Abstract
Terahertz (THz) time-of-flight tomography (TOFT), a nondestructive-evaluation technique for the stratigraphic characterization of structures with layers on the micron-to-millimeter scales, has proven to be challenging to apply to samples containing both micron-scale and millimeter-scale layers. In THz TOFT, echoes reflected from distant interfaces and defects are often obscured as they may be immersed in a noisy background as such features in the reflected signal may be weak due to attenuation and dispersion, leading to the loss of valuable information. Moreover, overlapping echoes from any optically thin layers, such as thin coatings on thick specimens, are likely to be mistaken for a single interface in reconstructing the stratigraphy. Thus, layered structures containing both thick and thin layers have proven problematic for THz TOFT characterization. In this paper, a sparse-deconvolution (SD) technique, based on an interior-point method, and including a propagation model accounting for dispersion is demonstrated. The method is shown to be successful in extracting the impulse response of samples that combine the challenges of both thick and thin layers. The robustness and effectiveness of this method are verified numerically and experimentally. While the proposed SD approach does not perform as well as cross-correlation (CC) techniques in terms of the maximum thickness, it can provide a clearer and more accurate reconstruction of moderately thick samples incorporating thin layers.
Similar content being viewed by others
References
J. Dong, J.B. Jackson, M. Melis, D. Giovanacci, G.C. Walker, A. Locquet, J.W. Bowen, and D.S. Citrin, “Terahertz frequency-wavelet domain deconvolution for stratigraphic and subsurface investigation of art painting,” Opt. Express, vol. 24, no. 23, pp. 26972-26985, 2016.
J. Dong, A. Locquet, M. Melis, and D.S. Citrin, “Global mapping of stratigraphy of an old-master painting using sparsity-based terahertz reflectometry,” Sci. Rep., vol. 7, no. 1, pp. 1-12, 2017.
C.L. Dandolo, J.P. Guillet, X. Ma, F. Fauquet, M. Roux, and P. Mounaix, “Terahertz frequency modulated continuous wave imaging advanced data processing for art painting analysis,” Opt. Express, vol. 26, no. 5, pp. 5358-5367, 2018.
M. Mikerov, R. Shrestha, P. van Dommelen, D.M. Mittleman, and M. Koch, “Analysis of ancient ceramics using terahertz imaging and photogrammetry,” Opt. Express, vol. 28, no. 15, pp. 22255-22263, 2020.
K. Krügener, J. Ornik, L.M. Schneider, A. Jäckel, C.L. Koch-Dandolo, E. Castro-Camus, N. Riedl-Siedow, M. Koch, and W. Viöl, “Terahertz inspection of buildings and architectural art,” Appl. Sci., vol. 10, no. 15, pp. 5166, 2020.
J. Dong, A. Locquet, and D.S. Citrin, “Terahertz quantitative nondestructive evaluation of failure modes in polymer-coated steel,” IEEE J Sel Top Quantum Electron., vol. 23, no. 4, pp. 1-7, 2016.
M. Zhai, A. Locquet, C. Roquelet, P. Alexandre, L. Dahéron, and D.S. Citrin, “Nondestructive measurement of mill-scale thickness on steel by terahertz time-of-flight tomography,” Surf. Coat. Technol., vol. 393, pp. 125765, 2020.
M. Zhai, A. Locquet, C. Roquelet, L.A. Ronqueti, and D.S. Citrin, “Thickness characterization of multi-layer coated steel by terahertz time-of-flight tomography,” NDT & E Int., vol. 116, pp. 102358, 2020.
F.Ellrich, M. Bauer, N. Schreiner, A. Keil, T. Pfeiffer, J. Klier, S. Weber, J. Jonuscheit, F. Friederich, and D. Molter, “Terahertz quality inspection for automotive and aviation industries,” J. Infrared Millim. Terahertz Waves, vol. 41, no. 4, pp. 470-489, 2020.
J. Wang, Q. Sun, R.I. Stantchev, T.W. Chiu, A.T. Ahuja, and E. Pickwell-MacPherson, “In vivo terahertz imaging to evaluate scar treatment strategies: silicone gel sheeting,” Biomed. Opt. Express, vol. 10, no. 7, pp. 3584-3590, 2019.
A. Gong, Y. Qiu, X. Chen, Z. Zhao, L. Xia, and Y. Shao, “Biomedical applications of terahertz technology,” Appl. Spectrosc. Rev., vol. 55, no. 5, pp. 418-438, 2020.
Y. Chen, S. Huang, and E. Pickwell-MacPherson, “Frequency-wavelet domain deconvolution for terahertz reflection imaging and spectroscopy,” Opt. Express, vol. 18, no. 2, pp. 1177-1190, 2010.
J. Dong, X. Wu, A. Locquet, and D.S. Citrin, “Terahertz superresolution stratigraphic characterization of multilayered structures using sparse deconvolution,” IEEE Trans Terahertz Sci Technol., vol. 7, no. 3, pp. 260-267, 2017.
M. Zhai, A. Locquet, M. Jung, D. Woo, and D.S. Citrin, “Characterization of nanoporous Al2O3 films at terahertz frequencies,” Opt. Lett., vol. 45, no. 14, pp. 4092-4095, 2020.
