Abstract

Terahertz time domain spectroscopy (TDS) was assessed as a nondestructive evaluation technique for aircraft composites. Damage to glass fiber was studied including voids, delaminations, mechanical damage, and heat damage. Measurement of the material properties on samples with localized heat damage showed that burning did not change the refractive index or absorption coefficient noticeably; however, material blistering was detected. Voids were located by TDS transmissive imaging using amplitude and phase techniques. The depth of delaminations was measured via the timing of Fabry-Perot reflections after the main pulse. Evidence of bending stress damage and simulated hidden cracks was also detected with terahertz imaging.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2008

Y. C. Shen, P. F. Taday, and M. Pepper, "Elimination of scattering effects in spectral measurement of granulated materials using terahertz time domain spectroscopy," Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

V. Myroshnychenko and C. Brosseau, "Effective complex permittivity of two-phase random composite media: a test of the two exponent phenomenological percolation equation," J. Appl. Phys. 103, 084112 (2008).
[CrossRef]

S. Lee, "Scattering by a dense layer of infinite cylinders at normal incidence," J. Opt. Soc. Am. A 25, 1022-1029 (2008).
[CrossRef]

2007

M. Naftaly and R. Miles, "Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties," J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostman, M. Koch, and T. Kurner, "Scattering analysis for the modeling of thz communication systems," IEEE Trans. Ant. Prop. 55, 3002-3009 (2007).
[CrossRef]

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, "Determination of additive content in polymeric compounds with terahertz time-domain spectroscopy," Polym. Test. 26, 614-618 (2007).
[CrossRef]

J. R. Fletcher, G. P. Swift, Dai De Chang, J. A. Levitt, and J. M. Chamberlain "Propagation of terahertz radiation through random structures: an alternative theoretical approach and experimental validation,"J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

W. Chan, J. Deibel, and D. Mittleman, "Imaging with terahertz radiation," Rep. Prog. Phys. 70, 1325-1379 (2007).
[CrossRef]

S. Wietzke, C. Jordens, N. Krumbholz, B. Baudrit, M. Bastian, and M. Koch, "Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints," J. Euro. Opt. Soc. 2, 07013 (2007).
[CrossRef]

2006

A. Cooney and J. Blackshire, "Advanced imaging of hidden damage under aircraft coatings," Proc. SPIE 617902, 1-11 (2006).

F. Rutz, R. Koch, S. Khare, M. Moneke, H. Richter, and U. Ewert, "Terahertz quality control of polymeric products," Int. J. Infrared Millim. Waves 27, 547-556 (2006).
[CrossRef]

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, "Terahertz birefringence of liquid crystal polymers," Appl. Phys. Lett. 89, 221911 (2006).
[CrossRef]

M. Reiten, L. Hess, and R. Cheville, "Nondestructive evaluation of ceramic materials using terahertz impulse ranging," Proc. SPIE 617905, 1-8 (2006).

J. Baxter and C. Schmuttenmaer, "Conductivity of ZnO nanowires, nanoparticles, and thin films using time-resolved terahertz spectroscopy," J. Phys. Chem. B 110, 25229-25239 (2006).
[CrossRef] [PubMed]

2005

K. J. Chau, S. Mujumdar, and A. Y. Elezzabi, "Terahertz propagation in non-homogeneous strongly scattering media," Proc. SPIE 5727, 177-185 (2005).
[CrossRef]

E. Tuncer, N. Bowler, and I. J. Youngs, "Application of the spectral density function method to a composite system," Physica B 373, 306-312 (2005).
[CrossRef]

2004

S. Wang and X. Zhang, "Pulsed terahertz tomography," J. Appl. Phys. D 37R1-R36 (2004).
[CrossRef]

2002

J. Pearce and D. Mittleman, "Scale model experimentation: using terahertz pulses to study light scattering," Phys. Med. Biol. 47, 3823-3830 (2002).
[CrossRef] [PubMed]

2001

1935

D. Bruggeman, "Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen," Ann. Phys. 24, 636 (1935).
[CrossRef]

Bastian, M.

S. Wietzke, C. Jordens, N. Krumbholz, B. Baudrit, M. Bastian, and M. Koch, "Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints," J. Euro. Opt. Soc. 2, 07013 (2007).
[CrossRef]

Baudrit, B.

S. Wietzke, C. Jordens, N. Krumbholz, B. Baudrit, M. Bastian, and M. Koch, "Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints," J. Euro. Opt. Soc. 2, 07013 (2007).
[CrossRef]

Baxter, J.

