Abstract

We develop a heat transfer model to reconstruct pulsed thermographic data of layered objects. One of its salient features is its incorporation of normalized variables for a generalized approach to such problems. Additionally, we establish a methodology to determine the spatial and temporal limits of the data reconstruction process. Moreover, we describe an effective nondestructive technique for detecting and characterizing internal defects in multilayer objects. This inspection technique is verified on the construction of physical models and their examination. The depth, transverse dimensions, and front-surface shape of the detected defects are straightforwardly obtained from 3D depthgrams.

© 2010 Optical Society of America

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  1. N. P. Avdelidis, B. C. Hawtin, and D. P. Almond, “Transient thermography in the assessment of defects of aircraft composites,” NDT & E Int. 36, 433-439 (2003).
    [CrossRef]
  2. E. Grinzato, V. Vavilov, P. G. Bison, and S. Marinetti, “Hidden corrosion detection in thick metallic components by transient IR thermography,” Infrared Phys. Technol. 49, 234-238(2007).
    [CrossRef]
  3. C. Ibarra-Castanedo and X. Maldague, “Defect depth retrieval from pulsed phase thermographic data on plexiglas and aluminum samples,” Proc. SPIE 5405, 348-356 (2004).
    [CrossRef]
  4. M. Strojnik and G. Paez, “Determination of temperature distributions with micrometer spatial resolution,” Opt. Eng. 46, 036401 (2007).
    [CrossRef]
  5. G. Busse, D. Wu, and W. Karpen, “Thermal wave imaging with phase sensitive modulated thermography,” J. Appl. Phys. 71, 3962-3965 (1992).
    [CrossRef]
  6. P. Cielo, “Pulsed photothermal evaluation of layered materials,” J. Appl. Phys. 56, 230-234 (1984).
    [CrossRef]
  7. X. Maldague, Theory and Practice of Infrared Technology for Nondestructive Testing (Wiley-Interscience, 2001).
  8. X. Maldague, A. Ziadi, and M. Klein, “Double pulse infrared thermography,” NDT & E Int. 37, 559-564 (2004).
    [CrossRef]
  9. G. Rieger, “Lockin and burst-phase thermography for NDE,” Quant. Infrared Thermography 3, 141-154 (2006).
    [CrossRef]
  10. G. Rieger, T. Zweschper, and G. Busse, “Lock-in thermography with eddy current excitation,” Quant. Infrared Thermography 1, 21-32 (2004).
  11. M. S. Scholl, “Target temperature distribution generated and maintained by a scanning laser beam,” Appl. Opt. 21, 2146-2152 (1982).
    [CrossRef] [PubMed]
  12. G. Paez and M. Strojnik, “Thermal contrast detected with a quantum detector,” Infrared Phys. Technol. 46, 141-145(2004).
    [CrossRef]
  13. M. Susa, H. D. Benitez, C. Ibarra-Castanedo, H. Loaiza, H. Bendada, and X. Maldague, “Phase contrast using a differentiated absolute contrast method,” Quant. Infrared Thermography 3, 219-230 (2006).
    [CrossRef]
  14. S. M. Shepard, J. R. Lhota, B. A. Rubadeux, T. Ahmed, and D. Wang, “Enhancement and reconstruction of thermographic data,” Proc. SPIE 4710, 531-535 (2002).
  15. D. A. Gonzalez, C. Ibarra-Castanedo, J. M. Lopez-Higuera, and X. Maldague, “New algorithm based on the Hough transform for the analysis of pulsed thermographic sequences,” NDT & E Int. 39, 617-621 (2006).
    [CrossRef]
  16. X. Maldague and S. Marineti, “Pulse phase infrared thermography,” J. Appl. Phys. 79, 2694-2698 (1996).
    [CrossRef]
  17. T. D'Orazio, C. Guaragnella, M. Leo, and P. Spagnolo, “Defect detection in aircraft composites by using a neural approach in the analysis of thermographic sequences,” NDT & E Int. 38, 665-673 (2005).
    [CrossRef]
  18. J. Sandoval, G. Paez, and M. Strojnik, “Heat transfer analysis of a dynamic infrared-to-visible converter,” Opt. Eng. 42, 3517-3523 (2003).
    [CrossRef]
  19. H. Carslaw and J. Jaeger, Conduction of Heat in Solids (Oxford Univ. Press, 1959).
  20. S. Lugin and U. Netzelmann, “A defect shape reconstruction algorithm for pulsed thermography,” NDT & E Int. 40, 220-228 (2007).
    [CrossRef]
  21. M. Branch, T. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” J. Sci. Comput. 21, 1-23 (1999).
  22. S. Lugin and U. Netzelmann, “An effective compression algorithm for pulsed thermography data,” NDT & E Int. 38, 485-490 (2005).
    [CrossRef]
  23. M. Omar, M. I. Hassan, K. Saito, and R. Alloo, “IR self-referencing thermography for detection of in-depth defects,” Infrared Phys. Technol. 46, 283-289 (2005).
    [CrossRef]
  24. M. S. Scholl, “Time and position varying infrared scene simulation,” Proc. SPIE 819, 297-301 (1987).
  25. M. S. Scholl, “Spatial and temporal effects due to target irradiation: a study,” Appl. Opt. 21, 1615-1620 (1982).
    [CrossRef] [PubMed]
  26. M. Omar, M. I. Hassan, and K. Saito, “Optimizing thermography depth probing with a dynamic thermal point spread function,” Infrared Phys. Technol. 46, 506-514 (2005).
    [CrossRef]
  27. M. S. Scholl, “Thermal considerations in the design of a dynamic IR source,” Appl. Opt. 21, 660-667 (1982).
    [CrossRef] [PubMed]

