Method for implementing depth deconvolution algorithm for enhanced thermal tomography 3d imaging

{
  "publication_number": "US2011299752A1",
  "country": "US",
  "kind": "A1",
  "title": "Method for implementing depth deconvolution algorithm for enhanced thermal tomography 3d imaging",
  "abstract": "A computer-implemented method, apparatus, and computer program product implement enhanced thermal tomography three-dimensional (3D) thermal effusivity imaging. Experimental thermal imaging data is acquired. A response function is derived and a convolution formulation is constructed from the experimental thermal imaging data. A deconvolution solution procedure is implemented that includes constructing a matrix solution equation with a damping parameter, and solving the matrix solution equation with a selected number of iterations to construct a plurality of effusivity images. Using the novel depth deconvolution algorithm with experimental data acquired from a one-sided pulsed thermal-imaging system provides greater sensitivity for internal sample features substantially eliminating degradation in depth resolution.",
  "claims": [
    "1. A computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging comprising: acquiring experimental thermal imaging data; deriving a response function and constructing a convolution formulation using the experimental thermal imaging data; performing a deconvolution solution process including: calculating an apparent effusivity function, and solving a matrix solution equation with a damping parameter with a selected number of iterations to construct a plurality of effusivity images. 2. The computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 1 wherein acquiring experimental thermal imaging data includes providing an input of heat with a flash lamp onto one surface of a sample. 3. The computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 2 includes measuring a transient temperature decay on said one surface of the sample. 4. The computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging 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 heating a first surface of a sample. 5. The computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 1 wherein deriving a response function and constructing a convolution formulation using the experimental thermal imaging data includes converting measured time variation of surface temperature into a depth distribution of thermal effusivity within a sample. 6. The computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 1 wherein deriving a response function and constructing a convolution formulation using the experimental thermal imaging data includes identifying thermal effusivity distribution as a function of depth is represented by E(z) and E  (z) = { ρ   ck, 0 L where z represents depth and L represents thickness of the sample, η is density, c is specific heat, k is thermal conductivity, z is coordinate in the depth direction, and z=0 is the sample surface receiving heating. 7. The computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 1 wherein deriving a response function and constructing a convolution formulation using the experimental thermal imaging data includes calculating a function R(z/l) represented by R  (z / l) = 1 z l [1 + 2  ∑ n = 1 ∞  exp  (- n 2  π 2  z 2 l 2)] where z is coordinate in the depth direction, and z=0 is the sample surface receiving heating, and the function R(z/l) is related to diffusion at an interface at l. 8. The computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 7 includes constructing a matrix [Dδ i,j +R i,j] where D is a positive constant defining a damping parameter, where R i,j =R(z i /l j), δ i,j is represented by: δ i, j = { 1, if   i = j 0, if   i ≠ j δ i,j is the Kronecker delta. 9. The computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 1 wherein performing a deconvolution solution process includes calculating an apparent effusivity function represented by: e a  (t) = Q T  (t)  π   t where Q is the pulsed energy absorbed on surface z=0 at t=0, T(t) is the surface temperature that is measured by an infrared detector during a thermal imaging test. 10. The computer-implemented method for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 1 wherein performing a deconvolution solution process includes solving said matrix solution equation represented by e a, i = Dp i n = ∑ j = 1 M  p j n + 1  [D   δ i, j + R i, j],   i = 1, 2, 3, …   M, n = 0, 1, 2, 3, …  where thermal effusivity E i depth distribution is identified by E i = ∑ j = i M  p j n + 1 for i, j=1, 2, 3,... M uniformly discretized number (1−M) of uniform grids of set size for an entire depth of a sample, the superscript n is the iteration number, p j is unknown parameter to be solved, and in the first step of the iteration, p j 0 =0; D is a positive constant defining a damping parameter, δ i,j is represented by: δ i, j = { 1, if   i = j 0, if   i ≠ j δ i,j is the Kronecker delta. 