U.S. patent application number 11/522757 was filed with the patent office on 2008-05-15 for method for thermal tomography of thermal effusivity from pulsed thermal imaging.
Invention is credited to Jiangang Sun.
Application Number | 20080111078 11/522757 |
Document ID | / |
Family ID | 39321648 |
Filed Date | 2008-05-15 |
United States Patent
Application |
20080111078 |
Kind Code |
A1 |
Sun; Jiangang |
May 15, 2008 |
METHOD FOR THERMAL TOMOGRAPHY OF THERMAL EFFUSIVITY FROM PULSED
THERMAL IMAGING
Abstract
A computer-implemented method for automated thermal computed
tomography includes providing an input of heat, for example, with a
flash lamp, onto the surface of a sample. The amount of heat and
the temperature rise necessary are dependent on the thermal
conductivity and the thickness of the sample being inspected. An
infrared camera takes a rapid series of thermal images of the
surface of the article, at a selected rate, which can vary from 100
to 2000 frames per second. Each infrared frame tracks the thermal
energy as it passes from the surface through the material. Once the
infrared data is collected, a data acquisition and control computer
processes the collected infrared data to form a three-dimensional
(3D) thermal effusivity image.
Inventors: |
Sun; Jiangang; (Westmont,
IL) |
Correspondence
Address: |
JOAN PENNINGTON
535 NORTH MICHIGAN AVENUE, UNIT 1804
CHICAGO
IL
60611
US
|
Family ID: |
39321648 |
Appl. No.: |
11/522757 |
Filed: |
September 18, 2006 |
Current U.S.
Class: |
250/341.6 |
Current CPC
Class: |
G01J 5/0003 20130101;
G01N 25/72 20130101; A61B 5/015 20130101; G01J 2005/0077
20130101 |
Class at
Publication: |
250/341.6 |
International
Class: |
G01J 5/02 20060101
G01J005/02 |
Goverment Interests
CONTRACTUAL ORIGIN OF THE INVENTION
[0001] The United States Government has rights in this invention
pursuant to Contract No. W-31-109-ENG-38 between the United States
Government and Argonne National Laboratory.
Claims
1. A computer-implemented method for automated thermal computed
tomography from one-sided pulsed thermal imaging comprising:
acquiring experimental thermal imaging data; calculating material
effusivity at a set number of depth grids using the acquired
experimental thermal imaging data; and constructing a plurality of
plane effusivity images corresponding to the calculated material
effusivity at said set number of depth grids.
2. A computer-implemented method for automated thermal computed
tomography as recited in claim 1 wherein acquiring experimental
thermal imaging data includes utilizing an infrared camera,
acquiring a series of thermal images responsive to a pulse of
thermal energy for heating a first surface of the sample.
3. A computer-implemented method for automated thermal computed
tomography as recited in claim 2 wherein acquiring said series of
thermal images includes said series of thermal images at a selected
rate, said selected rate within a range of 100 to 2000 frames per
second.
4. A computer-implemented method for automated thermal computed
tomography as recited in claim 2 wherein acquiring said series of
thermal images includes tracking the thermal energy passing from
the surface through the material.
5. A computer-implemented method for automated thermal computed
tomography as recited in claim 1 wherein calculating material
effusivity at a set number of depth grids using the acquired
experimental thermal imaging data includes converting measured
surface temperature into an apparent effusivity, said apparent
effusivity being related to thermal effusivity of an interior of
the sample.
6. A computer-implemented method for automated thermal computed
tomography as recited in claim 5 wherein determining a thermal
effusivity, said thermal effusivity represented by
e=(.rho.ck).sup.1/2 wherein .rho. represents density, c represents
specific heat, k represents thermal conductivity.
7. A computer-implemented method for automated thermal computed
tomography as recited in claim 1 wherein constructing a plurality
of plane effusivity images includes identifying a relationship
between depth and time to determine a speed of heat
propagation.
8. A computer-implemented method for automated thermal computed
tomography as recited in claim 7 wherein said relationship is
represented by z=(.pi..alpha.t).sup.1/2 wherein .alpha. represents
thermal diffusivity, t represents time.
9. A computer-implemented method for automated thermal computed
tomography as recited in claim 1 wherein calculating material
effusivity at a set number of depth grids using the acquired
experimental thermal imaging data includes calculating a material
effusivity function reDresented by e n = e ( z n ) = ne a ( t n ) -
i = 1 n - 1 e i ##EQU00011## where e.sub.n=e(z.sub.n) represents a
spatial distribution function of thermal effusivity for the
sample.
10. A computer-implemented method for automated thermal computed
tomography as recited in claim 1 wherein calculating material
effusivity at a set number of depth grids using the acquired
experimental thermal imaging data includes providing an initial
value of apparent effusivity for the sample.
11. A computer-implemented method for automated thermal computed
tomography as recited in claim 1 wherein acquiring experimental
thermal imaging data includes reading a predefined test
parameter.