2007

E. Grinzato, V. Vavilov, P. G. Bison, and S. Marinetti, “Hidden corrosion detection in thick metallic components by transient IR thermography,” Infrared Phys. Technol. 49, 234-238(2007).
[CrossRef]

M. Strojnik and G. Paez, “Determination of temperature distributions with micrometer spatial resolution,” Opt. Eng. 46, 036401 (2007).
[CrossRef]

S. Lugin and U. Netzelmann, “A defect shape reconstruction algorithm for pulsed thermography,” NDT & E Int. 40, 220-228 (2007).
[CrossRef]

2006

G. Rieger, “Lockin and burst-phase thermography for NDE,” Quant. Infrared Thermography 3, 141-154 (2006).
[CrossRef]

M. Susa, H. D. Benitez, C. Ibarra-Castanedo, H. Loaiza, H. Bendada, and X. Maldague, “Phase contrast using a differentiated absolute contrast method,” Quant. Infrared Thermography 3, 219-230 (2006).
[CrossRef]

D. A. Gonzalez, C. Ibarra-Castanedo, J. M. Lopez-Higuera, and X. Maldague, “New algorithm based on the Hough transform for the analysis of pulsed thermographic sequences,” NDT & E Int. 39, 617-621 (2006).
[CrossRef]

2005

T. D'Orazio, C. Guaragnella, M. Leo, and P. Spagnolo, “Defect detection in aircraft composites by using a neural approach in the analysis of thermographic sequences,” NDT & E Int. 38, 665-673 (2005).
[CrossRef]

S. Lugin and U. Netzelmann, “An effective compression algorithm for pulsed thermography data,” NDT & E Int. 38, 485-490 (2005).
[CrossRef]

M. Omar, M. I. Hassan, K. Saito, and R. Alloo, “IR self-referencing thermography for detection of in-depth defects,” Infrared Phys. Technol. 46, 283-289 (2005).
[CrossRef]

M. Omar, M. I. Hassan, and K. Saito, “Optimizing thermography depth probing with a dynamic thermal point spread function,” Infrared Phys. Technol. 46, 506-514 (2005).
[CrossRef]

2004

G. Paez and M. Strojnik, “Thermal contrast detected with a quantum detector,” Infrared Phys. Technol. 46, 141-145(2004).
[CrossRef]

G. Rieger, T. Zweschper, and G. Busse, “Lock-in thermography with eddy current excitation,” Quant. Infrared Thermography 1, 21-32 (2004).

