Abstract

In this paper, we demonstrated a novel thermal-wave radar imaging approach with use of a dual-directional (down then up) chirp (or linear frequency modulation, LFM) modulated laser as an external excitation source and signal processing by Fractional Fourier transform (FrFT), which can enhance the defect detectability and extend the depth-resolution dynamic range. The thermal-wave signal was reconstructed by use of dimensionless normalization scaling (DNS) method, and furthermore, it explored the centralized feature of energy spectral density in FrFT domain. The amplitude and phase angle at the peak energy density in FrFT domain were extracted to form the corresponding image and used for the defect detection and identification. The experiments were carried over a carbon fiber reinforced polymer (CFRP) specimen with the artificial flat bottom holes (FBHs) to validate the defect detection capability using FrFT based enhanced TWRI compared to the FFT based TWRI or conventional lock-in thermography (LIT) by taking the defect signal to noise ratio (SNR) into account.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  4. J. Y. Liu, Y. Wang, and J. M. Dai, “Research on thermal wave processing of lock-in thermography based on analyzing image sequences for NDT,” Infrared Phys. Technol. 53(5), 348–357 (2010).
    [Crossref]
  5. X. P. V. Maldague and S. Marinetti, “Pulsed phase infrared thermography,” J. Appl. Phys. 79(5), 2694–2698 (1996).
    [Crossref]
  6. N. Tabatabaei and A. Mandelis, “Thermal-wave radar: a novel subsurface imaging modality with extended depth-resolution dynamic range,” Rev. Sci. Instrum. 80(3), 034902 (2009).
    [Crossref] [PubMed]
  7. R. V. Hernandez, A. Melnikov, A. Mandelis, K. Sivagurunathan, and M. E. R. Garcia, “Non-destructive measurements of large case depths in hardened steels using the thermal-wave radar,” NDT Int. 45(1), 16–21 (2012).
    [Crossref]
  8. A. Mandelis, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part I: Theoretical,” Rev. Sci. Instrum. 57(4), 617–621 (1986).
    [Crossref]
  9. A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part II: Mirage effect spectrometer design and performance,” Rev. Sci. Instrum. 57(4), 622–629 (1986).
    [Crossref]
  10. A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part III: Mirage effect spectrometer, dynamic range, and comparison to pseudo-random-binary-sequence (PRBS) method,” Rev. Sci. Instrum. 57(4), 630–635 (1986).
    [Crossref]
  11. R. Mulaveesala and S. Tuli, “Theory of frequency modulated thermal wave imaging for nondestructive subsurface defect detection,” Appl. Phys. Lett. 89(19), 191913 (2006).
    [Crossref]
  12. R. Mulaveesala and S. Venkata Ghali, “Coded excitation for infrared non-destructive testing of carbon fiber reinforced plastics,” Rev. Sci. Instrum. 82(5), 054902 (2011).
    [Crossref] [PubMed]
  13. N. Tabatabaei, A. Mandelis, and B. T. Amaechi, “Thermophotonic radar imaging: An emissivity-normalized modality with advantages over phase lock-in thermography,” Appl. Phys. Lett. 98(16), 163706 (2011).
    [Crossref]
  14. N. Tabatabaei and A. Mandelis, “Thermal Coherence Tomography Using Match Filter Binary Phase Coded Diffusion Waves,” Phys. Rev. Lett. 107(16), 165901 (2011).
    [Crossref] [PubMed]
  15. A. Melnikov, K. Sivagurunathan, X. Guo, J. Tolev, A. Mandelis, K. Ly, and R. Lawcock, “Non-destructive thermal-wave-radar imaging of manufactured green powder metallurgy compact flaws (cracks),” NDT Int. 86, 140–152 (2017).
    [Crossref]
  16. B. Suresh, S. Subhani, A. Vijayalakshmi, V. H. Vardhan, and V. S. Ghali, “Chirp Z transform based enhanced frequency resolution for depth resolvable non stationary thermal wave imaging,” Rev. Sci. Instrum. 88(1), 014901 (2017).
    [Crossref] [PubMed]
  17. J. Gong, J. Liu, L. Qin, and Y. Wang, “Investigation of Carbon fiber reinforced polymer (CFRP) sheet with subsurface defects inspection using Thermal-wave radar imaging (TWRI) based on the Multi-Transform technique,” NDT Int. 62, 130–136 (2014).
    [Crossref]
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  19. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform (Wiley, 2001).
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    [Crossref]
  22. H. M. Ozaktas, O. Ankan, M. A. Kutay, and G. Bozdaki, “Digital Computation of Fractional Fourier Transform,” IEEE Trans. Signal Process. 44(9), 2141–2150 (1996).
    [Crossref]
  23. J. Y. Liu, Q. J. Tang, X. Liu, and Y. Wang, “Research on the quantitative analysis of subsurface defects for non-destructive testing by lock-in thermography,” NDT Int. 45(1), 104–110 (2012).
    [Crossref]

