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