X. Maldague, A. Ziadi, and M. Klein, “Double pulse infrared thermography,” NDT & E Int. 37, 559-564 (2004).
[CrossRef]

C. Ibarra-Castanedo and X. Maldague, “Defect depth retrieval from pulsed phase thermographic data on plexiglas and aluminum samples,” Proc. SPIE 5405, 348-356 (2004).
[CrossRef]

2003

N. P. Avdelidis, B. C. Hawtin, and D. P. Almond, “Transient thermography in the assessment of defects of aircraft composites,” NDT & E Int. 36, 433-439 (2003).
[CrossRef]

J. Sandoval, G. Paez, and M. Strojnik, “Heat transfer analysis of a dynamic infrared-to-visible converter,” Opt. Eng. 42, 3517-3523 (2003).
[CrossRef]

1999

M. Branch, T. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” J. Sci. Comput. 21, 1-23 (1999).

1996

X. Maldague and S. Marineti, “Pulse phase infrared thermography,” J. Appl. Phys. 79, 2694-2698 (1996).
[CrossRef]

1992

G. Busse, D. Wu, and W. Karpen, “Thermal wave imaging with phase sensitive modulated thermography,” J. Appl. Phys. 71, 3962-3965 (1992).
[CrossRef]

1987

M. S. Scholl, “Time and position varying infrared scene simulation,” Proc. SPIE 819, 297-301 (1987).

1984

P. Cielo, “Pulsed photothermal evaluation of layered materials,” J. Appl. Phys. 56, 230-234 (1984).
[CrossRef]

1982

Ahmed, T.

S. M. Shepard, J. R. Lhota, B. A. Rubadeux, T. Ahmed, and D. Wang, “Enhancement and reconstruction of thermographic data,” Proc. SPIE 4710, 531-535 (2002).

Alloo, R.

M. Omar, M. I. Hassan, K. Saito, and R. Alloo, “IR self-referencing thermography for detection of in-depth defects,” Infrared Phys. Technol. 46, 283-289 (2005).
[CrossRef]

Almond, D. P.

N. P. Avdelidis, B. C. Hawtin, and D. P. Almond, “Transient thermography in the assessment of defects of aircraft composites,” NDT & E Int. 36, 433-439 (2003).
[CrossRef]

Avdelidis, N. P.

N. P. Avdelidis, B. C. Hawtin, and D. P. Almond, “Transient thermography in the assessment of defects of aircraft composites,” NDT & E Int. 36, 433-439 (2003).
[CrossRef]

Bendada, H.

M. Susa, H. D. Benitez, C. Ibarra-Castanedo, H. Loaiza, H. Bendada, and X. Maldague, “Phase contrast using a differentiated absolute contrast method,” Quant. Infrared Thermography 3, 219-230 (2006).
[CrossRef]

Benitez, H. D.

M. Susa, H. D. Benitez, C. Ibarra-Castanedo, H. Loaiza, H. Bendada, and X. Maldague, “Phase contrast using a differentiated absolute contrast method,” Quant. Infrared Thermography 3, 219-230 (2006).
[CrossRef]

Bison, P. G.

E. Grinzato, V. Vavilov, P. G. Bison, and S. Marinetti, “Hidden corrosion detection in thick metallic components by transient IR thermography,” Infrared Phys. Technol. 49, 234-238(2007).
[CrossRef]

Branch, M.

M. Branch, T. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” J. Sci. Comput. 21, 1-23 (1999).

Busse, G.

G. Rieger, T. Zweschper, and G. Busse, “Lock-in thermography with eddy current excitation,” Quant. Infrared Thermography 1, 21-32 (2004).

G. Busse, D. Wu, and W. Karpen, “Thermal wave imaging with phase sensitive modulated thermography,” J. Appl. Phys. 71, 3962-3965 (1992).
[CrossRef]

Carslaw, H.

H. Carslaw and J. Jaeger, Conduction of Heat in Solids (Oxford Univ. Press, 1959).

Cielo, P.

P. Cielo, “Pulsed photothermal evaluation of layered materials,” J. Appl. Phys. 56, 230-234 (1984).
[CrossRef]

Coleman, T.

