elsewhere in this volume are presented
Algorithms
investigation procedures and image
Concerning detection algorithms, the
processing techniques useful for the Society o( Photo-Interpretive Euginet'I'S (SI'IE)
conference series on image processing
thermographic infrared testing in the algorithms is a good source of
information on this subject20 as also are
mobile or static co"nfiguration, either in Institute of Electrical and Electronics
Engineers (IEEE) transactions on Pattern
reflection or in transmission, with a heat Analysis and Machine Intelligence (PAlvll)
and on Systems, Man and Cybernetics
injection or heat removal approach. The (SMC).

ctetcctahility limit of thermal There exists a \Vide variety of
algorithms whose purposes are to perform
nondestructive testing based on the image sesmentatiou, that is, to separate
regions of interest in imagesZI-34
minimum ratio of radius to depth has
(decompose the image in rectangular
been reviewed. Techniques to improve regions to extract local background).
Techniques based on edge detection,Js-:n
discontinuity visibility on thermal growing of regions around key points
called seeds, histogram analysis (a widely
nondestructive testing images have been spread technique because it does not
require complex computations·lH) or
revie'wed. The following discussion
symbolic modeling have been published
includes discontinuity detection and exploit either discontinuity
information or characteristic attributes
algorithms. (such as pixel intensity or gradients) to
label all the pixels within the image and
In the case of repetitive thermal . associate them to a particular region.
Considering the wide variety of image
nondestructive testing, for instance on the analysis problems, the variety of
algorithms is extreme. Generally
production line, the automatic processing algorithms are ad hoc and, if applied in
another context, can fail pitifully.:w The
of the recorded thermograms is of main reason for this is because an image
represents an enormous number of
interest. possibilities. For instance, in one case of
infrared images produced by a
An algorithm for the automatic thermographic test station. Even with
their small size, 68 Uvfaxrow) x 1OS
detection and extraction of discontinuities {Jvfaxcol) = 7140 pixels on 8 bits, there arc
already (28)7140 possibilities.
observed on thermograms is presented
Another important aspect is the image
below. The goal is to produce a complete background. In thermal nondestructive
testing, because of heating effects
map of the tested component where both

discontinuity locations and gross shapes

are depicted. Because a list of

discontinuities with their approximate

sizes is available, automatic testing is

possible: tested components can be sorted

with an accept/reject criterion based on a

probability detection curve. Obviously,

the test technique must be able to identify

all the critical discontinuities with

reliability, so the detection critical

threshold must be greater than the

threshold for false alarms. Rejected

components must be eliminated from the

production line or fixed if the cost of

refurbishing is acceptable. In this case, a

more sensitive nondestructive test

technique such as ultrasonic testing can

be used to assess defective zones with

greater resolution.

Data Processing and Modeling for Infrared and Thermal Testing 367

(nonuniformity), image borders tend to be reported in the case of military target
hotter than other parts of the images. This detection. 49 To help compare algorithm
has inspired some authors to develop performance, the notion of pixels 011 tmgel
trend removal elimination procedures.40,41 (POT) are introduced with signal-to-noise
The basic idea is to produce a synthetic ratio evaluation.
image from the original image by using a
polynomial function to obtain, after Validity of Discontinuity Detection
subtraction or division of the synthetic Procedures
image with the original image, a uniform
background on which discontinuities A difficult question is whether or not the
appear more dearly. segmentation is valid. An approach to this
question is to consider the degree of
Next a threshold segmentation agreement \Vith the human
algorithm based on valley detection in the interpretation.so In fact the combination
imJge histogram42 is used to identify a of eye and brain is extraordinarily
threshold between the two modes powerful. About 50 percent of the cortex
(discontinuities and background) at either cells are dedicated to the vision task.
the glohal level (using the whole image)
or local level (using a small running This is why, in most cases, an
window over the image). However, this experienced operator is perfectly able to
technique does not work very well if the segment thermal nondestructive testing
separation between the two modes is not images as they appear originally. In fact, it
sharp (see the literature4:qs for a survey of seems the human nervous system
analyzes images using threshold
threshold techniques). Although the trend techniques that make it possible to
removal approach is well suited for some separate objects based on their relative
types of images such as radiographic intensity..SI,S2 Obviously a cultural aspect is
images, its results are deceptive in also necessary to perform such a task. This
thermographic images (Fig. 4). is why, for instance, a newborn baby hJs
to Jearn all about its surrounding
The transform approaches such as the environment before the baby can
fast fourier transform and the fast hartley recognize things and objects. This wltural
transform are very effective but are aspect corresponds to heuristic rules in the
impractical on the production line case of machine vision algorithms. This
because of the great computing power discussion shuws that image
associated with these techniques.46•4H transformation is not always necessary to
Other detection algorithms have been perform artifact detection in
nondestructive testing images. Additional
FIGURE 4. Motion of panel in field of view (mobile processing time is needed to convert
configuration in reflection). images in the transform domain (and
back). Finally, if comparisons are to be
Field of view made by human vision, it is also
important to realize that the eye response
C; . Cma.c« is logarithmic, which makes it possible to
have an extremely large dynamic range.
'-: -~-;:- -'el,,, , __L_lll---'--------'1 :~~~'~:~·~~
Image Formation
Moving ~ I
direction I. The technique described next is useful for
image formation. To obtain a high test
I rate, the aniount of computations to be
performed on the images obtained from
~'- - - - ~-Peoel_____,/'· the test station should be restricted to a
minimum. For this reason, the number of
:~·---- I images to analyze must be restricted as
----1· much as possible. Obviously, this
restriction contradicts the requirement to
1I catch abnormal transient thermal events
by recording the entire thermal history
___,,,c__~' ~L,.___ _ curve of the tested part after thermal
P_ao•l__,, stimulation.

legend As seen previously, images can he
obtained from either a static or a mobile
C =- column configuration. In the static configuration,
i = designation of given time the cmnera observes the same surface
j = designation of given column continuously and a succession of images
t = fie!d width (m) is obtained beginning at the instant t = 0
N = final image corresponding to the firing of thermal
t "'time

368 Infrared and Thermal Testing

pulse {for example, the time when have it sufficiently wide so that thermal
heating lamps are turned on). In some contrasts of potentially present
discontinuities have had the opportunity
cases, starting image acquisition slightly to develop sufficiently, taking into
before the thermal pulse may be desirable account the thermal ctiffusivity a of the
analyzed material. However, in practice,
to obtain a reference cold image that will this constraint is quite flexible. The image
make it possible to reduce the spurious I obtained in this fashion during time
window !ta/bJ corresponds to individual
effects of thermal reflections by images G(t;):
subtraction with other images.
It,,
For the static configuration, the
moment teclluique initially proposed by (7) 1 ~ G(t,)
llalageas53 can be used. Temporal moment
M of order zero for temperature T0 on a I,
sound area is defined:
In the case of the mobile configuration
(5) M f!!T(,(t)dt where the infrared camera records the
complete motion of the tested
0 component, this direct summation
process cannot be directly applied because
The 8 operator is the increase of the field of view is constantly changing.
temperature with respect to ambient room In this case a special technique can be
temperature J~: t~T = JQ - Ta. This used in which specific columns of pixels
moment M tends to infinity. If a are extracted from every recorded image
to reconstmct the whole component as
discontinuity is present, it is possible to seen at a particular time. Next, the
reconstructed images are summed
form [l!TD(t)- 1110(1)] where 'li, together following the technique of Eq. 7