2017 (2)

A. Melnikov, K. Sivagurunathan, X. Guo, J. Tolev, A. Mandelis, K. Ly, and R. Lawcock, “Non-destructive thermal-wave-radar imaging of manufactured green powder metallurgy compact flaws (cracks),” NDT Int. 86, 140–152 (2017).
[Crossref]

B. Suresh, S. Subhani, A. Vijayalakshmi, V. H. Vardhan, and V. S. Ghali, “Chirp Z transform based enhanced frequency resolution for depth resolvable non stationary thermal wave imaging,” Rev. Sci. Instrum. 88(1), 014901 (2017).
[Crossref] [PubMed]

2014 (1)

J. Gong, J. Liu, L. Qin, and Y. Wang, “Investigation of Carbon fiber reinforced polymer (CFRP) sheet with subsurface defects inspection using Thermal-wave radar imaging (TWRI) based on the Multi-Transform technique,” NDT Int. 62, 130–136 (2014).
[Crossref]

2012 (2)

R. V. Hernandez, A. Melnikov, A. Mandelis, K. Sivagurunathan, and M. E. R. Garcia, “Non-destructive measurements of large case depths in hardened steels using the thermal-wave radar,” NDT Int. 45(1), 16–21 (2012).
[Crossref]

J. Y. Liu, Q. J. Tang, X. Liu, and Y. Wang, “Research on the quantitative analysis of subsurface defects for non-destructive testing by lock-in thermography,” NDT Int. 45(1), 104–110 (2012).
[Crossref]

2011 (3)

R. Mulaveesala and S. Venkata Ghali, “Coded excitation for infrared non-destructive testing of carbon fiber reinforced plastics,” Rev. Sci. Instrum. 82(5), 054902 (2011).
[Crossref] [PubMed]

N. Tabatabaei, A. Mandelis, and B. T. Amaechi, “Thermophotonic radar imaging: An emissivity-normalized modality with advantages over phase lock-in thermography,” Appl. Phys. Lett. 98(16), 163706 (2011).
[Crossref]

N. Tabatabaei and A. Mandelis, “Thermal Coherence Tomography Using Match Filter Binary Phase Coded Diffusion Waves,” Phys. Rev. Lett. 107(16), 165901 (2011).
[Crossref] [PubMed]

2010 (1)

J. Y. Liu, Y. Wang, and J. M. Dai, “Research on thermal wave processing of lock-in thermography based on analyzing image sequences for NDT,” Infrared Phys. Technol. 53(5), 348–357 (2010).
[Crossref]

2009 (1)

N. Tabatabaei and A. Mandelis, “Thermal-wave radar: a novel subsurface imaging modality with extended depth-resolution dynamic range,” Rev. Sci. Instrum. 80(3), 034902 (2009).
[Crossref] [PubMed]

2006 (1)

R. Mulaveesala and S. Tuli, “Theory of frequency modulated thermal wave imaging for nondestructive subsurface defect detection,” Appl. Phys. Lett. 89(19), 191913 (2006).
[Crossref]

2003 (1)

N. P. Avdelidis, B. C. Hawtin, and D. P. Almond, “Transient thermography in the assessment of defects of aircraft composites,” NDT Int. 36(6), 433–439 (2003).
[Crossref]