12. A computer-implemented method for automated thermal computed
tomography as recited in claim 11 wherein reading a predefined test
parameter includes reading an imaging rate.
13. A computer-implemented method for automated thermal computed
tomography as recited in claim 11 wherein reading a predefined test
parameter includes reading a flash frame.
14. Apparatus for automated thermal computed tomography from
one-sided pulsed thermal imaging of a sample comprising: a flash
lamp applying a pulse of thermal energy for heating the first
surface of the sample an infrared camera acquiring a series of
thermal images responsive to said pulse of thermal energy for
heating the first surface of the sample; a data acquisition and
control computer, said data acquisition and control computer
calculating material effusivity at a set number of depth grids
using the acquired experimental thermal imaging data; and
constructing a plurality of plane effusivity images corresponding
to the calculated material effusivity at said set number of depth
grids.
15. Apparatus for automated thermal computed tomography as recited
in claim 14 wherein the acquired experimental thermal imaging data
includes temporal surface temperature data, and wherein said data
acquisition and control computer converts the temporal surface
temperature data into a spatial depth distribution of thermal
effusivity.
16. Apparatus for automated thermal computed tomography as recited
in claim 14 wherein said infrared camera acquiring a series of
thermal images includes said infrared camera acquiring said series
of thermal images at a selected rate, said selected rate within a
range of 100 to 2000 frames per second.
17. Apparatus for automated thermal computed tomography as recited
in claim 14 wherein said data acquisition and control computer
determines a thermal effusivity, said thermal effusivity
represented by e=(.rho.ck).sup.1/2 wherein .rho. represents
density, c represents specific heat, k represents thermal
conductivity.
18. Apparatus for automated thermal computed tomography as recited
in claim 14 wherein said data acquisition and control computer
identifies a relationship between depth and time to determine a
speed of heat propagation for constructing a plurality of plane
effusivity images.
19. Apparatus for automated thermal computed tomography as recited
in claim 18 wherein said relationship is represented by
z=(.pi..alpha.t).sup.1/2 wherein a represents thermal diffusivity,
t represents time.
20. Apparatus for automated thermal computed tomography as recited
in claim 14 wherein said data acquisition and control computer
calculates a material effusivity function represented by e n = e (
z n ) = ne a ( t n ) - i = 1 n - 1 e i ##EQU00012## where
e.sub.n=e(z.sub.n) represents a spatial distribution function of
thermal effusivity for the sample.
Description
FIELD OF THE INVENTION
[0002] The present invention relates to an improved method for
analyzing materials, which may be multilayer and inhomogeneous,
from one-sided pulsed thermal imaging. More specifically this
invention relates to a method for thermal computed tomography from
one-sided pulsed thermal imaging. Still more specifically this
invention-relates to a method and computer program product for
automated 3D imaging of subsurface material properties by one-sided
pulsed thermal imaging.
DESCRIPTION OF THE RELATED ART
[0003] Pulsed thermal imaging is widely used for nondestructive
evaluation (NDE) of advanced materials and components. The premise
is that internal flaws, such as, disbonds, voids or inclusions,
affect the flow of heat from the surface of a solid.
[0004] For example, U.S. Pat. No. 6,517,236 issued Feb. 11, 2003 to
Jiangang Sun, William A. Ellingson, and Chris M. Deemer discloses a
method and apparatus for automated non-destructive evaluation (NDE)
thermal imaging tests of combustor liners and other products. The
apparatus for automated NDE thermal imaging testing of a sample
includes a flash lamp positioned at a first side of the sample. An
infrared camera is positioned near a second side of the sample. A
linear positioning system supports the sample. A data acquisition
and processing computer is coupled to the flash lamp for triggering
the flash lamp. The data acquisition and processing computer is
coupled to the infrared camera for acquiring and processing image
data. The data acquisition and processing computer is coupled to
the linear positioning system for positioning the sample for
sequentially acquiring image data.
[0005] U.S. Pat. No. 6,542,849 issued Apr. 1, 2003 to Jiangang Sun
discloses a method and apparatus for determining the thickness of a
sample and defect depth using thermal imaging in a variety of
plastic, ceramic, metal and other products. A pair of flash lamps
is positioned at a first side of the sample. An infrared camera is
positioned near the first side of the sample. A data acquisition
and processing computer is coupled to the flash lamps for
triggering the flash lamps. The data acquisition and processing
computer is coupled to the infrared camera for acquiring and
processing thermal image data. The thermal image data are processed
using a theoretical solution to analyze the thermal image data to
determine the thickness of a sample and defect depth.
[0006] A problem is that current thermal imaging methods typically
only process the surface temperature in temporal domain to
determine one or several parameters under the surface (not a
distribution) based on a model of the material system and the
defect type.
[0007] These methods are considered 2D methods because they can
only determine a limited number of parameters under each surface
position (corresponding to a pixel in a 2D image). For example,
several methods were developed to detect crack (or delamination)
depth under the surface and the predicted depths at all surface
positions are usually presented in a 2D image corresponding to the
surface.