corresponds to the temperature above the to obtain the r image (the apostrophe
discontinuity zone. Consequently, the
indicates a reconstructed image).
temporal moment &\1 of order zero can
be evaluated. 1t can be demonstrated that ngure s illustrates the principle of
this moment has a finite value:
testing in the case of components in
(6) M motion in the field of view of width L and
at time t0, lt, ..., 1;, ... tN. This corresponds
0 to acquisition of N images during the test.
Figure 6 shows the reconstruction process
-':" l2
for the image GJ. obtained through
where Q corresponds to the absorbed
energy by the sample of thickness L juxtaposition (operator J) of columns
whereas l(ter is the thermal resistance of Ck{t1) extracted from images to, t 1, ... , ti,
the discontinuity and zdd is its depth. If
the sample is very thick, di\J becomes ... tN:
equal to Q·Rder and discontinuities will
appear with the same contrast, whatever FIGURE 5. Reconstruction process for images.
their depth. This relationship (Eq. 6) can
be applied simply by adding together all Cc,(t0} C0(11) CtJ(tl) ...
recorded images in the time domain.
Gi
This summation has also the advantage
of improving the signal-to-noise ratio by legend
the square root of the number of summed C =column
images. Consequently, if this summation G = reconstructed image
process is applied, it is not necessary to I= time
use noise reduction techniqut>s. Care must
be taken in this summation process not to 0... k... maxcol = sequence of columns
add all the images - for a given thermal 0,1 ,2 ... N "" sequence of moments in time-
event, the thermal contrast tends to
vanish as images in which it is absent are
summed together. 54

This summation technique can be
applied to reduce the number of images to
process following the thermal
nondestructive testing procedure. After or
during the experiment, it is necessary
only to add together all the acquired
images in a given time window. Care must
be taken when selecting this window to

Data Processing and Modeling for Infrared and Thermal Testing 369

(B) c; N reconstructed image GQ, ... G11ax..:ol· This
i=-0 obtained by
shifting of the image Gk

juxtaposition of the kth column of the N

acquired image can be evaluated. The

question is on which column of image Gk

where k = 0,1,2, ..., Maxcol-1 and Maxcol the point A that appears on column 0 of
is number of columns in one image.
image GQ will appear. This situation is
Because of the motion of the
component within the field of view, all depicted on Fig. 7. Because the point is
the reconstructed images Gi.. correspond to
the total observation of the component moving at speed 1', it will move from
when it is in the thermal state t(k) because
the component is observed at the same column c0 to Ck in the field of view in a
distance from the heating unit (same
extracted column kin the field of view). time interval given by Eq. 11 (sec Fig. 8):
The lateral speed 1' is constant (Fig. 6):
(11) I L ck

\' CMaxcol

(9) t(k) = -L'+ LC!c N images are obtained in time lNi one
I' l'CMaxcol image is thus acquired in ftN·N- 1] s.
_!_(L' + LC ) Consequently the point A will appear in
I' c?<..faxcol the column. The columns of the
reconstructed images correspond to image

number from 0 to N:

From this, it can be seen that images FIGURE 7. Reconstructed images.
G' correspond somC\'•lhat to images G of
Eq. 7 because: legend
A"' point
(10) Image At time Nco! C"' column
G = reconstructed image
l% [+Jt· 0
FIGURE 8. Shifting in reconst~ucted images.
u; [1][I'+ 1[ _s____) k
\' eM""'"! Field of view
[+JL'+L)
G~b\wl-1 }.faxcol-1 __c_'-~l

where Nw1 is the column number of the
original infrared images having Maxcol
columns.

In Fig. 6, the horizontal scale is a
temporal scale directly related to
acquisition time of images t0, t1, ..., til ...
tN, where every reconstructed image
corresponds to a particular thermal state
of the component (Eqs. 9 and !0),

Ho·wever, it can be noticed in this figure

(Fig. 6) that the component is not present
at the same positions in the sequence of

FIGURE 6. Geometry of lateral mof1on.

1-P<Jnel ' legend
' - -,-. . , -~, - - -~- - - - - - - - Moving
direction A= point
(9 C =column
line speed I' L "' field of view

heating Fie.ld of

V!CW

Co cma'CV\

legend

C "'column
l == Field width

370 Infrared and Thermal Testing

(12) Sh_col(k) c, the images to obtain quantitative
L CMaxcol information. In the case of the mobile
l' IN configuration, this processing can also be
done based on the individual
N reconstructed shifted SHIFT [Gi, Sh_col(k)]
images (Eq. 13). However, because of the
L NC, approximate nature of the reconstruction
process, the margin of error on such
L Rc, quantitative computations may be
unacceptable.
l' CMaxcol
To maximize the computational speed
where R is the acquisition rate (number of and take into account the previous
limitations on discontinuity size and
images acquired per second). Every Gk depth, the automatic detection algorithm
can be applied directly on raw thermal
image will thus have to be shifted by value images. This saves the time needed
Sh~col(k) columns before the summation to compute temperature. The fact that the
following Eq. 7 as in the static case (SC): algorithm works even without these
corrections is positive. Obviously, the
(13) I' G0 + Shift[G0,SC(l)+ ...J algorithm can be applied to temperature
converted images, the main difference
+ Shirt[c;,sc(i) + ...] between discontinuity dCtection on raw
and on corrected temperature images will
+ Shift[G,1c,SC(MC)+ ...] be the time needed to compute
MC temperatures.
I,shirt[c;,sc(i)]
Moreover, with the same desire to
i"'O maximize execution speed, images I orr
can be converted in unsigned character
where SHIFf [Gj, Sh_coi(i)] corresponds to type that takes less space in computer
memory. In this way one pixel is coded
the shifting operation of Sh_coi(i) on one byte in computer memory instead
columns on image Gj. of four or eight bytes required for the
coding of the floating point type of
This study shows it is possible to variables. This makes it possible to use an
obtain a reconstructed image corresponding integer arithmetic that is faster than the
the whole width of the tested component: floating point arithmetic of most computer
because of the lateral motion of the implementations. The conversion of an
component, its full width is tested. It is image in which pixels are expressed in
important to remember that this floating point values Unoat) to an image in
calculation (Eq. 13) is an approximation which pixels are expressed in characters
because it considers the apparent separation
of the image columns instead of the real Uchar) is performed as follows:
separation that considers the slit response
fimctiou, a simple technique to establish (14) lchar(i,;) = mlnoat(i,j) + b
the spatial resolution of an infrared
where: Bmax - Bmln
camera. Hmvever, this approximation is (15) Ill F;nax - .F;tlin
adequate for discontinuity detection
and where:
analysis.
Because the temporal information is and where Bwax is the maximum value of
image !char (in eight~bit implementations,
lost in the image formation process for
static configurations (Eq. 7) and dynamic Bmax = 255); Bmin is the minimum value of
image /char (in eight~bit implementations,
configurations (Eq. 13), the depth of
detected discontinuities cannot be Bmin = 0); Fmax is the maximum value
found in image /float; Fm1n is the minimum
computed unless it is known because of value found in image luoat; and i;j are
the geometry of the tested components, pixel positions in the images. Image
processing steps arc performed on images
as in the case of known depths in bonded
laminates. This is also the case of /d1ar or /::hap called simply J for
discontinuity size: no correcti\'e factor can convenience.
be computed to recover the real shape
In typical data processing of thermal
from the apparent size. However, these
limitations do not restrict automatic images, the thermal perturbation source