M. Branch, T. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” J. Sci. Comput. 21, 1-23 (1999).

D'Orazio, T.

T. D'Orazio, C. Guaragnella, M. Leo, and P. Spagnolo, “Defect detection in aircraft composites by using a neural approach in the analysis of thermographic sequences,” NDT & E Int. 38, 665-673 (2005).
[CrossRef]

Gonzalez, D. A.

D. A. Gonzalez, C. Ibarra-Castanedo, J. M. Lopez-Higuera, and X. Maldague, “New algorithm based on the Hough transform for the analysis of pulsed thermographic sequences,” NDT & E Int. 39, 617-621 (2006).
[CrossRef]

Grinzato, E.

E. Grinzato, V. Vavilov, P. G. Bison, and S. Marinetti, “Hidden corrosion detection in thick metallic components by transient IR thermography,” Infrared Phys. Technol. 49, 234-238(2007).
[CrossRef]

Guaragnella, C.

T. D'Orazio, C. Guaragnella, M. Leo, and P. Spagnolo, “Defect detection in aircraft composites by using a neural approach in the analysis of thermographic sequences,” NDT & E Int. 38, 665-673 (2005).
[CrossRef]

Hassan, M. I.

M. Omar, M. I. Hassan, K. Saito, and R. Alloo, “IR self-referencing thermography for detection of in-depth defects,” Infrared Phys. Technol. 46, 283-289 (2005).
[CrossRef]

M. Omar, M. I. Hassan, and K. Saito, “Optimizing thermography depth probing with a dynamic thermal point spread function,” Infrared Phys. Technol. 46, 506-514 (2005).
[CrossRef]

Hawtin, B. C.

N. P. Avdelidis, B. C. Hawtin, and D. P. Almond, “Transient thermography in the assessment of defects of aircraft composites,” NDT & E Int. 36, 433-439 (2003).
[CrossRef]

Ibarra-Castanedo, C.

M. Susa, H. D. Benitez, C. Ibarra-Castanedo, H. Loaiza, H. Bendada, and X. Maldague, “Phase contrast using a differentiated absolute contrast method,” Quant. Infrared Thermography 3, 219-230 (2006).
[CrossRef]

D. A. Gonzalez, C. Ibarra-Castanedo, J. M. Lopez-Higuera, and X. Maldague, “New algorithm based on the Hough transform for the analysis of pulsed thermographic sequences,” NDT & E Int. 39, 617-621 (2006).
[CrossRef]

C. Ibarra-Castanedo and X. Maldague, “Defect depth retrieval from pulsed phase thermographic data on plexiglas and aluminum samples,” Proc. SPIE 5405, 348-356 (2004).
[CrossRef]

Jaeger, J.

H. Carslaw and J. Jaeger, Conduction of Heat in Solids (Oxford Univ. Press, 1959).

Karpen, W.

G. Busse, D. Wu, and W. Karpen, “Thermal wave imaging with phase sensitive modulated thermography,” J. Appl. Phys. 71, 3962-3965 (1992).
[CrossRef]

Klein, M.

X. Maldague, A. Ziadi, and M. Klein, “Double pulse infrared thermography,” NDT & E Int. 37, 559-564 (2004).
[CrossRef]

Leo, M.

T. D'Orazio, C. Guaragnella, M. Leo, and P. Spagnolo, “Defect detection in aircraft composites by using a neural approach in the analysis of thermographic sequences,” NDT & E Int. 38, 665-673 (2005).
[CrossRef]

Lhota, J. R.

S. M. Shepard, J. R. Lhota, B. A. Rubadeux, T. Ahmed, and D. Wang, “Enhancement and reconstruction of thermographic data,” Proc. SPIE 4710, 531-535 (2002).

Li, Y.

M. Branch, T. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” J. Sci. Comput. 21, 1-23 (1999).

Loaiza, H.

M. Susa, H. D. Benitez, C. Ibarra-Castanedo, H. Loaiza, H. Bendada, and X. Maldague, “Phase contrast using a differentiated absolute contrast method,” Quant. Infrared Thermography 3, 219-230 (2006).
[CrossRef]

Lopez-Higuera, J. M.