J. Baxter and C. Schmuttenmaer, "Conductivity of ZnO nanowires, nanoparticles, and thin films using time-resolved terahertz spectroscopy," J. Phys. Chem. B 110, 25229-25239 (2006).
[CrossRef] [PubMed]

Blackshire, J.

A. Cooney and J. Blackshire, "Advanced imaging of hidden damage under aircraft coatings," Proc. SPIE 617902, 1-11 (2006).

Bowler, N.

E. Tuncer, N. Bowler, and I. J. Youngs, "Application of the spectral density function method to a composite system," Physica B 373, 306-312 (2005).
[CrossRef]

Brosseau, C.

V. Myroshnychenko and C. Brosseau, "Effective complex permittivity of two-phase random composite media: a test of the two exponent phenomenological percolation equation," J. Appl. Phys. 103, 084112 (2008).
[CrossRef]

Bruggeman, D.

D. Bruggeman, "Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen," Ann. Phys. 24, 636 (1935).
[CrossRef]

Chan, W.

W. Chan, J. Deibel, and D. Mittleman, "Imaging with terahertz radiation," Rep. Prog. Phys. 70, 1325-1379 (2007).
[CrossRef]

Chau, K. J.

K. J. Chau, S. Mujumdar, and A. Y. Elezzabi, "Terahertz propagation in non-homogeneous strongly scattering media," Proc. SPIE 5727, 177-185 (2005).
[CrossRef]

Cheville, R.

M. Reiten, L. Hess, and R. Cheville, "Nondestructive evaluation of ceramic materials using terahertz impulse ranging," Proc. SPIE 617905, 1-8 (2006).

Cooney, A.

A. Cooney and J. Blackshire, "Advanced imaging of hidden damage under aircraft coatings," Proc. SPIE 617902, 1-11 (2006).

Dai De Chang, G. P.

J. R. Fletcher, G. P. Swift, Dai De Chang, J. A. Levitt, and J. M. Chamberlain "Propagation of terahertz radiation through random structures: an alternative theoretical approach and experimental validation,"J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

Deibel, J.

W. Chan, J. Deibel, and D. Mittleman, "Imaging with terahertz radiation," Rep. Prog. Phys. 70, 1325-1379 (2007).
[CrossRef]

Elezzabi, A. Y.

K. J. Chau, S. Mujumdar, and A. Y. Elezzabi, "Terahertz propagation in non-homogeneous strongly scattering media," Proc. SPIE 5727, 177-185 (2005).
[CrossRef]

Ewert, U.

F. Rutz, R. Koch, S. Khare, M. Moneke, H. Richter, and U. Ewert, "Terahertz quality control of polymeric products," Int. J. Infrared Millim. Waves 27, 547-556 (2006).
[CrossRef]

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, "Terahertz birefringence of liquid crystal polymers," Appl. Phys. Lett. 89, 221911 (2006).
[CrossRef]

Fletcher, J. R.

J. R. Fletcher, G. P. Swift, Dai De Chang, J. A. Levitt, and J. M. Chamberlain "Propagation of terahertz radiation through random structures: an alternative theoretical approach and experimental validation,"J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

Hasek, T.

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, "Terahertz birefringence of liquid crystal polymers," Appl. Phys. Lett. 89, 221911 (2006).
[CrossRef]

Hess, L.

M. Reiten, L. Hess, and R. Cheville, "Nondestructive evaluation of ceramic materials using terahertz impulse ranging," Proc. SPIE 617905, 1-8 (2006).

Jansen, C.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostman, M. Koch, and T. Kurner, "Scattering analysis for the modeling of thz communication systems," IEEE Trans. Ant. Prop. 55, 3002-3009 (2007).
[CrossRef]

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, "Determination of additive content in polymeric compounds with terahertz time-domain spectroscopy," Polym. Test. 26, 614-618 (2007).
[CrossRef]

Jordens, C.

S. Wietzke, C. Jordens, N. Krumbholz, B. Baudrit, M. Bastian, and M. Koch, "Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints," J. Euro. Opt. Soc. 2, 07013 (2007).
[CrossRef]

Khare, S.