[0008] Another problem is that many known methods rely on physical
models of the specific material system under study and determine
characteristic variables (e.g., time) or fit model parameters to
derive the unknown parameters. In particular the material system
configuration must be specified in advance (e.g., 1-layer or
multi-layer system and defect type) and the material within each
layer must be homogeneous.
[0009] U.S. patent application Ser. No. 11/452,156 (attorney docket
ANL-IN-05-125) filed Jun. 13, 2006, by the present inventor
Jiangang Sun and assigned to the present assignee, entitled
"OPTICAL FILTER FOR FLASH LAMPS IN PULSED THERMAL IMAGING"
discloses an optical filter made from a borosilicate optical
material for flash lamps used in pulsed thermal imaging. The filter
substantially eliminates the infrared radiation from flash lamps to
allow for accurate detection of surface temperature during entire
pulsed thermal imaging tests.
[0010] U.S. patent application Ser. No. 11/452,052 (attorney docket
ANL-IN-05-121) filed Jun. 13, 2006, by the present inventor
Jiangang Sun and assigned to the present assignee, entitled "METHOD
FOR ANALYZING MULTI-LAYER MATERIALS FROM ONE-SIDED PULSED THERMAL
IMAGING" discloses a method for multilayer materials that was
developed to determine multiple material parameters including
conductivity, optical transmission, and thickness and/or crack
depth for each layer.
[0011] Thermal tomography methods to provide 3D imaging have been
proposed by a number of researchers but none of the proposed
methods provide an effective tomographic method.
[0012] A principal aspect of the present invention is to provide a
method for thermal computed tomography from one-sided pulsed
thermal imaging.
[0013] Another aspect of the present invention is to provide a
method and software for fast 3D imaging of subsurface material
properties by one-sided pulsed thermal imaging.
[0014] Other important aspects of the present invention are to
provide such method for thermal computed tomography from one-sided
pulsed thermal imaging substantially without negative effect and
that overcome some of the disadvantages of prior art
arrangements.
SUMMARY OF THE INVENTION
[0015] In brief, a method provides thermal tomography of subsurface
material distribution, and is achieved by converting the temporal
surface temperature data into a spatial depth distribution of
thermal effusivity under the surface.
[0016] The method of the invention includes providing an input of
heat, for example, with a flash lamp, onto the surface of a sample
or article to be examined. The amount heat and the temperature rise
necessary are dependent on the thermal conductivity and the
thickness of the material being inspected. An infrared camera then
takes a rapid series of thermal images of the surface of the
article, at a selected rate, which can vary from 100 to 2000 frames
per second. Each infrared frame tracks the thermal energy as it
passes from the surface through the material. Once the infrared
data is collected, it is processed to form a three-dimensional (3D)
image.
[0017] In accordance with features of the invention, the method
advantageously provides 3D image of an article that can be provided
in a very short period of time, that is, in a range of a few
minutes or less than one minute. The defects and their depths can
be seen in the generated 3D image with good image resolution.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] The present invention together with the above and other
objects and advantages may best be understood from the following
detailed description of the preferred embodiments of the invention
illustrated in the drawings, wherein:
[0019] FIG. 1 is a diagram illustrating a thermal imaging apparatus
for implementing a method for thermal computed tomography from
one-sided pulsed thermal imaging in accordance with the preferred
embodiment;
[0020] FIG. 2 is a flow chart illustrating exemplary steps for
implementing a method for thermal computed tomography from
one-sided pulsed thermal imaging in accordance with the preferred
embodiment;
[0021] FIGS. 3A and 3B are graphs respectively illustrating surface
apparent effusivity as a function of time, based on the thermal
properties of a single-layer predefined material with the
layer-thickness L=10 mm; and the material effusivity predicted by
the thermal tomography method from Eq. (9), as a function of depth
z for the single-layer predefined material system in accordance
with the preferred embodiment;
[0022] FIGS. 4A and 4B are graphs respectively illustrating surface
apparent effusivity as a function of time, based on the thermal
properties of a two-layer predefined material system; and the
material effusivity predicted by the thermal tomography method from
Eq. (9), as a function of depth z for the two-layer predefined
material system in accordance with the preferred embodiment;
[0023] FIG. 5 is a chart illustrating predicted material effusivity
profiles as function of depth for 2-layer material systems with
various thicknesses in the 2.sup.nd layer in accordance with the
preferred embodiment;
[0024] FIGS. 6A and 6B are graphs respectively illustrating surface
apparent effusivity as a function of time, based on the thermal
properties of a three-layer predefined material system; and the
material effusivity predicted by the thermal tomography method from
Eq. (9), as a function of depth z for the three-layer predefined
material system in accordance with the preferred embodiment;
[0025] FIG. 7 is a chart illustrating predicted material effusivity
profiles as function of depth for 3-layer material systems with
various thicknesses in the 3.sup.rd layer in accordance with the
preferred embodiment;
[0026] FIGS. 8A and 8B respectively provide a schematic diagram of
a sample including first and second cross-sections and a table
providing exemplary dimensions for the holes shown in the first and
second cross-sections of FIG. 8A in accordance with the preferred
embodiment; and
[0027] FIGS. 9A and 9B and FIGS. 9C and 9D respectively provide
predicted thermal effusivity images and diagrams of the first and
second cross-sections of FIG. 8A in accordance with the preferred
embodiment.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0028] In accordance with features of the invention, a thermal
tomography method converts the temporal series of 2D surface
temperature data into a spatial 3D distribution of material
effusivity under the surface.