D. A. Gonzalez, C. Ibarra-Castanedo, J. M. Lopez-Higuera, and X. Maldague, “New algorithm based on the Hough transform for the analysis of pulsed thermographic sequences,” NDT & E Int. 39, 617-621 (2006).
[CrossRef]

Lugin, S.

S. Lugin and U. Netzelmann, “A defect shape reconstruction algorithm for pulsed thermography,” NDT & E Int. 40, 220-228 (2007).
[CrossRef]

S. Lugin and U. Netzelmann, “An effective compression algorithm for pulsed thermography data,” NDT & E Int. 38, 485-490 (2005).
[CrossRef]

Maldague, X.

D. A. Gonzalez, C. Ibarra-Castanedo, J. M. Lopez-Higuera, and X. Maldague, “New algorithm based on the Hough transform for the analysis of pulsed thermographic sequences,” NDT & E Int. 39, 617-621 (2006).
[CrossRef]

M. Susa, H. D. Benitez, C. Ibarra-Castanedo, H. Loaiza, H. Bendada, and X. Maldague, “Phase contrast using a differentiated absolute contrast method,” Quant. Infrared Thermography 3, 219-230 (2006).
[CrossRef]

X. Maldague, A. Ziadi, and M. Klein, “Double pulse infrared thermography,” NDT & E Int. 37, 559-564 (2004).
[CrossRef]

C. Ibarra-Castanedo and X. Maldague, “Defect depth retrieval from pulsed phase thermographic data on plexiglas and aluminum samples,” Proc. SPIE 5405, 348-356 (2004).
[CrossRef]

X. Maldague and S. Marineti, “Pulse phase infrared thermography,” J. Appl. Phys. 79, 2694-2698 (1996).
[CrossRef]

X. Maldague, Theory and Practice of Infrared Technology for Nondestructive Testing (Wiley-Interscience, 2001).

Marineti, S.

X. Maldague and S. Marineti, “Pulse phase infrared thermography,” J. Appl. Phys. 79, 2694-2698 (1996).
[CrossRef]

Marinetti, S.

E. Grinzato, V. Vavilov, P. G. Bison, and S. Marinetti, “Hidden corrosion detection in thick metallic components by transient IR thermography,” Infrared Phys. Technol. 49, 234-238(2007).
[CrossRef]

Netzelmann, U.

S. Lugin and U. Netzelmann, “A defect shape reconstruction algorithm for pulsed thermography,” NDT & E Int. 40, 220-228 (2007).
[CrossRef]

S. Lugin and U. Netzelmann, “An effective compression algorithm for pulsed thermography data,” NDT & E Int. 38, 485-490 (2005).
[CrossRef]

Omar, M.

M. Omar, M. I. Hassan, K. Saito, and R. Alloo, “IR self-referencing thermography for detection of in-depth defects,” Infrared Phys. Technol. 46, 283-289 (2005).
[CrossRef]

M. Omar, M. I. Hassan, and K. Saito, “Optimizing thermography depth probing with a dynamic thermal point spread function,” Infrared Phys. Technol. 46, 506-514 (2005).
[CrossRef]

Paez, G.

M. Strojnik and G. Paez, “Determination of temperature distributions with micrometer spatial resolution,” Opt. Eng. 46, 036401 (2007).
[CrossRef]

G. Paez and M. Strojnik, “Thermal contrast detected with a quantum detector,” Infrared Phys. Technol. 46, 141-145(2004).
[CrossRef]

J. Sandoval, G. Paez, and M. Strojnik, “Heat transfer analysis of a dynamic infrared-to-visible converter,” Opt. Eng. 42, 3517-3523 (2003).
[CrossRef]

Rieger, G.

G. Rieger, “Lockin and burst-phase thermography for NDE,” Quant. Infrared Thermography 3, 141-154 (2006).
[CrossRef]

G. Rieger, T. Zweschper, and G. Busse, “Lock-in thermography with eddy current excitation,” Quant. Infrared Thermography 1, 21-32 (2004).

Rubadeux, B. A.