F. Rutz, R. Koch, S. Khare, M. Moneke, H. Richter, and U. Ewert, "Terahertz quality control of polymeric products," Int. J. Infrared Millim. Waves 27, 547-556 (2006).
[CrossRef]

Kleine-Ostman, T.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostman, M. Koch, and T. Kurner, "Scattering analysis for the modeling of thz communication systems," IEEE Trans. Ant. Prop. 55, 3002-3009 (2007).
[CrossRef]

Koch, M.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostman, M. Koch, and T. Kurner, "Scattering analysis for the modeling of thz communication systems," IEEE Trans. Ant. Prop. 55, 3002-3009 (2007).
[CrossRef]

S. Wietzke, C. Jordens, N. Krumbholz, B. Baudrit, M. Bastian, and M. Koch, "Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints," J. Euro. Opt. Soc. 2, 07013 (2007).
[CrossRef]

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, "Determination of additive content in polymeric compounds with terahertz time-domain spectroscopy," Polym. Test. 26, 614-618 (2007).
[CrossRef]

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, "Terahertz birefringence of liquid crystal polymers," Appl. Phys. Lett. 89, 221911 (2006).
[CrossRef]

Koch, R.

F. Rutz, R. Koch, S. Khare, M. Moneke, H. Richter, and U. Ewert, "Terahertz quality control of polymeric products," Int. J. Infrared Millim. Waves 27, 547-556 (2006).
[CrossRef]

Krumbholz, N.

S. Wietzke, C. Jordens, N. Krumbholz, B. Baudrit, M. Bastian, and M. Koch, "Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints," J. Euro. Opt. Soc. 2, 07013 (2007).
[CrossRef]

Kurner, T.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostman, M. Koch, and T. Kurner, "Scattering analysis for the modeling of thz communication systems," IEEE Trans. Ant. Prop. 55, 3002-3009 (2007).
[CrossRef]

Lee, S.

Miles, R.

M. Naftaly and R. Miles, "Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties," J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

Mittleman, D.

W. Chan, J. Deibel, and D. Mittleman, "Imaging with terahertz radiation," Rep. Prog. Phys. 70, 1325-1379 (2007).
[CrossRef]

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, "Determination of additive content in polymeric compounds with terahertz time-domain spectroscopy," Polym. Test. 26, 614-618 (2007).
[CrossRef]

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostman, M. Koch, and T. Kurner, "Scattering analysis for the modeling of thz communication systems," IEEE Trans. Ant. Prop. 55, 3002-3009 (2007).
[CrossRef]

J. Pearce and D. Mittleman, "Scale model experimentation: using terahertz pulses to study light scattering," Phys. Med. Biol. 47, 3823-3830 (2002).
[CrossRef] [PubMed]

J. Pearce and D. Mittleman, "Propagation of single-cycle terahertz pulses in random media," Opt. Lett. 26, 2002-2004 (2001).
[CrossRef]

Moneke, M.

F. Rutz, R. Koch, S. Khare, M. Moneke, H. Richter, and U. Ewert, "Terahertz quality control of polymeric products," Int. J. Infrared Millim. Waves 27, 547-556 (2006).
[CrossRef]

Mujumdar, S.

K. J. Chau, S. Mujumdar, and A. Y. Elezzabi, "Terahertz propagation in non-homogeneous strongly scattering media," Proc. SPIE 5727, 177-185 (2005).
[CrossRef]

Myroshnychenko, V.

V. Myroshnychenko and C. Brosseau, "Effective complex permittivity of two-phase random composite media: a test of the two exponent phenomenological percolation equation," J. Appl. Phys. 103, 084112 (2008).
[CrossRef]

Naftaly, M.

M. Naftaly and R. Miles, "Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties," J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

Pearce, J.

J. Pearce and D. Mittleman, "Scale model experimentation: using terahertz pulses to study light scattering," Phys. Med. Biol. 47, 3823-3830 (2002).
[CrossRef] [PubMed]

J. Pearce and D. Mittleman, "Propagation of single-cycle terahertz pulses in random media," Opt. Lett. 26, 2002-2004 (2001).
[CrossRef]

Pepper, M.

Y. C. Shen, P. F. Taday, and M. Pepper, "Elimination of scattering effects in spectral measurement of granulated materials using terahertz time domain spectroscopy," Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

Piesiewicz, R.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostman, M. Koch, and T. Kurner, "Scattering analysis for the modeling of thz communication systems," IEEE Trans. Ant. Prop. 55, 3002-3009 (2007).
[CrossRef]

Reiten, M.

M. Reiten, L. Hess, and R. Cheville, "Nondestructive evaluation of ceramic materials using terahertz impulse ranging," Proc. SPIE 617905, 1-8 (2006).

Richter, H.

F. Rutz, R. Koch, S. Khare, M. Moneke, H. Richter, and U. Ewert, "Terahertz quality control of polymeric products," Int. J. Infrared Millim. Waves 27, 547-556 (2006).
[CrossRef]

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, "Terahertz birefringence of liquid crystal polymers," Appl. Phys. Lett. 89, 221911 (2006).
[CrossRef]

Rutz, F.