[0029] In comparison, conventional thermal imaging methods only
process the surface temperature in temporal domain to determine one
or a few parameters at each surface position (a pixel in a 2D
image) based on a model of the material system; these methods are
considered 2D methods because they cannot provide the distribution
of material property under the surface. For example, several
methods were developed to detect crack, or delaminations, depth
under the surface and the predicted depths at all surface positions
are usually presented as a 2D depth map for the surface. Recently,
a method for multi-layer materials was developed by the present
inventor to determine multiple material parameters including
conductivity, optical transmission, and thickness and/or crack
depth for each layer. In principle, this method can determine as
many material parameters as needed, and each predicted parameter
could be plotted into a 2D image mapped over the specimen surface.
However, all these methods rely on physical models of the specific
material system under study and determine characteristic variables,
for example, time, or fit model parameters to derive the unknown
parameters. These methods cannot resolve superimposed features
along depth and can usually detect only one dominant feature under
the surface. In particular, the material system configuration must
be specified first in order to select an appropriate model for the
system, for example, 1-layer or multi-layer system, and the
material within each layer must be homogeneous. These methods are
therefore not suitable to characterize materials with inhomogeneous
material properties in the depth direction. One example of such
material system is the human skin.
[0030] Theoretical development of this invented method is now
described based on typical 1D solutions of the heat conduction
equation under pulsed thermal imaging condition.
Theoretical Development
[0031] The 1D governing equation for heat conduction in a solid
material is represented by the following equation (1):
.rho. c .differential. T .differential. t = .differential.
.differential. z ( k .differential. T .differential. z ) , ( 1 )
##EQU00001##
where T(z,t) is temperature, .rho. is density, c is specific heat,
k is thermal conductivity, t is time, z is coordinate in the depth
direction, and z=0 is the surface that receives flash heating. It
is noted that Eq. (1) contains only two independent thermal
parameters, the heat capacity pc and the thermal conductivity k,
both may vary with depth z, but are treated constant in the
following derivations.
[0032] During flash thermal imaging, an impulse energy Q is applied
on surface z=0 at t=0. An ideal condition is assumed for the
following derivation, i.e., (1) flash is instantaneous or flash
duration is zero and (2) flash heat is absorbed at a surface layer
of zero thickness. Other than the flash heating, all surfaces are
assumed to be insulated at all times. After the surface at z=0
receives initial heating and reaches a high temperature
(theoretically to infinity with the instantaneous heating), heat
conduction takes place in the z (or depth) direction. For a
semi-infinite material (0.ltoreq.z<.infin.), the solution of
surface temperature from the governing equation (1) under the ideal
condition is:
T ( t ) = T ( z = 0 , t ) = Q ( .rho. ck .pi. t ) 1 / 2 ( 2 )
##EQU00002##
where T(t) is the surface temperature that is continuously measured
by an infrared detector (a pixel in an infrared imaging array)
during the thermal imaging test. It is seen that there is a single
(combined) material thermal property in Eq. (2) which is commonly
defined as thermal effusivity e=(.rho.ck).sup.1/2 Equation (2) can
be rearranged as:
e a = Q T ( t ) .pi. t ( 3 ) ##EQU00003##
where ea is called the apparent thermal effusivity. Equation (3)
can be generalized as the definition for apparent effusivity, with
T(t) as the surface temperature measured from an arbitrary sample
during a pulsed thermal imaging test (not only for semi-infinite
medium as it was originally defined from). Because the deposited
heat Q is a constant (which can be measured), ea in general is a
function of time, i.e., e.sub.a=e.sub.a(t). From Eqs. (2) and (3),
it is seen that e.sub.a(t) is a constant and equals to the material
effusivity (.rho.ck).sup.1/2 for semi-infinite single-layer
materials. However, e.sub.a(t) normally differs from the material
effusivity for multi-layer and/or inhomogeneous materials.