S. M. Shepard, J. R. Lhota, B. A. Rubadeux, T. Ahmed, and D. Wang, “Enhancement and reconstruction of thermographic data,” Proc. SPIE 4710, 531-535 (2002).

Saito, K.

M. Omar, M. I. Hassan, K. Saito, and R. Alloo, “IR self-referencing thermography for detection of in-depth defects,” Infrared Phys. Technol. 46, 283-289 (2005).
[CrossRef]

M. Omar, M. I. Hassan, and K. Saito, “Optimizing thermography depth probing with a dynamic thermal point spread function,” Infrared Phys. Technol. 46, 506-514 (2005).
[CrossRef]

Sandoval, J.

J. Sandoval, G. Paez, and M. Strojnik, “Heat transfer analysis of a dynamic infrared-to-visible converter,” Opt. Eng. 42, 3517-3523 (2003).
[CrossRef]

Scholl, M. S.

Shepard, S. M.

S. M. Shepard, J. R. Lhota, B. A. Rubadeux, T. Ahmed, and D. Wang, “Enhancement and reconstruction of thermographic data,” Proc. SPIE 4710, 531-535 (2002).

Spagnolo, P.

T. D'Orazio, C. Guaragnella, M. Leo, and P. Spagnolo, “Defect detection in aircraft composites by using a neural approach in the analysis of thermographic sequences,” NDT & E Int. 38, 665-673 (2005).
[CrossRef]

Strojnik, M.

M. Strojnik and G. Paez, “Determination of temperature distributions with micrometer spatial resolution,” Opt. Eng. 46, 036401 (2007).
[CrossRef]

G. Paez and M. Strojnik, “Thermal contrast detected with a quantum detector,” Infrared Phys. Technol. 46, 141-145(2004).
[CrossRef]

J. Sandoval, G. Paez, and M. Strojnik, “Heat transfer analysis of a dynamic infrared-to-visible converter,” Opt. Eng. 42, 3517-3523 (2003).
[CrossRef]

Susa, M.

M. Susa, H. D. Benitez, C. Ibarra-Castanedo, H. Loaiza, H. Bendada, and X. Maldague, “Phase contrast using a differentiated absolute contrast method,” Quant. Infrared Thermography 3, 219-230 (2006).
[CrossRef]

Vavilov, V.

E. Grinzato, V. Vavilov, P. G. Bison, and S. Marinetti, “Hidden corrosion detection in thick metallic components by transient IR thermography,” Infrared Phys. Technol. 49, 234-238(2007).
[CrossRef]

Wang, D.

S. M. Shepard, J. R. Lhota, B. A. Rubadeux, T. Ahmed, and D. Wang, “Enhancement and reconstruction of thermographic data,” Proc. SPIE 4710, 531-535 (2002).

Wu, D.

G. Busse, D. Wu, and W. Karpen, “Thermal wave imaging with phase sensitive modulated thermography,” J. Appl. Phys. 71, 3962-3965 (1992).
[CrossRef]

Ziadi, A.

X. Maldague, A. Ziadi, and M. Klein, “Double pulse infrared thermography,” NDT & E Int. 37, 559-564 (2004).
[CrossRef]

Zweschper, T.

G. Rieger, T. Zweschper, and G. Busse, “Lock-in thermography with eddy current excitation,” Quant. Infrared Thermography 1, 21-32 (2004).

Appl. Opt.

Infrared Phys. Technol.

M. Omar, M. I. Hassan, and K. Saito, “Optimizing thermography depth probing with a dynamic thermal point spread function,” Infrared Phys. Technol. 46, 506-514 (2005).
[CrossRef]

M. Omar, M. I. Hassan, K. Saito, and R. Alloo, “IR self-referencing thermography for detection of in-depth defects,” Infrared Phys. Technol. 46, 283-289 (2005).
[CrossRef]

G. Paez and M. Strojnik, “Thermal contrast detected with a quantum detector,” Infrared Phys. Technol. 46, 141-145(2004).
[CrossRef]

E. Grinzato, V. Vavilov, P. G. Bison, and S. Marinetti, “Hidden corrosion detection in thick metallic components by transient IR thermography,” Infrared Phys. Technol. 49, 234-238(2007).
[CrossRef]