1998 (1)

1996 (3)

Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21(12), 842–844 (1996).
[Crossref] [PubMed]

H. M. Ozaktas, O. Ankan, M. A. Kutay, and G. Bozdaki, “Digital Computation of Fractional Fourier Transform,” IEEE Trans. Signal Process. 44(9), 2141–2150 (1996).
[Crossref]

X. P. V. Maldague and S. Marinetti, “Pulsed phase infrared thermography,” J. Appl. Phys. 79(5), 2694–2698 (1996).
[Crossref]

1994 (1)

L. B. Almeida, “Fractional Fourier Transform and Time-Frequency Representation,” IEEE Trans. Signal Process. 42(11), 3084–3091 (1994).
[Crossref]

1992 (1)

G. Busse, D. Wu, and W. Karpen, “Thermal-wave imaging with phase sensitive modulated thermography,” J. Appl. Phys. 71(8), 3962–3965 (1992).
[Crossref]

1986 (3)

A. Mandelis, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part I: Theoretical,” Rev. Sci. Instrum. 57(4), 617–621 (1986).
[Crossref]

A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part II: Mirage effect spectrometer design and performance,” Rev. Sci. Instrum. 57(4), 622–629 (1986).
[Crossref]

A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part III: Mirage effect spectrometer, dynamic range, and comparison to pseudo-random-binary-sequence (PRBS) method,” Rev. Sci. Instrum. 57(4), 630–635 (1986).
[Crossref]

Almeida, L. B.

L. B. Almeida, “Fractional Fourier Transform and Time-Frequency Representation,” IEEE Trans. Signal Process. 42(11), 3084–3091 (1994).
[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 Int. 36(6), 433–439 (2003).
[Crossref]

Amaechi, B. T.

N. Tabatabaei, A. Mandelis, and B. T. Amaechi, “Thermophotonic radar imaging: An emissivity-normalized modality with advantages over phase lock-in thermography,” Appl. Phys. Lett. 98(16), 163706 (2011).
[Crossref]

Ankan, O.

H. M. Ozaktas, O. Ankan, M. A. Kutay, and G. Bozdaki, “Digital Computation of Fractional Fourier Transform,” IEEE Trans. Signal Process. 44(9), 2141–2150 (1996).
[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 Int. 36(6), 433–439 (2003).
[Crossref]

Borm, L. M. L.

A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part II: Mirage effect spectrometer design and performance,” Rev. Sci. Instrum. 57(4), 622–629 (1986).
[Crossref]

A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part III: Mirage effect spectrometer, dynamic range, and comparison to pseudo-random-binary-sequence (PRBS) method,” Rev. Sci. Instrum. 57(4), 630–635 (1986).
[Crossref]

Bozdaki, G.

H. M. Ozaktas, O. Ankan, M. A. Kutay, and G. Bozdaki, “Digital Computation of Fractional Fourier Transform,” IEEE Trans. Signal Process. 44(9), 2141–2150 (1996).
[Crossref]

Busse, G.

G. Busse, D. Wu, and W. Karpen, “Thermal-wave imaging with phase sensitive modulated thermography,” J. Appl. Phys. 71(8), 3962–3965 (1992).
[Crossref]

Chen, N. X.

Cong, W. X.

Dai, J. M.

J. Y. Liu, Y. Wang, and J. M. Dai, “Research on thermal wave processing of lock-in thermography based on analyzing image sequences for NDT,” Infrared Phys. Technol. 53(5), 348–357 (2010).
[Crossref]

Dorsch, R. G.

Garcia, M. E. R.

R. V. Hernandez, A. Melnikov, A. Mandelis, K. Sivagurunathan, and M. E. R. Garcia, “Non-destructive measurements of large case depths in hardened steels using the thermal-wave radar,” NDT Int. 45(1), 16–21 (2012).
[Crossref]

Ghali, V. S.

B. Suresh, S. Subhani, A. Vijayalakshmi, V. H. Vardhan, and V. S. Ghali, “Chirp Z transform based enhanced frequency resolution for depth resolvable non stationary thermal wave imaging,” Rev. Sci. Instrum. 88(1), 014901 (2017).
[Crossref] [PubMed]

Gong, J.