[0033] Equation (3) converts the measured surface temperature into
an apparent effusivity which is related to the real thermal
effusivity of the sample's interior. In order to establish a
formulation between the time-dependent apparent effusivity with the
spatial-dependent material effusivity, it is necessary to determine
the relationship between time and space under pulsed thermal
imaging condition (or to determine the speed of heat transfer). For
this purpose, we examine another solution. For a finite-thickness
plate (0.ltoreq.z.ltoreq.L), the surface temperature solution from
the governing Eq. (1) is
T ( t ) = T ( z = 0 , t ) = Q .rho. cL [ 1 + 2 n = 1 .infin. exp (
- n 2 .pi. 2 L 2 .alpha. t ) ] ( 4 ) ##EQU00004##
where .alpha.(=k/.rho.c) is thermal diffusivity which is commonly
understood to be relevant to the speed of heat conduction in
transient heat transfer process. Note that the parameter
.alpha.t/L.sup.2 is a nondimensional parameter, or it can be
considered as a parameter that relates the temporal time t with
spatial distance L. The present invention has identified a unique
relationship determined from Eq. (4) under the constraint
d.sup.2(InT)/d(Int).sup.2=0, which is: L=(.pi..alpha.t).sup.1/2.
This can also be generalized to:
z=(.pi..alpha.t).sup.1/2 (5)
[0034] Equation (5) is assumed to be the general relationship
between spatial distance z and time t for heat transfer process. It
also indicates that the heat-transfer "speed" dz/dt varies (or
decreases) with time. The material parameter that determines the
heat transfer "speed" is the thermal diffusivity .alpha..
[0035] The final step in the development of this thermal tomography
method is to derive the solution for the spatial distribution of
the material thermal effusivity from the time-dependent apparent
effusivity defined in Eq. (3). In this invention, it is postulated
that the measured apparent effusivity at a certain time t
corresponds directly to the averaged material effusivity within a
certain depth z, where z and t are related by Eq. (5). This
postulation converts the temporal-domain apparent effusivity into
the spatial-domain depth distribution of the actual material
effusivity. Physically, it emphasizes the fact that heat conduction
is a finite-speed process with heat being deposited along its
propagation path, so surface information at a certain time can only
come from the material information within a finite depth that heat
has propagated through within that time period. In this invention,
however, the diffusive/dissipative nature of the heat transfer
process is not addressed (the leading edge of the heat propagation
gradually diffuses); it will be a topic of future studies. Based on
this postulation, we have:
e a ( t ) = 1 z .intg. 0 z e ( z ) z . ( 6 ) ##EQU00005##
[0036] It is recognizable that Eq. (6) is a simple convolution
formulation, with a convolution kernel function of unity within the
integral. In discrete-increment form, Eq. (6) can be expressed
as:
e a ( t n ) = i = 1 n e i .DELTA. z i i = 1 n .DELTA. z i , and z n
= .pi. .alpha. t n = i = 1 n .DELTA. z i n = 1 , 2 , 3 , ( 7 )
##EQU00006##
where e.sub.i=e(z.sub.i) is a spatial distribution function. When
the increment z.sub.i is constant, we have:
e a ( t n ) = 1 n i = 1 n e i n = 1 , 2 , 3 , ( 8 )
##EQU00007##
Therefore, e.sub.n can be solved from:
e n = e ( z n ) = ne a ( t n ) - i = 1 n - 1 e i n = 1 , 2 , 3 , (
9 ) ##EQU00008##
where z.sub.n=(.pi..alpha.t.sub.n).sup.1/2 with .alpha. being the
thermal diffusivity. It is seen that the deconvolution formulation
Eq. (9) is explicit, so it can be calculated very efficiently.
[0037] In brief, this invention provides a completely new approach
to process thermal imaging data so, for the first time, 3D imaging
of entire sample volume is achieved. It is based on several
postulations and generalizations of simple solutions of the
governing heat transfer equation under pulsed thermography test
condition. In particular, the invention consists of three findings
or components.
[0038] (1) It identified that the thermal effusivity
e=(.rho.ck).sup.1/2, which is related to the thermal impedance of a
material, is a suitable imaging parameter to construct the 3D image
of the test material.
[0039] (2) This invention determined a relationship between the
space (depth) and the time, i.e., z=(.alpha..pi.t).sup.1/2, which
shows that the "speed" dz/dt of heat propagation is related to the
thermal diffusivity and time so it is not constant for each
material but decreases with time.
[0040] (3) This invention has established a deconvolution algorithm
to solve the depth profile of the material thermal effusivity from
the measured surface temperature data. The predicted effusivity is
a direct function of depth, not an average or convolved parameter,
so it is an accurate (and more sensitive) representation of local
property along depth. In conventional (2D) thermal imaging methods,
however, final results are usually presented in images of the
measured surface temperature T(t) (including its derivatives) and
apparent effusivity ea, these data are difficult to be used to
interpret the detailed structures within the material.
[0041] The governing heat conduction equation (1) contains two
independent thermal properties, heat capacity pc and thermal
conductivity k. These parameters are converted into two new
independent thermal properties, the thermal effusivity e and the
thermal diffusivity .alpha.. This conversion is unique, and can be
done vice versa. Therefore, the invented thermal tomography method
should preserve all information in the original governing
equation.