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, "Determination of additive content in polymeric compounds with terahertz time-domain spectroscopy," Polym. Test. 26, 614-618 (2007).
[CrossRef]

F. Rutz, R. Koch, S. Khare, M. Moneke, H. Richter, and U. Ewert, "Terahertz quality control of polymeric products," Int. J. Infrared Millim. Waves 27, 547-556 (2006).
[CrossRef]

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, "Terahertz birefringence of liquid crystal polymers," Appl. Phys. Lett. 89, 221911 (2006).
[CrossRef]

Schmuttenmaer, C.

J. Baxter and C. Schmuttenmaer, "Conductivity of ZnO nanowires, nanoparticles, and thin films using time-resolved terahertz spectroscopy," J. Phys. Chem. B 110, 25229-25239 (2006).
[CrossRef] [PubMed]

Shen, Y. C.

Y. C. Shen, P. F. Taday, and M. Pepper, "Elimination of scattering effects in spectral measurement of granulated materials using terahertz time domain spectroscopy," Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

Swift, G. P.

J. R. Fletcher, G. P. Swift, Dai De Chang, J. A. Levitt, and J. M. Chamberlain "Propagation of terahertz radiation through random structures: an alternative theoretical approach and experimental validation,"J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

Taday, P. F.

Y. C. Shen, P. F. Taday, and M. Pepper, "Elimination of scattering effects in spectral measurement of granulated materials using terahertz time domain spectroscopy," Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

Tuncer, E.

E. Tuncer, N. Bowler, and I. J. Youngs, "Application of the spectral density function method to a composite system," Physica B 373, 306-312 (2005).
[CrossRef]

Wang, S.

S. Wang and X. Zhang, "Pulsed terahertz tomography," J. Appl. Phys. D 37R1-R36 (2004).
[CrossRef]

Wietzke, S.

S. Wietzke, C. Jordens, N. Krumbholz, B. Baudrit, M. Bastian, and M. Koch, "Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints," J. Euro. Opt. Soc. 2, 07013 (2007).
[CrossRef]

S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, "Determination of additive content in polymeric compounds with terahertz time-domain spectroscopy," Polym. Test. 26, 614-618 (2007).
[CrossRef]

Youngs, I. J.

E. Tuncer, N. Bowler, and I. J. Youngs, "Application of the spectral density function method to a composite system," Physica B 373, 306-312 (2005).
[CrossRef]

Zhang, X.

S. Wang and X. Zhang, "Pulsed terahertz tomography," J. Appl. Phys. D 37R1-R36 (2004).
[CrossRef]

Ann. Phys.

D. Bruggeman, "Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen," Ann. Phys. 24, 636 (1935).
[CrossRef]

Appl. Phys. Lett.

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, "Terahertz birefringence of liquid crystal polymers," Appl. Phys. Lett. 89, 221911 (2006).
[CrossRef]

Y. C. Shen, P. F. Taday, and M. Pepper, "Elimination of scattering effects in spectral measurement of granulated materials using terahertz time domain spectroscopy," Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

IEEE Trans. Ant. Prop.

R. Piesiewicz, C. Jansen, D. Mittleman, T. Kleine-Ostman, M. Koch, and T. Kurner, "Scattering analysis for the modeling of thz communication systems," IEEE Trans. Ant. Prop. 55, 3002-3009 (2007).
[CrossRef]

Int. J. Infrared Millim. Waves

F. Rutz, R. Koch, S. Khare, M. Moneke, H. Richter, and U. Ewert, "Terahertz quality control of polymeric products," Int. J. Infrared Millim. Waves 27, 547-556 (2006).
[CrossRef]

J. Appl. Phys.

V. Myroshnychenko and C. Brosseau, "Effective complex permittivity of two-phase random composite media: a test of the two exponent phenomenological percolation equation," J. Appl. Phys. 103, 084112 (2008).
[CrossRef]

J. R. Fletcher, G. P. Swift, Dai De Chang, J. A. Levitt, and J. M. Chamberlain "Propagation of terahertz radiation through random structures: an alternative theoretical approach and experimental validation,"J. Appl. Phys. 101, 013102 (2007).
[CrossRef]

M. Naftaly and R. Miles, "Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties," J. Appl. Phys. 102, 043517 (2007).
[CrossRef]

J. Appl. Phys. D

S. Wang and X. Zhang, "Pulsed terahertz tomography," J. Appl. Phys. D 37R1-R36 (2004).
[CrossRef]

J. Euro. Opt. Soc.

S. Wietzke, C. Jordens, N. Krumbholz, B. Baudrit, M. Bastian, and M. Koch, "Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints," J. Euro. Opt. Soc. 2, 07013 (2007).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. Chem. B

J. Baxter and C. Schmuttenmaer, "Conductivity of ZnO nanowires, nanoparticles, and thin films using time-resolved terahertz spectroscopy," J. Phys. Chem. B 110, 25229-25239 (2006).
[CrossRef] [PubMed]

Opt. Lett.