J. Gong, J. Liu, L. Qin, and Y. Wang, “Investigation of Carbon fiber reinforced polymer (CFRP) sheet with subsurface defects inspection using Thermal-wave radar imaging (TWRI) based on the Multi-Transform technique,” NDT Int. 62, 130–136 (2014).
[Crossref]

Gu, B. Y.

Guo, X.

A. Melnikov, K. Sivagurunathan, X. Guo, J. Tolev, A. Mandelis, K. Ly, and R. Lawcock, “Non-destructive thermal-wave-radar imaging of manufactured green powder metallurgy compact flaws (cracks),” NDT Int. 86, 140–152 (2017).
[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 Int. 36(6), 433–439 (2003).
[Crossref]

Hernandez, R. V.

R. V. Hernandez, A. Melnikov, A. Mandelis, K. Sivagurunathan, and M. E. R. Garcia, “Non-destructive measurements of large case depths in hardened steels using the thermal-wave radar,” NDT Int. 45(1), 16–21 (2012).
[Crossref]

Karpen, W.

G. Busse, D. Wu, and W. Karpen, “Thermal-wave imaging with phase sensitive modulated thermography,” J. Appl. Phys. 71(8), 3962–3965 (1992).
[Crossref]

Kutay, M. A.

H. M. Ozaktas, O. Ankan, M. A. Kutay, and G. Bozdaki, “Digital Computation of Fractional Fourier Transform,” IEEE Trans. Signal Process. 44(9), 2141–2150 (1996).
[Crossref]

Lawcock, R.

A. Melnikov, K. Sivagurunathan, X. Guo, J. Tolev, A. Mandelis, K. Ly, and R. Lawcock, “Non-destructive thermal-wave-radar imaging of manufactured green powder metallurgy compact flaws (cracks),” NDT Int. 86, 140–152 (2017).
[Crossref]

Liu, J.

J. Gong, J. Liu, L. Qin, and Y. Wang, “Investigation of Carbon fiber reinforced polymer (CFRP) sheet with subsurface defects inspection using Thermal-wave radar imaging (TWRI) based on the Multi-Transform technique,” NDT Int. 62, 130–136 (2014).
[Crossref]

Liu, J. Y.

J. Y. Liu, Q. J. Tang, X. Liu, and Y. Wang, “Research on the quantitative analysis of subsurface defects for non-destructive testing by lock-in thermography,” NDT Int. 45(1), 104–110 (2012).
[Crossref]

J. Y. Liu, Y. Wang, and J. M. Dai, “Research on thermal wave processing of lock-in thermography based on analyzing image sequences for NDT,” Infrared Phys. Technol. 53(5), 348–357 (2010).
[Crossref]

Liu, X.

J. Y. Liu, Q. J. Tang, X. Liu, and Y. Wang, “Research on the quantitative analysis of subsurface defects for non-destructive testing by lock-in thermography,” NDT Int. 45(1), 104–110 (2012).
[Crossref]

Ly, K.

A. Melnikov, K. Sivagurunathan, X. Guo, J. Tolev, A. Mandelis, K. Ly, and R. Lawcock, “Non-destructive thermal-wave-radar imaging of manufactured green powder metallurgy compact flaws (cracks),” NDT Int. 86, 140–152 (2017).
[Crossref]

Maldague, X. P. V.

X. P. V. Maldague and S. Marinetti, “Pulsed phase infrared thermography,” J. Appl. Phys. 79(5), 2694–2698 (1996).
[Crossref]

Mandelis, A.