[0042] Having reference now to the drawings, FIG. 1 illustrates a
thermal imaging apparatus or system for implementing methods for
thermal computed tomography from one-sided pulsed thermal imaging
in accordance with the preferred embodiment and generally
designated by the reference numeral 100, such as a sample 102
including such as a three layers L.sub.1, L.sub.2, L.sub.3. Thermal
imaging system 100 includes a flash lamp 104 providing a pulse of
thermal energy for heating a first surface of the sample 102.
Thermal imaging system 100 includes, for example, a high-resolution
and high-sensitivity infrared camera 106, for example, with
256.times.256 pixel focal plane array of infrared sensors for
taking a rapid series of thermal images of the surface of the
article, at a rate which can vary from 100 to 2000 frames per
second. Each infrared frame tracks the thermal energy as it passes
from the surface through the material. Infrared camera 106 is
positioned on the same side of the sample 102 as the flash lamps
104. Thermal imaging system 100 includes a data acquisition and
control computer 110 for implementing methods in accordance with
the preferred embodiment. Once the infrared data is collected, it
is processed to form the 3D images. A major advantage of the method
is that the 3D image of an article can be provided in a very short
period of time, i.e., a matter of minutes or less.
[0043] Referring now FIG. 2, there are shown exemplary steps for
implementing a method for thermal computed tomography from
one-sided pulsed thermal imaging in accordance with the preferred
embodiment.
[0044] As indicated in a block 200, first initialization of the
thermal imaging system is preformed and thermal imaging data is
acquired as indicated in a block 202. Multiple test parameters are
read, for example, imaging rate, flash frame, and the like, as
indicated in a block 204. Next a total heat transfer depth is
calculated from Eq. (5);
z=(.pi..alpha.t).sup.1/2 (5)
and the total depth is divided into 100 depth grids as indicated in
a block 206. The number of depth grids can be changed.
[0045] A pixel (i, j) loop is obtained as indicated in a block 208,
then as indicated in a block 210 an initial apparent effusivity is
set at 2000 providing a material effusivity near surface was set to
2000 J/m.sup.2-K-s.sup.1/2. If this material value is known, it can
be used. The apparent effusivity function is calculated from Eq.
(3);
e a = Q T ( t ) .pi. t ( 3 ) ##EQU00009##
Next as indicated in a block 212, material effusivity is calculated
at the 100 dept grids from Eq. (9)
[0046] e n = e ( z n ) = ne a ( t n ) - i = 1 n - 1 e i ( 9 )
##EQU00010##
Therefore, a total of 100 plane effusivity images corresponding to
these depths are constructed. Then checking whether the loop ended
as indicated in a decision block 214. When the loop has not ended,
then a next pixel (i, j) loop is obtained at block 208 and the
processing continues with the next pixel (i, j) loop. When the loop
has ended, then plane and cross-section effusivity images are
constructed as indicated in a block 216. This completes the thermal
imaging data processing as indicated in a block 218.
Validation Examples
[0047] The invented thermal tomography method is validated by using
multilayer materials. Multilayered material systems have abrupt
changes in material properties. The challenge is to resolve both
the abrupt changes between layer boundaries as well as gradual
variation of material property within all layers. None of the
conventional thermal imaging methods is potentially capable for
this challenge. Analysis and imaging of these materials therefore
represent the ultimate tests for validating the performance of this
thermal tomographic method. Most real inhomogeneous materials (such
as skin) exhibit only gradual variation of property along depth, so
the performance and accuracy of this method would be better for
typical inhomogeneous materials than that for multilayer materials.
In the following, several examples are presented to demonstrate the
characteristics (uniqueness and stability) of this method. A
material system with up to 3 layers, as illustrated in FIG. 1, is
used in the calculations. Two sets of material properties,
identified as materials no. 1 and 2, are used and listed in Table
1.
TABLE-US-00001 TABLE 1 List of thermal properties for two
postulated materials used in examples Material Conductivity k Heat
capacity .rho.c Diffusivity .alpha. Effusivity e no. (W/m-K)
(J/m.sup.3-K) (mm.sup.2/s) (J/m.sup.2-K-s.sup.1/2) 1 2 2 .times.
10.sup.6 1 2000 2 1 1 .times. 10.sup.6 1 1000
[0048] First, a single-layer material is evaluated. For this
material system, the theoretical solution of surface temperature
T(t) from Eq. (4) can be directly used to calculate the apparent
effusivity in Eq. (3).
[0049] FIG. 3A shows the surface apparent effusivity as a function
of time, based on the thermal properties of the material no. 1 with
the layer thickness L=10 mm. The apparent effusivity is constant in
early times and decreases in later times, indicating a constant
material property up to some depth. However, it does not provide
information for 1.sup.st-layer material thickness and the property
of the 2.sup.nd-layer material (in this case, the second layer has
no material so its effusivity should be zero).
[0050] FIG. 3B shows the material effusivity predicted by the
thermal tomography method from Eq. (9), as a function of depth z.