J. Dong, A. Locquet, and D.S. Citrin, “Depth resolution enhancement of terahertz deconvolution by autoregressive spectral extrapolation,” Opt. Lett., vol. 42, no. 9, pp. 1828-1831, 2017.
M. Zhai, A. Locquet, C. Roquelet, and D.S. Citrin, “Terahertz Time-of-Flight Tomography Beyond the Axial Resolution Limit: Autoregressive Spectral Estimation Based on the Modified Covariance Method,” J. Infrared, Millim Terahertz Waves, vol. 41, no. 8, pp. 926-939, 2020.
K. Su, Y.C. Shen, and J.A. Zeitler, “Terahertz sensor for non-contact thickness and quality measurement of automobile paints of varying complexity,” IEEE Trans Terahertz Sci Technol., vol. 4, no. 4, pp. 432-439, 2014.
S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett., vol. 109, no. 2, pp. 021105, 2016.
T. Chang, Q. Guo, L. Liu, and H.L. Cui, “Hilbert-transform-based accurate determination of ultrashort-time delays in terahertz time-domain spectroscopy,” IEEE Trans Terahertz Sci Technol., vol. 7, no. 5, pp. 514-520, 2017.
M. Zhai, A. Locquet, and D.S. Citrin, “Pulsed THz imaging for thickness characterization of plastic sheets,” NDT & E Int., vol. 116, pp. 102338, 2020.
B. Qiao, X. Zhang, J. Gao, R. Liu, and X. Chen, “Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction,” Mech Syst Signal Process., vol. 83, pp. 93-115, 2017.
A. Beck, and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J Imaging Sci., vol. 2, no. 1, pp. 183-202, 2009.
I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math., vol. 57, no. 11, pp. 1413-1457, 2004.
J.M. Bioucas-Dias, and M.A. Figueiredo, "Two-step algorithms for linear inverse problems with non-quadratic regularization," in Proc. IEEE Int. Conf. Image Process (ICIP), 2007, vol. 1, pp. I-105. https://doi.org/10.1109/ICIP.2007.4378902.
J.M. Bioucas-Dias, and M.A. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans Image Process., vol. 16, no. 12, pp. 2992-3004, 2007.
X. Huang, K. He, S. Yoo, O. Cossairt, A. Katsaggelos, N. Ferrier, and M. Hereld, "An Interior Point Method for Nonnegative Sparse Signal Reconstruction," In Proc. 25th IEEE Int. Conf. Image Process. (ICIP), 2018, pp. 1193–1197. https://doi.org/10.1109/ICIP.2018.8451710.
K. Koh, S.J. Kim, and S. Boyd, “An interior-point method for large-scale l1-regularized logistic regression,” J Mach Learn Res. vol. 8, pp. 1519-1555, 2007.
M. Naftaly, and R.E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE, vol. 95, no. 8, pp. 1658-1665, 2007.
M.S. Islam, C.M.B. Cordeiro, M.J. Nine, J Sultana, A.L.S. Cruz, A. Dinovitser, B.W. Ng, H. Ebendorff-heidepriem, D. Losic, and D. Abbott, “Experimental Study on Glass and Polymers: Determining the Optimal Material for Potential Use in Terahertz Technology,” IEEE Access, vol. 8, 97204-97214, 2020.
D.M. Mittleman, R.H. Jacobsen, and M.C. Nuss, “T-ray imaging,” IEEE J Sel Top Quantum Electron., vol. 2, no. 3, pp. 679-692, 1996.
J. Pei, P. Ye, and W. Xie, "Optimal wavelet analysis for THz-TDS pulse signals," In Proc.Vol. 7277, Photonics and Optoelectronics Meetings (POEM) 2008: Terahertz Science and Technology, 2009, vol. 7277, p. 727708 (2009). https://doi.org/10.1117/12.819905.
M. Srivastava, C.L. Anderson, and J.H. Freed, “A new wavelet denoising method for selecting decomposition levels and noise thresholds,” IEEE Access, vol. 4, pp. 3862-3877, 2016.
Y.S. Jin, G.J. Kin, and S.G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc., vol. 49, no. 2, pp. 513-517, 2006.
Y. Chang, Y. Zi, J. Zhao, Z. Yang, W. He, and H. Sun, “An adaptive sparse deconvolution method for distinguishing the overlapping echoes of ultrasonic guided waves for pipeline crack inspection,” Meas Sci Technol., vol. 28, no. 3, pp. 035002, 2017.
Y. Xu, X. Fang, S. Fan, L. Zhang, R. Yan, and X. Chen, “Double Gaussian mixture model-based terahertz wave dispersion compensation method using convex optimization technique,” Mech. Syst. Signal Process., vol. 164, pp. 108223, 2022.
Acknowledgements
We gratefully acknowledge the support of Conseil Régional Grand Est and CPER SusChemProc.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhai, M., Citrin, D.S. & Locquet, A. Terahertz Nondestructive Stratigraphic Analysis of Complex Layered Structures: Reconstruction Techniques. J Infrared Milli Terahz Waves 42, 929–946 (2021). https://doi.org/10.1007/s10762-021-00819-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10762-021-00819-1