11. An apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging comprising: a flash lamp applying a pulse of thermal energy heating a first surface of a sample; an infrared camera acquiring experimental thermal imaging data 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 deriving a response function and constructing a convolution formulation using the experimental thermal imaging data; said data acquisition and control computer performing a deconvolution solution process including: calculating an apparent effusivity function, and solving a matrix solution equation with a damping parameter with a selected number of iterations to construct a plurality of effusivity images. 12. The apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 11 wherein said infrared camera acquires a series of thermal images responsive to said pulse of thermal energy heating a first surface of a sample. 13. The apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 11 wherein said data acquisition and control computer includes a control program embodied in a machine readable medium and storing a depth deconvolution algorithm; said control program used for controlling said data acquisition and control computer for constructing effusivity images. 14. The apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 11 wherein said data acquisition and control computer deriving a response function and constructing a convolution formulation using the experimental thermal imaging data includes said data acquisition and control computer converting measured time variation of surface temperature into a depth distribution of thermal effusivity within a sample. 15. The apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 11 wherein said data acquisition and control computer deriving a response function and constructing a convolution formulation using the experimental thermal imaging data includes said data acquisition and control computer identifying thermal effusivity distribution as a function of depth is represented by E(z) and E  (z) = { ρ   ck, 0 L where z represents depth and L represents thickness of the sample, η is density, c is specific heat, k is thermal conductivity, z is coordinate in the depth direction, and z=0 is the sample surface receiving heating. 16. The apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 11 wherein said data acquisition and control computer deriving a response function and constructing a convolution formulation using the experimental thermal imaging data includes said data acquisition and control computer calculating a function R(z/l) represented by R  (z / l) = 1 z l [1 + 2  ∑ n = 1 ∞  exp  (- n 2  π 2  z 2 l 2)] where z is coordinate in the depth direction, and z=0 is the sample surface receiving heating, and the function R(z/l) is related to diffusion at an interface at l. 17. The apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 16 includes said data acquisition and control computer constructing a matrix [Dδ i,j +R i,j] where D is a positive constant defining a damping parameter, where R i,j =R(z i /l j), δ i,j is represented by: δ i, j = { 1, if   i = j 0, if   i ≠ j δ i,j is the Kronecker delta. 18. The apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 11 wherein said data acquisition and control computer performing a deconvolution solution process includes said data acquisition and control computer calculating an apparent effusivity function represented by: e a  (t) = Q T  (t)  π   t where Q is the pulsed energy absorbed on surface z=0 at t=0, T(t) is the surface temperature that is measured by an infrared detector during a thermal imaging test. 19. The apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 11 wherein said data acquisition and control computer performing a deconvolution solution process includes said data acquisition and control computer solving said matrix solution equation represented by e a, i = Dp i n = ∑ j = 1 M  p j n + 1  [D   δ i, j + R i, j],   i = 1, 2, 3, …   M, n = 0, 1, 2, 3, … where thermal effusivity E i depth distribution is identified by E i = ∑ j = i M  p j n + 1 for i, j=1, 2, 3,... M uniformly discretized number (1−M) of uniform grids of set size for an entire depth of a sample, the superscript n is the iteration number, p j is unknown parameter to be solved, and in the first step of the iteration, p j 0 =0; D is a positive constant defining a damping parameter, δ i,j is represented by: δ i, j = { 1, if   i = j 0, if   i ≠ j δ i,j is the Kronecker delta. 20. The apparatus for implementing thermal tomography three-dimensional (3D) thermal effusivity imaging as recited in claim 11 includes said data acquisition and control computer constructing plane and cross-section effusivity images."
  ],
  "cpc": [
    "G06V 20/64",
    "G06V 10/143"
  ],
  "assignees": [
    "SUN JIANGANG",
    "UCHICAGO ARGONNE LLC"
  ],
  "filing_date": "2010-06-04",
  "publication_date": "2011-12-08",
  "priority_date": "2010-06-04",
  "application_number": "US-79382910-A",
  "family_id": "45064504",
  "citations": [
    "US2001007571A1",
    "US2002018510A1",
    "US5639162A"
  ]
}