A. Melnikov, K. Sivagurunathan, X. Guo, J. Tolev, A. Mandelis, K. Ly, and R. Lawcock, “Non-destructive thermal-wave-radar imaging of manufactured green powder metallurgy compact flaws (cracks),” NDT Int. 86, 140–152 (2017).
[Crossref]

R. V. Hernandez, A. Melnikov, A. Mandelis, K. Sivagurunathan, and M. E. R. Garcia, “Non-destructive measurements of large case depths in hardened steels using the thermal-wave radar,” NDT Int. 45(1), 16–21 (2012).
[Crossref]

N. Tabatabaei and A. Mandelis, “Thermal Coherence Tomography Using Match Filter Binary Phase Coded Diffusion Waves,” Phys. Rev. Lett. 107(16), 165901 (2011).
[Crossref] [PubMed]

N. Tabatabaei, A. Mandelis, and B. T. Amaechi, “Thermophotonic radar imaging: An emissivity-normalized modality with advantages over phase lock-in thermography,” Appl. Phys. Lett. 98(16), 163706 (2011).
[Crossref]

N. Tabatabaei and A. Mandelis, “Thermal-wave radar: a novel subsurface imaging modality with extended depth-resolution dynamic range,” Rev. Sci. Instrum. 80(3), 034902 (2009).
[Crossref] [PubMed]

A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part III: Mirage effect spectrometer, dynamic range, and comparison to pseudo-random-binary-sequence (PRBS) method,” Rev. Sci. Instrum. 57(4), 630–635 (1986).
[Crossref]

A. Mandelis, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part I: Theoretical,” Rev. Sci. Instrum. 57(4), 617–621 (1986).
[Crossref]

A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part II: Mirage effect spectrometer design and performance,” Rev. Sci. Instrum. 57(4), 622–629 (1986).
[Crossref]

Marinetti, S.

X. P. V. Maldague and S. Marinetti, “Pulsed phase infrared thermography,” J. Appl. Phys. 79(5), 2694–2698 (1996).
[Crossref]

Melnikov, A.

A. Melnikov, K. Sivagurunathan, X. Guo, J. Tolev, A. Mandelis, K. Ly, and R. Lawcock, “Non-destructive thermal-wave-radar imaging of manufactured green powder metallurgy compact flaws (cracks),” NDT Int. 86, 140–152 (2017).
[Crossref]

R. V. Hernandez, A. Melnikov, A. Mandelis, K. Sivagurunathan, and M. E. R. Garcia, “Non-destructive measurements of large case depths in hardened steels using the thermal-wave radar,” NDT Int. 45(1), 16–21 (2012).
[Crossref]

Mendlovic, D.

Mulaveesala, R.

R. Mulaveesala and S. Venkata Ghali, “Coded excitation for infrared non-destructive testing of carbon fiber reinforced plastics,” Rev. Sci. Instrum. 82(5), 054902 (2011).
[Crossref] [PubMed]

R. Mulaveesala and S. Tuli, “Theory of frequency modulated thermal wave imaging for nondestructive subsurface defect detection,” Appl. Phys. Lett. 89(19), 191913 (2006).
[Crossref]

Ozaktas, H. M.

H. M. Ozaktas, O. Ankan, M. A. Kutay, and G. Bozdaki, “Digital Computation of Fractional Fourier Transform,” IEEE Trans. Signal Process. 44(9), 2141–2150 (1996).
[Crossref]

Qin, L.

J. Gong, J. Liu, L. Qin, and Y. Wang, “Investigation of Carbon fiber reinforced polymer (CFRP) sheet with subsurface defects inspection using Thermal-wave radar imaging (TWRI) based on the Multi-Transform technique,” NDT Int. 62, 130–136 (2014).
[Crossref]

Sivagurunathan, K.

A. Melnikov, K. Sivagurunathan, X. Guo, J. Tolev, A. Mandelis, K. Ly, and R. Lawcock, “Non-destructive thermal-wave-radar imaging of manufactured green powder metallurgy compact flaws (cracks),” NDT Int. 86, 140–152 (2017).
[Crossref]

R. V. Hernandez, A. Melnikov, A. Mandelis, K. Sivagurunathan, and M. E. R. Garcia, “Non-destructive measurements of large case depths in hardened steels using the thermal-wave radar,” NDT Int. 45(1), 16–21 (2012).
[Crossref]

Subhani, S.