The dashed rectangular region superimposed in FIG. 3B represents
the real material property (effusivity and thickness). It is seen
that at the back surface, where z=10 mm, the predicted effusivity
does not immediately reduce to zero. This "diffusion" result at a
sharp boundary is due to the loss of high-frequency components in
the predicted effusivity profile because of the
diffusive/dissipative nature of the heat transfer process. The area
under the predicted effusivity profile is found to be equal to the
area of the dashed rectangle, indicating the conservation of total
effusivity from the prediction which further validates the physical
postulation used to derive the deconvolution formulation Eq.
(9).
[0051] Referring to FIGS. 4A and 4B, a 2-layer material system is
evaluated. The first layer contains material no. 1 and the second
layer contains material no. 2. The governing equation (1) for the
2-layer system is solved numerically to obtain the surface
temperature data T(t) under pulsed thermal imaging condition.
[0052] FIG. 4A shows the apparent effusivity calculated from Eq.
(3) as a function of time for the 2-layer materials of thicknesses
1 and 10 mm, respectively. Again, the apparent diffusivity does not
provide enough information to interpret the material system under
study. The predicted material effusivity as a function of depth
using the invented thermal tomography method (Eq. 9) is plotted in
FIG. 4B, with the material effusivity distribution (dashed line) as
a function of depth superimposed in the figure. It is clearly seen
that the predicted system consists of two layers: the predicted
effusivity is equal to the effusivity of the first-layer material
(e=2000 J/m.sup.2-K-s.sup.1/2) within shallow depths and approaches
to that of the second-layer material (e=1000 J/m.sup.2-K-s.sup.1/2)
after the depth of the first layer (1 mm). The predicted effusivity
in the 2.sup.nd layer first reaches a minimum value at 876
J/m.sup.2-K-s.sup.1/2, indicating that the prediction overshoots
the real value of 1000 J/m.sup.2-K-s.sup.1/2 by about 13%. However,
as depth increases, the predicted effusivity recovers, and will
eventually approach to the exact effusivity of the 2.sup.nd-layer
material.
[0053] FIG. 5 illustrates the predicted effusivity for several
2-layer material systems with 2.sup.nd-layer thicknesses up to 40
mm. It is seen that the predicted effusivity profile is unique in
early times (insensitive to the thickness change of the 2.sup.nd
layer). The exact effusivity of the 2.sup.nd layer is recovered
after the depth of -20 mm deep, and it remains constant until heat
transfer reaches the back surface. This result demonstrates that
the deconvolution method, Eq. (9), is robust and stable, and it
converges to exact result except near depths of sharp property
changes due to the thermal diffusion effect. The diffusion effect
appears stronger with the increase of depth.
[0054] Referring to FIGS. 6A and 6B, a 3-layer material system is
evaluated. It is assumed that the 1.sup.st and 3.sup.rd layers
consist of material no. 1 and the 2.sup.nd layer consists of
material no. 2. Again, the governing equation (1) for the 3-layer
system is solved numerically to obtain the surface temperature data
T(t) under pulsed thermal imaging condition.
[0055] FIG. 6A shows the apparent effusivity calculated from Eq.
(3) as a function of time for the 3-layer material system with
thicknesses of 1, 5, and 30 mm, respectively, for the three layers.
The predicted material effusivity as a function of depth by the
invented thermal tomography method (Eq. 9) is plotted in FIG. 6B.
The material effusivity distribution is illustrated in dashed line
as a function of depth superimposed in FIG. 6B.
[0056] FIG. 6B shows that the predicted effusivity within the first
2 layers follows the same trend as that in the 2-layer system shown
in FIG. 4B. The predicted effusivity for the 3.sup.rd layer also
exhibits an overshoot to a maximum value of 2310
J/m.sup.2-K-s.sup.1/2, or 15.5% higher than the effusivity of the
3.sup.rd layer. Again, in deeper depths of the 3.sup.rd layer, the
predicted effusivity will eventually approach to the correct
effusivity of the 3.sup.rd-layer material.
[0057] FIG. 7 shows the predicted effusivity profiles with various
thicknesses of the 3.sup.rd-layer material. It is seen that the
correct effusivity of the 3.sup.rd layer is obtained at the depth
about 45 mm deep, and it remains at that value until nearing the
back-surface depth. These results, together with those for one- and
two-layer materials, demonstrated the robustness and stability of
the deconvolution method developed in this invention.
[0058] FIG. 8A provides a schematic diagram of a sample including
first and second cross-sections in a flat-bottom-hole plate. FIG.
8B is a table providing exemplary dimensions for the holes shown in
the first and second cross-sections of FIG. 8A of a
flat-bottom-hole plate. 3D imaging of a plate sample with
flat-bottom holes is illustrated and described with respect to
FIGS. 9A and 9B and FIGS. 9C and 9D.
[0059] Referring now to FIGS. 9A and 9B and FIGS. 9C and 9D
respectively provide predicted thermal effusivity images and
diagrams of the first and second cross-sections of FIG. 8A.