J. Appl. Phys.

G. Busse, D. Wu, and W. Karpen, “Thermal wave imaging with phase sensitive modulated thermography,” J. Appl. Phys. 71, 3962-3965 (1992).
[CrossRef]

P. Cielo, “Pulsed photothermal evaluation of layered materials,” J. Appl. Phys. 56, 230-234 (1984).
[CrossRef]

X. Maldague and S. Marineti, “Pulse phase infrared thermography,” J. Appl. Phys. 79, 2694-2698 (1996).
[CrossRef]

J. Sci. Comput.

M. Branch, T. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” J. Sci. Comput. 21, 1-23 (1999).

NDT & E Int

S. Lugin and U. Netzelmann, “A defect shape reconstruction algorithm for pulsed thermography,” NDT & E Int. 40, 220-228 (2007).
[CrossRef]

NDT & E Int.

S. Lugin and U. Netzelmann, “An effective compression algorithm for pulsed thermography data,” NDT & E Int. 38, 485-490 (2005).
[CrossRef]

T. D'Orazio, C. Guaragnella, M. Leo, and P. Spagnolo, “Defect detection in aircraft composites by using a neural approach in the analysis of thermographic sequences,” NDT & E Int. 38, 665-673 (2005).
[CrossRef]

D. A. Gonzalez, C. Ibarra-Castanedo, J. M. Lopez-Higuera, and X. Maldague, “New algorithm based on the Hough transform for the analysis of pulsed thermographic sequences,” NDT & E Int. 39, 617-621 (2006).
[CrossRef]

N. P. Avdelidis, B. C. Hawtin, and D. P. Almond, “Transient thermography in the assessment of defects of aircraft composites,” NDT & E Int. 36, 433-439 (2003).
[CrossRef]

NDT & E Inte.

X. Maldague, A. Ziadi, and M. Klein, “Double pulse infrared thermography,” NDT & E Int. 37, 559-564 (2004).
[CrossRef]

Opt. Eng.

M. Strojnik and G. Paez, “Determination of temperature distributions with micrometer spatial resolution,” Opt. Eng. 46, 036401 (2007).
[CrossRef]

J. Sandoval, G. Paez, and M. Strojnik, “Heat transfer analysis of a dynamic infrared-to-visible converter,” Opt. Eng. 42, 3517-3523 (2003).
[CrossRef]

Proc. SPIE

S. M. Shepard, J. R. Lhota, B. A. Rubadeux, T. Ahmed, and D. Wang, “Enhancement and reconstruction of thermographic data,” Proc. SPIE 4710, 531-535 (2002).

C. Ibarra-Castanedo and X. Maldague, “Defect depth retrieval from pulsed phase thermographic data on plexiglas and aluminum samples,” Proc. SPIE 5405, 348-356 (2004).
[CrossRef]

M. S. Scholl, “Time and position varying infrared scene simulation,” Proc. SPIE 819, 297-301 (1987).

Quant. Infrared Thermography

G. Rieger, “Lockin and burst-phase thermography for NDE,” Quant. Infrared Thermography 3, 141-154 (2006).
[CrossRef]

G. Rieger, T. Zweschper, and G. Busse, “Lock-in thermography with eddy current excitation,” Quant. Infrared Thermography 1, 21-32 (2004).

M. Susa, H. D. Benitez, C. Ibarra-Castanedo, H. Loaiza, H. Bendada, and X. Maldague, “Phase contrast using a differentiated absolute contrast method,” Quant. Infrared Thermography 3, 219-230 (2006).
[CrossRef]

Other

H. Carslaw and J. Jaeger, Conduction of Heat in Solids (Oxford Univ. Press, 1959).

X. Maldague, Theory and Practice of Infrared Technology for Nondestructive Testing (Wiley-Interscience, 2001).

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Figures (9)

Fig. 1
Fig. 1

Compression of thermographic data for an object with two layers ( j = 2 ) . With the proposed thermal model, a sequence with any number of frames may be compressed to 2 j matrices.

