Abstract-Terahertz Time-of-Flight Tomography Beyond the Axial Resolution Limit: Autoregressive Spectral Estimation Based on the Modified Covariance Method

Min Zhai, Alexandre Locquet, Cyrielle Roquelet,  D. S. Citrin

https://link.springer.com/article/10.1007/s10762-020-00722-1

We present a time-of-flight tomography method for exceeding the naïve axial (i.e., depth) resolution limit of terahertz (THz) deconvolution by autoregressive spectral extrapolation (AR) based on the modified covariance method (AR/MCM). In contrast to Wiener filtering combined with wavelet denoising, AR/MCM does not discard any frequency components in the low signal-to-noise (SNR) regions of the measured data, and unlike the AR approach based on the Burg method (AR/BM), no peak splitting (single peaks in the impulse response function appearing as double peaks) as well as frequency bias (spectral peaks shifted with respect to their correct positions) is observed after deconvolution. After verifying the advantages of AR/MCM over Wiener filtering in conjunction with wavelet denoising as well as over AR/BM, using synthetic data, AR/MCM is employed to reconstruct a single layer of mill scale on a steel coupon from experimental THz time-of-flight tomography data. The reconstruction shows good agreement with the film thickness obtained from destructive cross-sectional measurements. In addition, unlike AR/BM, optimizing the parameters to obtain stable reconstruction is straightforward relying of Akaike’s information criterion suggesting that AR/MCM can be an easier to implement for THz nondestructive characterization of stratigraphy under noisy conditions, particularly when estimates of the stratigraphy may not a priori be available.

Abstract-Nondestructive measurement of mill-scale thickness on steel by terahertz time-of-flight tomography

Min Zhai, Alexandre Locquet, Cyrielle Roquelet, Patrice Alexandre, Laurence Daheron, D.S.Citrin,



https://www.sciencedirect.com/science/article/abs/pii/S0257897220304345

We measure in a nondestructive and noncontact fashion the thicknesses of three scale films with thicknesses 28.5 ± 1.4 μm, 13.4± 0.9 μm, and 5.1 ± 0.3 μm on steel substrates employing terahertz time-of-flight tomography combined with advanced signal-processing techniques. Wüstite is the dominant phase in the scale films, though magnetite and hematite are also present. Because wüstite is electrically insulating, the incident terahertz electromagnetic pulses largely penetrate into the scale film; however, the pulses are entirely reflected by the underlying electrically conductive steel substrate. Because the film layers are thin, in some cases optically thin, the distinct pulses reflected at the air/scale and scale/steel interfaces overlap in time and thus are not visually evident in the reflected terahertz signal, necessitating the use of deconvolution techniques to recover the sample structure. We compare the merits of three deconvolution techniques, one unsuccessful (frequency-wavelet domain deconvolution) and two successful (sparse deconvolution and autoregressive extrapolation), to characterize the thicknesses of these scale films.