discontinuity detection as mentioned

before.
Corrections are needed to apply to raw

images for temperature conversion. In the
case of the static configuration for which

the whole temperature history curve of
detected discontinuities is available, after

the discontinuity detection step, it is
necessary only to reprocess and correct

Data Processing and Modeling for Infrared and Thermal Testing 371

dt'posits energy on the specimens and linearly, S = X1W1 + XzWz + ... + X11Ww The
tests proceed in reflection. Consequently, output signal y is not significant unless it
potential discontinuities are represented reaches a certain threshold T that fires the
in images by areas of temperature higher neuron: y = f(S- T). From this single
than their immediate surroundings. building block neuron, various
Discontinuity edges are represented by architectures are possible with many
ramps of temperature that span a few neuron layers, feedforward and feedback
pixels because of tridimensional spreading systems and with supervised or
of the heat flow. Edge detector operators unsupervised learning. (Learning means
often are inadequate in representing this specifying values for weights W;.) S6
ramp phenomenon.
It has been said about neural networks:
Artificial Intelligence
Tile beauty is that they work; tile problem is
A brief mention on the topic of artificial that it is hard to know why. Nevertheless
intelligence may be useful. These many groups are now implementing
processing techniques are applied in diagnostic tools based on neural networks.
infrared thermography with the basic goal For instance, in one study, neural
of enabling automatic data interpretation. networks have been trained to
automatically detect discontinuities
Expert Systems subsequently sorted as a function of

Some studies have reported the depth. 57 • 5 ~
implementation of an automatic
discontinuity detection and sizing In a typical pulse thermography
diagnosis based on an expert system that application, timegram and maxigram
proceeds with fusion of information from images have been generated from a
the thermograms and from the sequence of thermograms to reduce the
description of the inspected part based on amount of data to handle. (A maxigrmn is
a computer aided design drawing. 55 a maximum value of thermal contrasti a
Basically, the approach is as follows. timegram is the time at which it occurs.)
Pixel by pixel, these values are passed to a
1. In a first step, thermograms are two-input one-output four-layer neural
segmented into regions of similar network. The output of this network is an
thermal behavior. accept/reject status. In a second step, a SO-
input 13-output three-layer neural
2. These regions are associated to network serves for the characterization.
relevant structures in the computer The inputs are 50 points extracted on the
aided design drawing with two criteria contrast profile of suspected bad pixels
of shape and location. recognized in the first step. The outputs
are 12 discontinuity depth classes and one
3. The expert system selects discontinuity free class. The first step
discontinuities among the permits reduction of the processing time
unassociated regions. because only the suspected pixels are
processed for depth classification. These
4. Discontinuity characterization networks are independently trained with
proceeds for these regions (depth, the back propagation algorithm on a
sizing, thermal resistance evaluation). specific data set.

5. An accept/reject diagnosis takes into
account criteria such as those
developed by corporate research.

An expert system is a system based on a
set of rules often obtained after
interviewing human experts such as
experienced operators. The expert system
program next mimics the expert
judgment to bring out its own
interpretation.

Neural Networks

Neural networks offer interesting
properties for thermographic analysis
because they are adaptive and robust.
Their architecture is inspired from
biology. The basic idea is really simple.
A neuron is like a cell with various inputs
X1 1 X2, ... X11 and one scalar output)'. Tht>
neuron multiplies the inputs by weights
l\'1 to W11 and combines these products

372 Infrared and Thermal Testing

PART 3. Quantitative Inversion and Discontinuity
Characterization

Introduction Common Discontinuities in
Engineering Components
Composite materials are widely used in
consumer goods and have been adopted Table 1 lists discontinuities found in
in high technology. These materials have engineering materials. These anomalies
gained ground in public domains such as are caused by mechanisms in layered
automobile or sport industries. As their structures (nonuniformity of resin,
name indicates, they are actually misorientation of fibers); in bonds
arrangements of homogeneous materials (insufficient glue, surface contamination;
of different nature and structure. Such a corrosion);59 and in thermal barrier
combination of mechanical, physical and coatings (porosity, cross cracks,
chemical properties will create a high delamination).
performance material intended for a
particular application. In the aeronautical Quantitative Inversion
industry, for example, the weight savings
with composite materials and useful The solution of a problem dedicated to
consequences like fuel savings or flying thermophysical characterization of
range increase, continually raise the materials or to thermal nondestructive
interest of the manufacturers in these testing can be divided into three stages.
materials. Some examples of composite
materials are the following. 1. A fonvard problem mathematically
describes the space time evolution of
1. Stratified composites are formed by a the temperature field as accurately and
stack of single layers or orthotropic simply as possible, given the
folds themselves composed of long knowledge of the medium and
fibers {glass, aramid, carbon, boron) illuminating source. The forward
drowned in a thermoset or problem entails the following:
thermoplastic organic matrix. (1) simplicity in formalism and
structure; (2) swift execution;
2. Sandwich structures are obtained by (3) reasonable memory size on
sticking or welding h\'0 thin computer; (4) accuracy of the
composite strips on a lighter core calculation to approximate the true
{typically a honeycomb structure of solution with minimum error.
aluminum leaves) that maintains the
gap in between. 2. A metrology problem gives the most
accurate and the least noisy output
3. Coatings on homogenous substrates to signal. A priori information can
protect them against corrosion, complete the information given by
abrasion or thermal shocks. this signal.

The complex manufacturing processes 3. An inverse problem permits estimation
of such materials increase the risk of of parameters (constant
discontinuity appearance with crucial thermophysical properties or
consequences. Nondestructive testing boundary and interface conditions
methods at various stages of uniform in space and constant in
manufacturing, operation and time)60 or functions (boundary and
maintenance prove to be very useful. The interface conditions nonuniform in
presence of anomalies in the tested space and changing with time or
medium does not necessarily condemn temperature)/'1 This task is
the part to rejection. Discontinuity accomplished by seeking reversible
characterization by thermal quantitative operators or optimization techniques
techniques or others will allow judging to get a minimum deviation between
their severity with respect to a tolerance the measured data and the forward
threshold accepted for a given problem.
application. Thermal science suggests
several nondestructive techniques. The Fundamentally, the estimation problem
most interesting are the active techniques1 of a function B(s) - where s belongs to a
which entail subjecting the test material domain I' and may be a point P{X,)~z) of
to thermal irradiation followed by the the geometric domain, time tor
observation of their relaxation. Below are
presented examples of these techniques.