Fig. 2
Fig. 2

Differentiated absolute contrast difference ( Δ θ ) corresponding to a defective zone of an object. The defect is detected when Δ θ differs from zero at ξ = ξ .

Fig. 3
Fig. 3

Scheme of the objects considered in our simulations. The front layer of each plate is PVC, while the rear layers of plates 2 and 3 are made of Duralumin. Dimensions are in millimeters.

Fig. 4
Fig. 4

Thermograms of the simulated sequences illustrating the effects of the internal defects. The crosses indicate the location of the reference region. (a), (b), and (c) correspond to plates 1, 2, and 3, respectively.

Fig. 5
Fig. 5

(a) Average noise N r m s and (b) average signal-to-noise ratio SNR of the reconstruction process of simulated data corresponding to plate 3 for different pixel densities and integration times. These profiles allow us to determine the limits of the reconstruction process for this geometry, since further noise reduction for pixel densities higher than 300   pixels / mm 2 and integration times shorter than 1 ms is marginal.

Fig. 6
Fig. 6

The experimental setup is a reflection mode configuration that includes a data processing system, an IR camera, and two identical flash lamps synchronized to each other.

Fig. 7
Fig. 7

Experimental thermograms illustrating the real effects of the internal defects in plates (a) 1, (b) 2, and (c) 3. The crosses indicate the location of the reference region.

Fig. 8
Fig. 8

Typical reconstruction of pulsed thermographic data. These profiles correspond to the reference area of plate 3. They are obtained by applying Eqs. (5, 6) to T S M (dots) and T S R generated with the developed model (solid curve) and with a traditional model (dashed curve). The agreement between the dots and the solid curve demonstrates the accuracy of the developed model, Eq. (7). It also confirms the negligible contributions of convective and radiative losses. The error of the traditional model is appreciably higher.

Fig. 9
Fig. 9

3D depthgrams illustrating the detected defects inside plates (a) 1, (b) 2, and (c) 3. The upper and lower planes represent the front and rear surfaces of the object, respectively. Any dent on the upper plane indicates the existence of an internal defect, and its depth is straightforwardly read from the scale.

Tables (6)

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Table 1 Thermal Properties of Materials Employed

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Table 2 Coefficients of the Thermal Model Employed in the Simulations

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Table 3 Results from Reconstruction of Simulated Sequences

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Table 4 Parameters of Sequences Acquired During Inspection of Plates

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Table 5 Results from Reconstruction of Sequences Acquired During Inspections

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Table 6 Results of Characterization of Internal Defects Detected in Plates

Equations (14)

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· [ k ( x , y , z ) · T ( x , y , z , t ) ] p ( x , y , z , t ) = ρ c p T ( x , y , z , t ) t .
z [ k z ( z ) T ( x , y , z , t ) z ] = ρ ( z ) c p ( z ) T ( x , y , z , t ) t .
T ( x , y , z , t ) = T f + i = 1 j A i exp ( α i B i 2 t + B i z ) .
T S ( x , y , t ) = T f + i = 1 j A i exp ( t / τ i ) .
ξ ( t ) = t t f
θ = T S 0 T S T S 0 T S f .
θ ( x , y , ξ ) = 1 i = 1 j β i exp ( ξ / ψ i ) .
Δ θ ( x , y , ξ ) = | θ ( x , y , ξ ) θ ref ( x , y , ξ ) | .
d ( x , y ) = i = 1 g 1 ( α i t i ) 1 / 2 + { α g [ t f ξ ( x , y ) i = 1 g 1 t i ] } 1 / 2 .
N ( c , r , l ) = T S M ( c , r , l ) T S R ( c , r , l ) .
N r m s ( c , r ) = { [ l = 1 m N 2 ( c , r , l ) ] / m } 1 / 2 .
SNR ( c , r ) = 10 log { l = 1 m [ T S M ( c , r , l ) ] 2 l = 1 m [ N ( c , r , l ) χ ] 2 } .
N r m s = 1 p q c = 1 p r = 1 q N r m s ( c , r ) .
SNR = 1 p q c = 1 p r = 1 q SNR ( c , r ) .

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