B. Suresh, S. Subhani, A. Vijayalakshmi, V. H. Vardhan, and V. S. Ghali, “Chirp Z transform based enhanced frequency resolution for depth resolvable non stationary thermal wave imaging,” Rev. Sci. Instrum. 88(1), 014901 (2017).
[Crossref] [PubMed]

Suresh, B.

B. Suresh, S. Subhani, A. Vijayalakshmi, V. H. Vardhan, and V. S. Ghali, “Chirp Z transform based enhanced frequency resolution for depth resolvable non stationary thermal wave imaging,” Rev. Sci. Instrum. 88(1), 014901 (2017).
[Crossref] [PubMed]

Tabatabaei, N.

N. Tabatabaei and A. Mandelis, “Thermal Coherence Tomography Using Match Filter Binary Phase Coded Diffusion Waves,” Phys. Rev. Lett. 107(16), 165901 (2011).
[Crossref] [PubMed]

N. Tabatabaei, A. Mandelis, and B. T. Amaechi, “Thermophotonic radar imaging: An emissivity-normalized modality with advantages over phase lock-in thermography,” Appl. Phys. Lett. 98(16), 163706 (2011).
[Crossref]

N. Tabatabaei and A. Mandelis, “Thermal-wave radar: a novel subsurface imaging modality with extended depth-resolution dynamic range,” Rev. Sci. Instrum. 80(3), 034902 (2009).
[Crossref] [PubMed]

Tang, Q. J.

J. Y. Liu, Q. J. Tang, X. Liu, and Y. Wang, “Research on the quantitative analysis of subsurface defects for non-destructive testing by lock-in thermography,” NDT Int. 45(1), 104–110 (2012).
[Crossref]

Tiessinga, J.

A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part III: Mirage effect spectrometer, dynamic range, and comparison to pseudo-random-binary-sequence (PRBS) method,” Rev. Sci. Instrum. 57(4), 630–635 (1986).
[Crossref]

A. Mandelis, L. M. L. Borm, and J. Tiessinga, “Frequency modulated (FM) time delay photoacoustic and photothermal wave spectroscopies. Technique, Instrumentation, and detection. Part II: Mirage effect spectrometer design and performance,” Rev. Sci. Instrum. 57(4), 622–629 (1986).
[Crossref]

Tolev, J.

A. Melnikov, K. Sivagurunathan, X. Guo, J. Tolev, A. Mandelis, K. Ly, and R. Lawcock, “Non-destructive thermal-wave-radar imaging of manufactured green powder metallurgy compact flaws (cracks),” NDT Int. 86, 140–152 (2017).
[Crossref]

Tuli, S.

R. Mulaveesala and S. Tuli, “Theory of frequency modulated thermal wave imaging for nondestructive subsurface defect detection,” Appl. Phys. Lett. 89(19), 191913 (2006).
[Crossref]

Vardhan, V. H.

B. Suresh, S. Subhani, A. Vijayalakshmi, V. H. Vardhan, and V. S. Ghali, “Chirp Z transform based enhanced frequency resolution for depth resolvable non stationary thermal wave imaging,” Rev. Sci. Instrum. 88(1), 014901 (2017).
[Crossref] [PubMed]

Venkata Ghali, S.

R. Mulaveesala and S. Venkata Ghali, “Coded excitation for infrared non-destructive testing of carbon fiber reinforced plastics,” Rev. Sci. Instrum. 82(5), 054902 (2011).
[Crossref] [PubMed]

Vijayalakshmi, A.

B. Suresh, S. Subhani, A. Vijayalakshmi, V. H. Vardhan, and V. S. Ghali, “Chirp Z transform based enhanced frequency resolution for depth resolvable non stationary thermal wave imaging,” Rev. Sci. Instrum. 88(1), 014901 (2017).
[Crossref] [PubMed]

Wang, Y.