Data Processing and Modeling for Infrared and Thermal Testing 373

temperature T- is different from that In function estimation as in parameter
estimating parameters because the
function has an infinite dimension if it is estimation a simultaneous analysis of the
defined in a limited interval [50 ,s1]. sensitivity coefficients is of paramount
Furthermore, the values of function p(s)
arc linked together and also have the importance, because it allows detection of
same physical dimension. As an example, an eventual correlation between the
if the function is a boundary condition parameters or whether some parameters
T(x), it is evident that this one ·will
change in a continuous way and T(x1) arc very sensitive to the measurement
will he close to T(x2) as soon as the noise. In this case, the simultaneous
distance xrx1 will be small enough. This
expresses thus a certain regularity of the identification of all the parameters is
function p(s). Function inversion is harder impossible and the inverse problem has to
to perform than inversion of a certain
number of scalar parameters because in be reconsidered (change of the
practice the function P(s) is changed into
a parameter vector of a finite number of parameterization or the identification
components: interval or the physical field or other
considerations). The smsitil'ity coefficient is
(17) Jl ~ (Jl,,Jl,, .. , Jl,) defined as the first derivative of the

The problem arises of parameterization physical field lj(u,Jl) that is defined in a
finesse. The finer this parameterization -
that is, the larger u- the more the domain Q and that will feed the inverse
measurement noise induces an error that
will become dominant near the true algorithm, for example the temperature,
parameterized value ~· This error generally with respect to parameter ~;-
makes the problems of functions
estimation ill posed in Hadamard's ~ense. ~~ (u,Jl)
To alleviate the error, information is
introduced on the unknown solution - In practice, the measurements are
in particular inversion algorithms such as degraded by random noise. 'With the
Tikhonov's technique,62 Beck's future assumption of an additive noise, the
times technique61 and ldurio's experimental field is written:
mollification technique.63
(19) y.

'

Them components )'i and Ei of the
experimental field and its associated noise
can be grouped in a measured field vector

TABlE 1. Discontinuities in Engineering Materials Cause or location
Discontinuity

In layered Structures accidental insertion of foreign bodies during manufacturing
Inclusions and contamination incomplete ejection of volatile components during heating
Microporosities and cavities insufficient or excess heating of matrix
Poor mechanical properties local variation
Nonuniform concentration of resin local variation
Change in specimen thickness air pocket betvv"een two layers
Delamination or disbond error in layup of stratified composite
Wrong relative orientations of strata thermal or mechanical strain
Break of fibers and matrix cracking
volatile liquids inside adhesive or insufficient glue
In Structures joined by Gluings9 thermal stresses inside adhesive during polymerization
Porosity corrosive agents
Cracks oil spreading or local oxidation before sticking
Chemical degradation of adhesive between edges of honeycomb core and strips in sandwich structures
Contamination of joined surfaces local swatting
Excess or lack of glue local deformation of strips
Disband of honeycomb core
Disbond in sandwich structure at coating-to-substrate interface
residual stresses relaxation after thermal spraying of coating
In Thermal Barrier Coatings imperfect squeezing of particles sprayed in liquid state
Delamination
Cross cracks
Porosity in coating

374 Infrared and Thermal Testing

Y and in a noise vector e; the same making it possible to detect an eventual
operation is applied to the true field 11: linear dependence between these ones.

(20) y ~ ~(P) + E In the specific case of function
identification, the solution of the inverse
Inverse problems often lead to solving a problem using the least squares technique
first kind Fredholm's integral equation:64 often leads to oscillations of the unknmvn
function, to which may be expected to
J(21) ~(u,P) ~ K(u,s) p(s) ds have soft changes. It is thus necessary to
find a compromise between the regularity
r of the solution and the instability caused
by the random character of errors. The
where 11 E n. simplest means to reach this compromise
The latter can be transformed by a is to define two distance measurements

simple quadrature for solving a linear set: !11 (~, flm,) and L>z(~ .P.tbetweeq P~nd

(22) y ~ xp + • two extreme solutions ~me and !}..,. ~me is
the very unstable solutton of the least
X is the sensitivity matrix of size [m,n] squares technique and ~"' is an a priori
whose elements are defined by: solution with very sqft variations. The
regularized solution p(p, Y) is the solution
(23) X;; ~ S;(u;,P) of the new problem:

Even though this restriction of the (26) Jl(Jl, Y) Arg minp { A,(P,Jlmc)
problem to the linear case seems to be a
little simplified, it constitutes the basis of l+ Jl l>z (P,q
the majority of solutions of nonlinear
problems. Ip the linear case, the The choice of the distance
measurements is a qualitative choice that
estimation pof the true vector pstarting
indicates the way the regularization is
from the data vector Y is obtained directly performed. The choice of the values of p
by the least squares technique:
is a quantitative choice indicating that
(24) iPimc ~ .(x'x)-' x' v until that point the regularization is done.
Perfect faithfulness to the data
But in the presence of noise, this
solution is generany not adapted because corresponds to p = 0; perfect faithfulness
the matrix X1X is often ill conditioned to the a priori corresponds to J.l = oo. The
and results in an amplification of the literature shows that the simplest
noise that then exceeds all tolerated
Jevels.65,66 This is illustrated by the technique to use is the regularization
presence of the inverse of the above technique developed by Thikonov in the
mentioned matrix in }he equation of the forties.62 Its optimality criterion is given
covariance matrix of !lmc:
by:
(25) Cov(Pmc) ~ a2(x'.x(
(27) Jl(Jl, Y) Arg minp {liP - (l,., 2
where cr is the measurement noise
standard deviation, assumed to be 11
constant. This means if the sensitivity
coefficients (the columns of matrix X) are 2
proportional, almost proportional or
generally constitute a linear combination. + 11 11 Dk Pll }
The determinant of X1X tends therefore
toward zero and the standard deviations where the norms are euclidean distances
of the estimation errors will tend toward
the infinity even if the errors on the field and Dk is a k order differences operator
measurement are weak. For this reason (k is usually chosen equal to 0, 1 or 2)
the simultaneous plot of the sensitivity used to soften the solution. The
coefficients as a function of the
explicative variable is fundamental, techniques described above require the
knowledge of the coefficient p. The

literature suggests some techniques to
determine this parameter.67

Examples of Discontinuity
Characterization

Flat Discontinuity Inspection

Interface flat discontinuities are tbe
consequence of a structural discontinuity
between two materials. Examples can be

