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.

中文翻译：

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超出轴向分辨率极限的太赫兹飞行时间层析成像：基于修正协方差方法的自回归谱估计

我们提出了一种基于改进的协方差方法（AR / MCM）的飞行时间层析成像方法，该方法通过自回归谱外推（AR）超过太赫兹（THz）反卷积的原始轴向（即深度）分辨率极限。与维纳滤波结合小波去噪相比，AR / MCM不会丢弃测量数据的低信噪比（SNR）区域中的任何频率分量，与基于Burg方法的AR方法（AR / BM）不同），在解卷积之后，未观察到峰分裂（脉冲响应函数中的单个峰显示为双峰）以及频率偏差（谱峰相对于其正确位置发生了偏移）。在使用综合数据验证了AR / MCM优于Wiener滤波结合小波去噪以及AR / BM的优势之后，AR / MCM用于从实验THz飞行时间断层扫描数据重建钢样板上的单层氧化皮。重建结果与从破坏性横截面测量获得的膜厚显示出良好的一致性。此外，与AR / BM不同，优化参数以获得稳定的重建直接依赖于Akaike的信息标准，这表明AR / MCM可以在嘈杂条件下更容易实现太赫兹地层的非破坏性表征，尤其是在地层估计值较高的情况下。没有先验的。