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J. Pearce and D. Mittleman, "Scale model experimentation: using terahertz pulses to study light scattering," Phys. Med. Biol. 47, 3823-3830 (2002).
[CrossRef] [PubMed]

Physica B

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[CrossRef]

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S. Wietzke, C. Jansen, F. Rutz, D. Mittleman, and M. Koch, "Determination of additive content in polymeric compounds with terahertz time-domain spectroscopy," Polym. Test. 26, 614-618 (2007).
[CrossRef]

Proc. SPIE

M. Reiten, L. Hess, and R. Cheville, "Nondestructive evaluation of ceramic materials using terahertz impulse ranging," Proc. SPIE 617905, 1-8 (2006).

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D. Zimdars, J. White, G. Stuk, A. Chernovsky, G. Fichter, and S. Williamson, "Large area terahertz imaging and non-destructive evaluation applications," presented at the Fourth International Workshop on Ultrasonic and Advanced Methods for Nondestructive Testing and Material Characterization, UMass Dartmouth, N. Dartmouth, MA, 19 June 2006.

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Figures (13)

Fig. 1.
Fig. 1.

THz TDS system used in transmission configuration for imaging and material parameter measurements.

Fig. 2.
Fig. 2.

Photograph showing the 5 glass fiber samples: (1) thickness calibration sample, (2) & (3) burn samples, (4) mechanical stress sample, and (5) hidden defect sample showing the hidden location of two of the eight defects.

Fig. 3.
Fig. 3.

THz TDS (a) pulse and (b) amplitude spectra for air reference and through glass fiber.

Fig. 4.
Fig. 4.

THz TDS material parameter measurements using actual thickness measurements for polyimide showing (a) index of refraction and (b) absorption coefficient. The calculated scattering coefficient for the glass fiber composite is shown in part c.

Fig. 5.
Fig. 5.

THz TDS material parameter measurements using actual thickness measurements for burn damage areas showing (a) indices of refraction and (b) absorption coefficients.

Fig. 6.
Fig. 6.

THz TDS material parameter measurements, assuming the same thickness, for burn damage areas showing (a) indices of refraction and (b) absorption coefficients.

Fig. 7.
Fig. 7.

THz TDS images showing a section of the glass fiber that had been milled to two different thicknesses using peak pulse amplitude (a) and peak pulse position (b) techniques.

Fig. 8.
Fig. 8.

THz TDS images for three burn areas on glass fiber samples: (a) 440°C for 4 minutes, (b) 430°C for 6 minutes, and (c) 425°C for 20 minutes.

Fig. 9.
Fig. 9.

THz TDS (a) pulse and (b) amplitude spectra for undamaged glass fiber sample and for an area with burn damage (440°C for 4 minutes).

Fig. 10.
Fig. 10.

THz TDS images showing 3 mm diameter milled area hidden between two glass fiber strips using (a) peak pulse amplitude and (b) peak pulse position. Linear slit void (6 mm length) (c) also hidden between two strips of glass fiber.

Fig. 11.
Fig. 11.

THz TDS image showing bend damage across the central bend axis.

Fig. 12.
Fig. 12.

THz pulses after propagating through (a) laminated and delaminated portions of a glass fiber strip. (b) Autocorrelation of each of the two pulses showing the approximate location of Fabry-Perot reflections. THz pulse propagation in the opposite direction showing pulses and their autocorrelations (c), (d).

Fig. 13.
Fig. 13.

Chart showing the relative strength of the first Fabry-Perot reflection after traveling through various thicknesses of glass fiber material.

Equations (8)

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n ( ω ) = 1 + c [ ϕ sam ( ω ) ϕ ref ( ω ) ] ω d
a ( ω ) = 2 d ln [ E sam ( ω ) T ( ω ) E ref ( ω ) ]
T ( ω ) = 4 n ( ω ) ( n ( ω ) + 1 ) 2 .
f [ ε i ε eff ε i + K ε eff ] + ( 1 f ) [ ε h ε eff ε h + K ε eff ] = 0
σ TM = 2 π 5 a 4 λ 3 ( m 2 1 ) 2
σ TE = 4 π 5 a 4 λ 3 [ m 2 1 m 2 + 1 ] 2
μ s ( ω ) = [ n 0 σ s ( ω ) ]
μ e = μ s + a .

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