Data Processing and Modeling for Infrared and Thermal Testing 375

found in the delaminations ·within \Vhat has been described above for two
laminated composites or bonding different experiments (R::::: 0: sound slab,
discontinuities at tile interface of a R -:t 0: anomalous slab) can also apply to
coating on a substrate. Usually, they are the same unique slab if the sound
characterized by the depth beneath the thermogram is recorded on a point P0 far
surface, the lateral extent and the air gap from they location of the discontinuity
tllickness or its thermal resistance. The whereas the anomalous one corresponds
discontinuities can be detected and to a point Pat the same level (same y) as
possibly estimated quantitatively by using the discontinuity. The contrast
nondestructive thermal techniquesf,R· 74 thermogram!!.T(t) ::::: T- T0 constitutes
therefore a signature of the discontinuity.
One alternative to conventional It is positive for front side detection
nondestructive testing techniques is the (Fig. 1Oa) and negative for rear side
pulsed photothermal technique, known as detection (Pig. 10b)J3·76 Figure 11 shmvs
tJ1e flash technique. In this technique, the the effect of the discontinuity depth in a
plate to be tested is submitted to a heat one-dimensional configuration (applicable
pulse on one of its faces while an infrared for cases where the discontinuity extent is
camera records the temporal evolution of large) on the thermal contrast on the
its surface temperature, either on the front and rear faces, respectively. 1:or rear
face detection the contrast remains
heated front face or on the opposite rear unchanged for two discontinuity
face. The presence of a discontinuity locations symmetric with respect to. the
inside the material slmvs down heat middle depth of the slab; it would thus be
diffusion and so induces a perturbation iHusory to reverse the depth using the rear
on the observed temperature field. contrast. The problem do not have a
Thermal detection makes it possible to single solution. Figure 11 shows the
measure this perturbation and to localize transient contrast for a discontinuity
and characterize subsurface located at middle depth caused by a range
discontinuities. The discontinuity is a of thermal resistances. The resistance
thermal interface resistance R, located at
depth .x beneath the stimulated face FIGURE 10. Thermograms and contrast for
(Fig. 9). one-dimensional case of temperature T:
(a) front face; (b) rear face.
Because of the absorption of the flash
energy (absorbed energy surface density (a)
Q) by the slab front face, diffusion of heat
in the material produces thermograms 0 C_j 1.0
0 0.2 0.4 0.6 0.8
(temperature T versus time t curves)
Timet (fourier number)
whose qualitative shape is shnwn in
Fig. 1Oa - curve T0(t) for a point located
on front face- and in Fig. lOb- curve
T0(t) for a point located on rear face- if
no discontinuity is present in the slab
(R ::::: 0). The presence of a discontinuity
(R i' 0) will affect heat diffusion: the
corresponding surface temperature curve
T(t) will decrease more slowly after the
theoretical infinite level reached for a
dirac heat pulse for a point located on
front face (Fig. 1Oa) whereas its rise will be
slower on a point on its rear face
(Fig. !Oh).

FiGURE 9. One-dimensional thermal modeling. Discontinuity (b) - - tr---
l
assumed of infinite lateral extent is characterized by thermal 1.2 - t- I
resistance R and depth x. Sample is pulse heated by surface
density energy Q.

Thermal energy Q

~-t ~ t t t t t t t tfmotfece t _ _j_ _I_ l- _j
Interface depth x
E- - - - - - !1Rear face 0.2 0.4 0.6 0.8 1.0
I I~y
Thermal resistance R Time l (fourier number)

376 Infrared and Thermal Testing

effect is similar on both faces and could analysis to the two discontinuity
parameters may allow their better
be recovered from both of them. identification. An example is a case of
Furthermore, the maximum contrasts calculation illustrating this fundamental
point of the inverse problems (Fig. 12).
(tm~x' 8Tmaxl depend on the On the rear face, the extreme values of S_,
discontinuity's parameters x and R. It is appear for times longer than those of SR,
therefore possible to use this particular which means that the simultaneous
point to identify these two parameters identification of the two parameters is
starting from the experimental contrast77 possible. However, because depth
{other particular points could also be inversion from the rear signal does not
considered like the halfway up point or have a single solution, only resistance
the halfway down point). identification can be conceivable. On the

For an assumed discontinuity of
infinite extent, the contrast sensitivity

FIGURE 11. One-dimensional simulations of influence of disc;ontinuity parameters on thermal contrast on both faces: (a) effect
of discontinuity depth on front face contrast where R= 0.5; (b) effect of discontinuity depth on rear face contrast where

R= 0.5; (c) effect of resistance rear contrast where x =0.5; (d) effect of resistance on front face contrast where x = 0.5.

(a) (c)

~rX= 0.2 0.3

:2

c

~
c
r-R == 0.3
:be 0.2
"" R= 0.2

It:

g R=O.l
c
I
8 0.1
kA--"'·t-
"v~
~1

:!!

0 0.2 0.4 0.6 0 0.2 0.4 0.6 0.8 1.0
0 Fourier number 0.8 0 Fourier number

(b) (d) i l

0.3 0.25 i
I
:c2 :2 ~-ir : - 0 5
~
c 0.20 -II R=0.3
c
~ 0.2 ~ R= 0.2
.te
{' gc

"t": :e 0.15

~ "gt:"
1'
v0 0.1 c 0.10
-- - - - 0v

"v~ "v~
~
~ 0.05
""~' r= 0.2 and~:~
""'~
0 0.2 0.4 0.6 0.2 0.4 0.6 0.8 1.0
0 Fourier number 0 Fourier number
0

0.8

legend

R == thermal resistance (arbitrary unit)
x =discontinuity depth (pm) [1.0 jlm = 4 x 10-5 in.]

Data Processing and Modeling for Infrared and Thermal Testing 377

front face, the times of the extreme values This technique l1as the drawback that
are almost the same, which reveals a it is applicable only for cases of
correlation behveen the parameters to one~dimensional heat transfer. It is
identify and therefore makes their evident that a threshold of the
simultaneous estimation hazardous.60·6' discontinuity extent exists, beneath which
The optimal inversion procedure should the temperature does not obey the
then be to estimate the resistance by one~dimensional model. Simulated
using a rear face experiment and the calculations based on a two-directional
depth starting from a front face operation. model illustrate the effect of the
discontinuity extent on the central
To recover the two parameters, contrastJ2·74.78 See Fig. 13.
nomograms formed by isodepth and
isoresistance curves have been constructed Several forward and inverse problems
have been developed to take into account
on both faces in the {tma.v dTmax) plane. the multidirectional effects of heat
Placing the extremum of the experimental diffusion. In these problems the
contrast in the nomogram will coincide discontinuity is characterized either by
with the intersection of two isovalue constant scalar parameters (a depth/ a
curves that therefore identify the resistance and a lateral cxtent),78·80 or by a
discontinuity's parameters.77 constant depth and a function of one or
two space variables R(y) or R(y,z)
FiGURE 12. Sensitivity of contrast to parameters: (a) on rear representative of the thermal resistance
face, sensitivities of contrast to resistance and depth are depending on whether the heat diffusion
linearly independent, which permits their simultaneous is two-directional or three-directional.
identification; (b) on front face, times of extreme values are
identical, which reveals difficulty in correlation of parameters. For illustration purposes, in the
following only the example of heat
(a) 0.15 ,-----.-----,--------------.---- ------ transfer across a thermal resistance R(y) is
sensitivity to x (R = 0.5, x = 0.6) considered.72·75 This case will show the
'·0c -----0.05 contribution of the regularization on the
0 0.10 / sought solution and also the influence of
the parameterization. The inverse problem
c -- --I/ associated to R(y) is iH posed according to
:be I Hadamard. This phenomenon is
demonstrated here by the instability of
:""f 0 ~ the inverted solution of the resistance
simulated by a two-humps function
·"~c \-0.05 / (Fig. 14). A regularization procedure in
\-0.10 this problem has enormously reduced the
~ v/ oscillations and the solution is very close
\-0.15 of the true function drawn on the same
"u~ \ figure.