[0060] A SiC/SiNC ceramic matrix composite plate with machined
flat-bottom holes was used to demonstrate 3D imaging performance of
the invented thermal tomography method. This plate, illustrated in
FIG. 8A and FIGS. 9C and 9D, is 5 cm.times.5 cm in size, and its
thickness varies from 2.3 to 2.7 mm. Seven flat-bottom holes (Holes
A-G) of various diameters and depths were machined from the back
surface, as illustrated in FIG. 8A. The depths of the holes, listed
in FIG. 8B, refer to the distance from the hole bottoms to the
front surface where pulsed thermography data were taken. The
composite plate was not completely densified so it contains some
near-surface defects and distributed porosities.
[0061] Pulsed thermography data (surface temperature images) were
obtained from the front surface of the plate using a one-sided
thermal imaging system 100. The imaging rate was 170 Hz, with a
total of 700 frames taken for a test duration of 4.1 s. Thus, at
each surface pixel (i, j), its surface temperature T.sub.ij(t) was
acquired for a total of 700 time steps with a time increment t at
1/170=0.0059 s. The temperature data T.sub.ij(t) is converted to
the apparent effusivity e.sub.aij(t) by Eq. (3), which is then
deconvolved into the subsurface material effusivity distribution
e.sub.ij(z) according to Eqs. (9) and (5). Once e.sub.ij(z) for all
pixels are calculated and composed together, thermal effusivity
distribution in the entire 3D volume of the plate is obtained. The
3D effusivity data are similar to 3D x-ray CT data, which can be
sliced in arbitrary planes, such as lateral or cross-sectional
slices, to examine the internal material property distribution. The
data processing is very fast, for example, typically within a
minute for deriving the entire volume data.
[0062] FIGS. 9A and 9B show the predicted cross-sectional
effusivity images and FIGS. 9C and 9D show corresponding
cross-sectional diagrams along the two horizontal lines marked in
FIG. 8A. It is seen that all flat-bottom holes are imaged with
detailed depth resolution of flat-bottom-hole surfaces. Note that
all holes have inclined bottom surface due to a machining error. In
addition, many shallow defects, darker spots, are resolved with
good image resolution. These defects are small voids due to
incomplete densification of the plate. However, the effusivity
images in FIGS. 9A and 9B show clearly the degradation of spatial
resolution with depth due to the 3D diffusion effect, and a
slightly lower effusivity prediction just under surface because of
the finite flash duration effect, flash duration effect easily can
be corrected. Nevertheless, this invented thermal tomography method
provides the first effective 3D imaging method based on pulsed
thermography and the result is already superior than any other
thermal imaging methods currently available.
[0063] From the examples presented, it is demonstrated that the
thermal tomographic method developed in this invention is robust
and stable and produces unique results. The predicted effusivity
value always converges to the exact material effusivity in depth
regions of constant properties. The prediction deviates from exact
solution near depths with abrupt property changes. This is
represented by a gradual transition, due to loss of the
high-frequency components, followed by an overshoot of the
predicted effusivity at a sharp boundary (this problem is common to
all tomographic techniques). The maximum overshoot error is less
than 16% for the examples presented above. However, there is no
overshoot in regions of zero effusivity (i.e., outside material
after passing the back surface). These favorable characteristics
are attributed to the high stability of the deconvolution scheme
from this thermal tomography method. The robustness and stability
of this method also allows for future implementation of
diffusion/dissipation reduction schemes that usually introduce some
instability because they attempt to recover the higher-frequency
components in the solution. Nevertheless, without any modification,
this invented method can be directly used for tomographic
reconstruction of various different layered and inhomogeneous
materials. Examples of these material systems include skin/tissue
and composite materials. Currently, no other thermal imaging method
can determine property distribution under surface for layered
and/or inhomogeneous materials.
[0064] In brief summary, the invented thermal tomographic method is
the first practical method capable of 3D imaging of material's
interior. 3D imaging solves all deficiencies in conventional 2D
thermal imaging methods, which are limited to detecting only one
dominant defect under surface and requiring specific models in data
processing/interpretation for specific material systems. It was
demonstrated to imaging the entire 3D volume of a ceramic matrix
composite plate with flat-bottom holes machined from a back
surface. All defects within the plate were detected with high
sensitivity and resolution, especially near the subsurface region.
The data processing for constructing the entire 3D image is very
fast, typically less than a minute for a large data set. Because
the imaged parameter is a material property (thermal effusivity),
the image data can be easily interpreted, for example, see FIGS. 9A
and 9B. While in conventional thermal imaging methods, the final
image data are mostly based on the measured surface temperature
T(t) (such as its derivatives), interpretation of these data is not
straight forward and requires knowledge of fundamental thermal
imaging theories. In addition, this method does not require
calibration and is fully automated, so an operator does not need
any formal training to use it.
[0065] While the present invention has been described with
reference to the details of the embodiments of the invention shown
in the drawing, these details are not intended to limit the scope
of the invention as claimed in the appended claims.
* * * * *