J. Gong, J. Liu, L. Qin, and Y. Wang, “Investigation of Carbon fiber reinforced polymer (CFRP) sheet with subsurface defects inspection using Thermal-wave radar imaging (TWRI) based on the Multi-Transform technique,” NDT Int. 62, 130–136 (2014).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 One-dimensional thermal-wave diffusion diagram.
Fig. 2
Fig. 2 The calculated results, (a) surface temperature, and (b) thermal-wave signal.
Fig. 3
Fig. 3 Thermal-wave radar signal FrFT processing block diagram.
Fig. 4
Fig. 4 The FrFT modulus distribution of calculated TWR signal, (a) TWR signal of defective region, and (b) TWR signal of healthy region.
Fig. 5
Fig. 5 (a) Experimental setup and (b) CFRP sheet specimen with artificial FBHs.
Fig. 6
Fig. 6 The responses of dual chirp modulated heat stimulus, chirp parameters: 0.2Hz-0.02Hz-0.2 Hz, frequency sweep rate of 0.0018 Hz/s, (a) surface temperature, and (b) thermal-wave radar signals.
Fig. 7
Fig. 7 (a) The FrFT modulus distribution of TWR signal in the healthy region with the fractional order range of 0<p<1, (b) the FrFT modulus peak comparisons at the fractional order p = 0.9323, and (c) the FFT modulus of TWR signal. Chirp parameters: 0.2Hz-0.02Hz-0.2Hz, frequency sweep rate of 0.0018Hz/s.
Fig. 8
Fig. 8 The amplitude and phase images from FrFT and FFT based, (a) FrFT peak amplitude (b) FrFT peak phase, (c) FFT amplitude, and (d) FFT phase, chirp parameters: 0.2Hz-0.02Hz-0.2Hz, frequency sweep rate of 0.0018Hz/s.
Fig. 9
Fig. 9 Profiles along the lines passing through the centers of defects, (a) FrFT amplitude, (b) FrFT phase, (c) FFT-amplitude and (d) FFT-phase.
Fig. 10
Fig. 10 The SNRs comparisons, (a) the SNRs of FrFT and FFT based amplitudes, and (b) the SNRs of FrFT and FFT based phases.
Fig. 11
Fig. 11 (a) FrFT peak ration angle (α = ppeakπ/2) image, and (b) the horizontal profiles of FrFT peak ration angle.
Fig. 12
Fig. 12 Defect depth scan using FrFT based analysis, (a) the real part of FrFT, (b) the imaginary part of FrFT and (c) FrFT phase.

Tables (1)

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Table 1 Estimated the size of defect using differential normalized distribution method

Equations (17)

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q(t)={ q 0 2 { 1cos[ 2π( f 0 + f e f 0 2 T s t )t ] } 0t T s q 0 2 { 1+cos[ 2π( f e f e f 0 2 T s (t T s ) )( t T s ) ] } T s t2 T s
T dc (t)= m=0 M A m t m
T ac (t)= T sur (t) T dc (t)
2 T(z,t) z 2 = ρc k z T(z,t) t
T d (0,t)= Q(ω) kσh r e 2σH +1 r 2 e 2σH 1 e jωt dt+ T 0
T h (0,t)= Q(ω) kσh r e 2σL +1 r 2 e 2σL 1 e jωt dt+ T 0
r= kσ+h kσh
σ= (1+j) Λ ;Λ= 2k ρcω = k ρcπf(t)
F α [ u,sTWR(t) ]= A α exp[ jπ( cotαcscα ) u 2 ] × exp[ jπcscα ( ut ) 2 ]exp[ jπ( cotαcscα ) t 2 ]sTWR(t)dt
A α = exp[ jπsgn( sinα )+ jα 2 ] | sinα | α pπ 2 ,0<| p |<2.
A m peak =max( | F α (u) | )
(p= p peak ,u= u peak ){ | F α (u) | p =0 | F α (u) | u =0
P h peak =atan{ Im[ F α (u) ]| | F α (u)|=max(| F α (u)|) Re[ F α (u) ]| | F α (u)|=max(| F α (u)|) }
SNR= | mean[I (x,y) x,y R D ]mean[I (x,y) x,y R H ] | σ( R H )
σ( R H )=std[I (x,y) x,y R H ]
A m R (α)=real [ F α (u) ] | F α (u) |=max| F α (u) |
A m I (α)=imag [ F α (u) ] | F α (u) |=max| F α (u) |

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