0 -0.20

""~" sensitivity toR (R = 0.5, x = 0.6 or 0.4)
-0.25 ~----------------- --~____J

0 0.2 0.4 0.6 0.8 1.0

Fourier number FIGURE 13. Simulations of influence of discontinuity extent on
thermal contrast above center of 0.5 J-lffi (2 x l0-5 in.) thick
(b)
discontinuity in two-dimensional heat transfer configuration,
0.025 where resistance R= 0.5. Where discontinuity width w ~ 3

Z' 0.0 mm, center of discontinuity corresponds to one-dimensional

'§ ---0.025 model (1 mm = 0.04 in.).

-l0.3 ; -

·"c' w=o.sl

Fourier number 0 0.2 0.4 0.6 _J

legend c 0.8 1.0
R "" thermal resistance {arbitrary unit)
x = discontinuity depth {pm) [1.0 vm "'4 x J0-5 in.] :be 0.2

""bc"

u0 0.1

"~

u

0

-a
~

""
0

0

Time t (fourier number)

378 Infrared and Thermal Testing

If the thermal resistance had been the impact of these parameters on the
simulated by a set of constant parameters, detectivity. M.P. Connolly79 has analyzed
the result would have been the one seen the detectivity on the front face of a
on Fig. 15. lt remains rather representative discontinuity at a coating-to-substrate
of the discontinuity but less accurate than interface. The detectivity was defined as
the solution obtained by a function
simulation. In short, the problem of the ratio of the temperature rise on the
parameters estimation is often easier to surface above the center of the
solve compared to the function one but
the actual description of the changing discontinuity divided by the temperature
physical entity is often better described by rise on the surface at a sound region.
a function than a series of parameters.
The influence of the coating and the
From the practical point of view, apart substrate thermal properties has been
from the geometrical and physical
parameters intrinsic to the discontinuity, analyzed for different combinations of the
the detectivity is also affected by other following materials: zirconia with
external factors like the nature of the host diffusivity 0.22 x l0-6 m2-s-1; inconel,
material and the thermal impulse 3.15 x 10-6 m2-s-1; aluminum,
duration. lvfany researchers have analyzed 46.70 x 10--6 m2·s-1.

Figure 16 shows the maximum
detectivity versus the ratio of coating to

fiGURE 14. Inversion of "two-humps" resistance function. fiGURE 16. Discontinuity detectivity with discontinuity depth
Oscillations in first solution illustrate ill posed character of of 0.1 mm (0.004 in.) and discontinuity width of 0.2 mm
problem. Second stable curve shows effect of regularization: (0.008 in.): (a) for different coating-to-substrate
regularized resistance distribution is very close to true combinations and pulse of duration of 0.01 s; (b) as function
resistance distribution. of pulse duration.

0.125 -+-Regularized inversion . -~-~ j-----j (a)
0.100 ·';1-h----+---1 -
2.4
0.075 --+--+-+-··---+-
Umlab!e inversion 2.2

0.050 .£ 2.0
:0
0.025
tl 1.8
ti
"u 1.6

o~;
0 1.4

0 1.2
0
2 68 10
Reduced coordinate (series)
1.0 0 23
-3 -2 -1

fiGURE 15. Comparison of function with parameter LOg (diffusivity coating to diffusivity sub5trate)
characterizations. (b)

2.2

0.100 2.0

0.075 g 1.8

0.050 :0

0.025 l _ _True _j L_ tl
0.0
function ~ 1.6

"u
10 1.4

0

1.2

-0.025 L--~-- ---~----' 8 10 1.0 0.1 0.2 0.3 0.4 0.5
0 246 0.0

Reduced coordinate (series) Pulse duration (s)

Data Processing and Modeling for Infrared and Thermal Testing 379

substrate thermal diffusivity. It is worth \'\1hen the coating and the substrate
noting that the larger the substrate physical properties are known} the
diffusivity is relative to the coating discontinuity charactf'ristics can be
diffusivity, the larger the detectivity. calculated after the measurement of the
Furthermore, the duration of a square phase curves that are more sensitive. The
pulse was analyzed on two different effectiveness of an identification
combinations of coating and substrate. technique of the thermal resistance of an
Figure 16 shows that detectivity decreases adhesion disconthtuity simulated by an
·with increasing pulse duration and that a air disk at an aluminum-to-steel interface,
test conducted with long pulse duration 20 J.Un (8.0 x 1()-4 in.) of air beneath
or continuous heating will be less 500 pm (0.02 in.) of aluminum coating,
sensitive than a test that uses very short has been put to the test. 82 It is a matter of
duration pulses. However1 the heating fitting the experimental points of the
pulse should also deliver sufficient heat to phase signal to the theoretical curve based
increase the surface temperature by an on a one-dimensional model, valid only if
amount detectable by the infrared sensor. the discontinuity diameter is large enough
A compromise should thus be done (for small diameters a three-dimensional
between the shortness of the pulse approach is necessary). In such situations,
duration and the injected energy. the discontinuity depth is known - it is
the coating thickness. The discontinuity
An alternative to transient techniques can be simulated by omitting to sandblast
described above is the amplitude a region 3 mm (0.12 in.) wide before
modulated techniques. The application of plasma spraying.
tnodulated heating techniques to
discontinuity detection and The periodic technique has the
characteriz.ation has been the center of advantage of permitting signal averaging
interest of the scientific community since over a large number of cycles and thus
the 1970s. Similarly to the pulsed mode1 provides a good signal~to-noise ratio ·with
the technique consists in comparing the limited injected energy ·when the depth to
signals extracted from the surface above be tested is smalL However, for the testing
the discontinuity and on a sound region, of relatively thick materials, the
respectively. If the amplitude and phase of measurement time tends to be extremely
the recorded signal are plotted at different long because of the need to extend the
modulation frequencies1 curves are measurement over several heating cycles.
obtained of the kind shown in Fig. 171 Furthermore} as for the heat pulsed
·which contains similar curves of technique, the dctectivity of the periodic
temperature versus time in the pulsed technique is highly dependent on the
approach. 80 impedance (product of thermal
conductivity times thermal wave number)
The analysis of these curves can give ratio of the host material to the air
information about anomalous featmes but enclosed in the delamination. The larger
numerous works on this technique show the value of this ratio, the greater the
that the phase shift angle signal is more phase shift.83
sensitive to subsurface discontinuities
than the amplitude signal. The complex Cracks Inspection
modifications brought to the phase and
amplitude curves by changes in thermal Detection of vertical cracks depends on
resistance at an enamel-to-steel interface the heat diffusion parallel to the sample
have been considered for illustration.81 surface. By using a local excitation, a
perturbation of the surface temperature
FIGURE 17. Shape of response for modulated pattern appears near this kind of
heating for sound specimen (continuous discontinuity. Typically, a laser beam b
line) and anomalous region (dotted line). focused on the sample to create the
required lateral heat flow.
- ..- -~...- --------
In the modulated technique, the laser
····... beam is chopped and moved from spot to
spot on the sample to constitute a phase
···... or an amplitude image of the surface
(Fig. 18). The heating is kept long enough
\ in each point to reach a steady state
temperature. Many types of noncontact
··.. sensors can be used to measure the surface
temperature. Infrared wdiometry is one of
Frequency (relative 5cale) the commonly used procedures. The
detection patch can be either behind,
centered on or ahead of the heating spot.

