# Nondestructive Tomographic Imaging of Rust with Rapid THz Time-Domain Spectroscopy
## 3 Results and Discussion  
Figure 2b shows the THz-TOF image of the rusted metal plate covered by a paint film, as shown in the photograph in Figure 2a. To verify the usefulness of our technique, we sprayed a paint layer with a thickness of 230 \(\upmu\)m on a partially rusted metal film. The inset  
Figure 1: Schematic illustration of the THz-TOF imaging equipment. Tx and Rx denote the THz emitter and receiver, respectively, from the OSCAT THz-TDS system. of Figure 2a shows a photograph when we removed the paint film. Figure 2b shows the time-integrated C-scan data (plotted as a function of the \(x\)- and \(y\)-axes). The THz envelope signal obtained via the Hilbert transformation was time-integrated for each pixel. Here, the envelope function was obtained from the complex function, \(\widetilde{E}_{\text{THz}}=E_{\text{THz}}+iH(E_{\text{THz}})\), where \(E_{\text{THz}}\) is the phase-sensitive THz amplitude from the measurement, and \(H\)(\(x\)) is the Hilbert transformation of \(x\)[29]. The scan range was 20 \(\times\) 30 mm\({}^{2}\) with a pixel size of 80 \(\times\) 120 pixel\({}^{2}\). The bright signal in the upper middle region indicates the conductive metal region without rust formation, whereas the other regions are severely corroded. The formation of iron oxides, which strongly absorb the THz waves, is responsible for the reduced reflection in the rust region, and has been addressed elsewhere [30; 31; 32]. Two-dimensional tomographic images allow us to obtain depth profiles of the objects, reconstructed from the original 3D binary data. In other words, Figure 2c is a B-scan image in which the THz envelope signal is shown as a function of position (\(x\)) along the horizontal dashed line in Figure 2b and time (\(T\)). Another B-scan image is shown in Figure 2d, which was taken along the vertical dashed line in Figure 2b. The rusted (where the reflected signal is weak) and the nonrusted regions can be clearly distinguished. The THz reflection at the paint's top surface and metal surface appeared at \(T\) = 24 and 26 ps, respectively, as shown in the inset of Figure 2d. The TOF time difference of 2 ps between the top and bottom is consistent with the paint thickness of 230 \(\upmu\)m, considering the refractive index of the paint (\(n\) = 2.6). The rusted area can be clearly identified in the TOF imaging, whereas the time-integrated imaging does not distinguish between the low reflection originating from the rust and that from the destructive interference. Therefore, THz-TOF imaging is advantageous over conventional NDT imaging techniques that are frequently obscured by the presence of lift-off in the paint layer [9]. Figure 3a shows a series of frequency-resolved C-scan images obtained using a Fourier transformation of the phase-sensitive THz amplitudes, which allows us to inspect the objects at specific spectral ranges. In other words, C-scan images were obtained for 0.4, 0.7, 1.0, and 1.3 THz (from left to right in the figure). As discussed earlier, the transverse resolution can be substantially improved by employing high-frequency components; in other words, the signal resolution improves from 1.8 mm at 0.4 THz to 700 \(\upmu\)m at 1.0 THz [28]. In addition to the improved spatial resolution, the reflection from the rust-rich region is suppressed more for the high-frequency components in general, whereas some of iron oxides have a relative strong absorption below 1 THz [31]. Figure 3b shows plots of the THz amplitude as a function of position along the vertical dashed line in Figure 3a, taken for different frequency components. THz reflection was suppressed relatively strongly at the rusted area (for \(y\) > 15 mm) with increasing frequency. Therefore, it is desirable to have THz sources with higher frequency ranges for efficient nondestructive testing of the rusted metal with a better image contrast and transverse resolution. Figure 2: (**a**) Photograph of rusted metal concealed by paint. (**b**) Time-integrated C-scan image (in terms of envelope function) for (**a**).