The crack is usually characterized by a
thermal resistance or considered as an

380 Infrared and Thermal Testing

FIGURE 18. Discrete scanning procedure. Modulated laser insulating boundary and its depth is
beam and radiometer are moved from spot to spot on assumed infinite.H4-86 Other parameters
surface specimen (in numerical order as illustrated) to create such as the angular orientation of the
phase or amplitude image. Heating is kept long enough in crack with respect to the scanning
each point to reach steady state temperature. direction and the angular orientation with
respect to the vertical for tilted cracks
Radiometric detector patch Discrete scan direction could be also investigated.H6 'l)'pical phase
and amplitude average temperature
,----, ~----, ,- --, • ''r----~ '' • ''r----~ patterns while scanning across a vertical
crack can be calculated according to a
L~-~~-~ ','__ --''' ''1_____1 J_ ____l model proposed by McDonald.l'.7 The zero
3 position coordinate corresponds to the
4 5 time the heat spot and the detection
patch are centered over the crack. The
Heating spot / spot and the patch are concentric.
Calculations where the laser spot was off
Crack center of the detection patch revealed
that the curves were not symmetric. Trial
fiGURE 19. Calculations for angular orientations of square and error can be used to estimate the
detector patch parallel to and at 60 degrees with respect to width of the crack by matching tlw
crack: (a) schematic; (b) curves resulting from scan measured phase or amplitude tempcrature
orientation. to the theoretical model.

(a) To obtain these results, the scanning
direction ·was considered normal to the
crack. The influence of the orientation of
the scanning path was investigated by
some researchers who reported that the

-t I FIGURE 20. Experimental results obtained in discrete scanning
across crack of 0.05 mm (0.002 in.) in steel surface at 10 Hz:
1 mm -®-- (a) amplitude; (b) relative phase.
(0.04 in.) (a)

-~ IDP 5
I~ l~m ~
(0.04 in.) 27

(b)
8.4 (15.1)

u:- '\ 25 1.0 2.0 3.0 4.0 5.0
"y-- (0.04) (0.08) (0.12) (0.16) (0.20)
\ ~
0 I \ ~ Relative location, mm (in.)
\
" 8.0 (14.4) \ "~' (b)
\
hd \ "0 18
\ 16
<1 ~
'' 14
~ .mc
23 ~ 12
"0 10

.E 8

o_ 6
E
4
<{
2
7.5 (13.5) 21 ~
2.0 m- L..__ _..L__ __L_~L____
1.0 (0.08)
(0.04) .oc.%~ 0
0 1.0 2.0 3.0 4.0
~>~:""S' (0.04) (0.08) (0.12) (0.16)

~
~

Separation di5tance L, mm (in.) 5.0
(0.20)
legend
Relative location, mm (in.)
DP "' radiometric detector patch
L = separation distance
¢ = orientation angle of crack relative to detector patch (degrees)

---K-- = amplitude with scan orientation of 0 degrees
- - - = amplitude with phase= 60 degrees
---- = phase with scan orientation of 0 degrees
- - - = phase with scan orientation of 60 degrees

Data Processing and Modeling for Infrared and Thermal Testing 381

amplitude and phase signals are curves is impossible because they do not
insensitive to this parameter.S-" This may coincide with the forward model.
make its eventual identification from
experimental data inaccurate. Figure 19 Other researchers refine the modeling
illustrates the discrepancies on the surface to corroborate the images obtained from
temperature caused by a scanning samples containing plane cracks tilted
orientation of 60 degrees compared to an with respect to the face place.R6 The
orientation of 0 degrees. These results are proportionality has been established
obtained assuming the vertical crack as an between, on one hand, the photoacoustic
insulating boundary, a square patch of signal in the case of a heating beam
1 x 1 mm (0.04 x 0.04 in.), a laser spot of focused on a certain region and, on the
0.063 mm (2.5 x 1Q-3 in.) radius and a other hand, the average temperature in
modulated frequency of 10Hz. the same region. The confrontation of the
calculated and experimental phase curves
The same researchers applied this for three different slopes 22.5, 45 and 67.5
technique to detect a vertical crack degrees, is illustrated Fig. 21. It can be
0.05 mm (0.002 in.) wide in a steel sample seen that the shapes of the experimental
(Fig. 20). Both phase and amplitude curves are consistent with those of the
signals reveal the crack as a strong peak. theoretical curves. However, the deep
Prediction of the crack's width from such notch observed on the experimental
signal at the location of the crack is due
FIGURE 21. Phase curves for three different to the heating of the glue (the crack is
crack slopes of 22.5, 45 and 67.5 degrees: simulated by cutting a rectangular block
(a) calculated curves; (b) experimental at the appropriate angle and sticking it
traces. with a thin layer of glue) when it is
(a) directly excited by the laser.

22.5 degrees Cracks can be readily detected by the
modulated technique but point-by-point
45 degrees scanning is slow and therefore unsuited to
most industrial applications. A faster
67.5 degrees detection technique was found to be a
system that injected heat continuously
-5.00 -3.00 -1.00 1.00 3.00 5.00 into a small spot on the sample surface by
X (arbitrary unit) means of a laser and then measured the
resulting temperature wake at or near that
(b) spot with a radiometer. The source and
the radiometer patch are optically
scanned in synchrony to form an image
of the entire surface. This scheme is
usually known as the dynamic
phototllermal technique or as flying spat
tl1ennal wave infrared imaging
(Fig. 22).ss,88·90

By scanning at constant velocity, each
point on the surface receives the same
amount of energy over the same period of
time. Therefore, the wake shape of the
surface temperature near the heating spot
will be the same for each point. As the

FIGURE 22. Flying spot thermal wave infrared
imaging scheme. Heating and radiometer
patches are optically scanned at constant
speed to form image of entire surface.

I Radiometric Heating I

detectoc pole~-~-->pot

,'''' _____ ,''''

Constant 5peed U

Crack

382 Infrared and Thermal Testing

heating spot approaches an open or a heated area is a square of 250 x 250 pm
subsurface crack, heat flow is blocked by (I X J0-4 in.').

the crack, this one acts as a quasi It should be pointed out also that the
insulating bOundary. Therefore, the shape is affected by the separation of the
laser spot and the detection patch. The
natural shape of the surface temperature best separation distance depends on the
is disturbed and a signature of the crack is scanning velocity, the thermal properties
of the material being tested and the kind
observed. I:igure 23 shows the influence of crack (a crack open to the surface or a
of the speed and the relative areas of the subsurface crack). An illustration of the
separation between the laser and the
focused detector and laser beam on the sensor spots is shown in Fig. 24.
radiometric response.as The crack and the Figure 24a, where the two spots are
detector patch coincide at time t = 0, the concentric, shows the signature of a
scratch. Figure 24b, where the two spots
top curves represent the average are separated, shows not only the scratch
temperature on a square patch of but also a disbanded region. 9n
250 x 250 ~m (1 x J0-4 in.Z) and the
bottom curves correspond to a square
patch of 1 mm' (1.6 x J0-3 in. 2). The

fiGURE 23. Computed average temperature in detector patch FiGURE 25. Computed thermograms for irradiated material:
(a) one-dimensional pulsed; (b) step heating.
for continuous scanning with three different speeds. Crack
and centerline of detector patch coincide at t:::: 0. Top curves (a)
are for detector patch of 0.25 x 0.25 mm (0.01 x 0.01 in.);
bottom curves are for detector patch of-1.0 mm x 1.0 mm 10 (10) [18]
(0.04 x 0.04 in.).

spotBHootedConstant
speed U

30 (54) Detector "' 1.0 (1.0) [1.8]
patch
25 (45) l
0.10 1.00 10.00
G:" 20 (36) .us Time (s)

'y-' ~

0 15 (27) il 0.1 (0.1) [0.18]

">"--' R

<l 10 (18) E
~
5 (9)
O.Dl (0.01 )[0.018]
0.01

(b)
10 (10) [18]

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 1.0 (1.0) [1.8] A
Time t (s)
0.1 (0.1) [0.18]'-"'----~-
FIGURE 24. Image of scratched paint panel: 0.01 0.10
(a) no separation of source and detector;
(b) with delay.
(a) (b)

1.00 10.00

Time {s)

Legend

A. Uncoated soft steel.
B. Steel with 0.2 mm (0.008 in.) thick zirconium d1oxide wating.
C. Steel with 0.4 mm (0.016 in.) thick zirconium dioxide coating.

Data Processing and Modeling for Infrared and Thermal Testing 383

Coating Thickness Inspection Coating thickness may be estimated by

Another application of thermal testing is a fitting procedure to appropriate models
the thkkness evaluation of t11ermal
barrier coatings. Medium conductive or by a calibration technique. An example
metal or ceramic coatings are thermally
sprayed on metallic substrates for of inversion of the coating thickness in a
corrosion or wear protection. The control
of the coating uniformity and its absolute pulsed heating operation is based on I he
thickness are necessary during the process
to ensure that spraying coincide with the value of the coating fourier number when
required specifications.
the logarithmic derivative of the
If the pulsed or the step heating temperature decay is extrcmum.92 This
response of a semiinfinite substrate coated
extremum occurs at almost the same
with a layer is referred to, the surfa~e
fourier number whatever the effusivity
temperature is controlled at short tnn.e~
by the coating and then, after a tra~lsrtiOn ratio (Fig. 26). From this reduced time, the
period, by the substrate when con.sidered
coating thickness is calculated by
separately (see Fig. 25). The graphic
representations using logarithmic scales measuring the time of the extremum in
reveal more clearly the phenomenon: at
short and long times, the thermogram the experimental data if the coating
(temperature versus time) is assimilated to
line portions that have the same slope diffusivity is known. Another example of
and whose vertical gap depends on. the
thermal properties of the two the identification of the coating thickness

substances.91 It has to be kept in mind based on the derivative of t11e tcmpewture
that ·wJmtever the chosen option for the
thickness inversion, the accuracy will be logarithm in a step heating solicitation is
all the higher because the thermal
properties of the two substances are well reported in the literature.80 The
different the case of an insulating coating
on a higi1 conductivity substrate (ceramic reported calibration curve corresp~nds to
on metal for example) is the most
favorable. a time 0.3 s after starting the heatmg of a

zirconium dioxide thermal barrier coating

on a steel substrate.80 Various particular

times can be considered to obtain other

calibration curves.

In the modulated alternative, a laser

beam is usually used to generate thermal

waves in the coating. \'\1hen this wave

reaches the substrate a perturbation is

observed in the output infrared signal at

the surface. The output signal has a phase

difference from the input signal and has

an amplitude related to the coating

thickness. Changes in the amplitude and

phase shift as a function of the coating

thickness I (normalized by the heat

diffusion length) are plotted in Fig. 27.

FIGURE 26. logarithmic derivative of pulsed thermogram for The curves arc shown for several v.:1lucs of
different coating-to-substrate effusivity ratios with curve
peaks at almost same normalized time. the reflection coefficient Rh (ratio of the

difference between the coating and

substrate effusivities to their sum)Y3 This

ratio is negative when the coating is less

eb·e1 1 = 0.1 0.4 I effusive than the substrate.

0.7 I Usually, the phase signal is preferred to

11 the amplitude signal because the phase

1' signal is less sensitive to the coating
il
I emissivity changes. As an example of
~
1/0.7 : inversion, the phase of the photothermal

"'Q. I signal collected by scanning a nickel
E
3 chromium carbide coating on a steel

"'u sample is considered.94 The coating

~ 1/0.1 thickness changes in a number of steps:

~ 80 J.1111 (3.1 x 1o-3 in.), 140 J.lm .

v>

(5.51 x J0-3 in.), 190 J.1111 (7.50 x J0-·1 m.),

! I II 240 J.l!ll (9.45 x JQ-3 in.) and 270 11m
(1.065 x J0-2 in.). The modulation
0.1 1.0 10.0
frequency of 25 Hz seems to be more
Normalized time tn (s)
24.1 appropriate to characterize the thinnest
Legend
0 1 = film diffusivily coatings whereas the frequency of 10Hz
~ = bulk effusivity
e1 = film effusivity allows a better discretization of higher
11 = film or coating
t = time thicknesses. The experimental nomograms
ln = normalize time= Ho- 1
deriving from this experiment (coating
to= ftl·Dr1
thickness versus phase delay) have been

reported. It must be noted that these

curves correspond only to a portion of the

theoretical bell shaped curve shown

earlier, because even for the thinnest

coating, 80 pm (3.1 X 1Q-] in.), the

384 Infrared and Thermal Testing

FIGURE 27. Surface temperature variation normalized coating thickness is still larger
with reduced coating thickness for different than 0.3, the theoretical normalized
coating-to-substrate reflection coefficients thickness ·where the maximum phase shift
R0 : (a) amplitude; (b) phase. occurs.
(a)
Conclusion
2.0
A general overvie'w above highlights the
1.5 main difficulties met in invcrst.' problems,
particularly the ill posed ones. Aspects
1.0 such as parameter or function
parameterization, correlation between
0.5 parameters, ~l'll',itivity analysis and
regularization techniques are briefly
discussed. To give a clear idea of these
aspects, examples arc given particularly in
the flat discontinuity identification
problem.

Extensive descriptions of inverse
problems are available elsewhere.r.o.(d,<JS

0 23
0

Coating thickness normalized by
thermal diffusion (a·/)

(b)

40

30

20

-;;-
~
"'~
10
~

~
~0
mc"'

Lv -10
~
ro
L Rb"' +0.3
~

-20

-30

23

Coating thickness normalized by
thermal diffusion (u.·l)

Legend
u. = thermal diffusion
I = coating thickness (l-Im)
Rt> = reflection coefficient
t..¢ = phase change (degrees)

Data Processing and Modeling for Infrared and Thermal Testing 385