## 3 Results
First, we opened the plastic lid of the upper part and joined the upper and the lower parts together to obtain a THz image as shown in Figure 5b. In the image, various metallic parts were clearly imaged including metal wiring patterns on the board and small electronic components. In addition, we could clearly see a USB connector and internal structures in the lower part of the pointer. Then, we imaged the pointer after closing the lid to demonstrate the see-through capability of the THz imaging system (Figure 5c). In the image, the battery was clearly shown, but details such as thin metal patterns, small electronic components on the board inside the pointer, and the USB connector were hardly recognized. Moreover, the contrast of the metal wiring patterns on the PCB board was reversed in some parts of the imaged area (see Figure A3 of Appendix A). We identified two major problems. The first problem is the absorption by the plastic lid. We measured the plastic lid by the THz time-domain spectroscopy (THz-TDS) and found that the absorption coefficient increases as the frequency increases and becomes larger than 5 cm\({}^{-1}\) at 0.5 THz (see Figure A4 of Appendix A). Unlike Teflon or high-density polyethylene, many commercial plastics absorb THz wave at high frequencies [18]. As a result, although high-frequency images provide high resolution, the frequency is practically limited by the signal-to-noise ratio of the system and the absorption loss of the material. The second problem is false contrast by the interference. As an example, at 0.67 THz, even a sheet of paper generates significant interference fringes in the image (see Figure A5 of Appendix A). The fault contrast of the metal patterns could be attributed to the interference effect and becomes a serious problem for higher frequencies. If the false contrast is due to interference, it can be removed by averaging the image over a range of frequencies. Thus, we scanned the imaging frequency at each pixel to obtain a broadband image. Besides, to further improve the detected signal intensity, we inserted the reference mirror M3 to utilize the homodyne amplification mechanism as explained in the following. Figure 5: THz see-through images of a laser pointer. (**a**) The photograph of the pointer (inside and outside). (**b**) The THz image at 0.67 THz after opening the lid of the upper part. (**c**) The THz image was obtained after closing the lid. (**d**) Broadband interferometric image. The images were obtained in mode 2. The current-voltage (I-V) characteristics of SBDs can be approximated by Taylor expansion as follows. \[I_{\text{SBD}}=I_{0}\Big{(}e^{V_{\text{THz}}/V_{\text{t}}}-1\Big{)}\sim I_{0} \Bigg{\{}\frac{V_{\text{THz}}}{V_{\text{t}}}+\frac{1}{2}\Big{(}\frac{V_{\text{ THz}}}{V_{\text{t}}}\Big{)}^{2}+\cdots\Bigg{\}} \tag{7}\]  
Here, \(V_{\text{t}}\) is the turn-on voltage of the SBD, and \(V_{\text{THz}}\) is the voltage generated by the input THz wave that can be expressed by,  
\[V_{\text{THz}}=V_{\text{Obj}}+V_{\text{Ref}}\propto A\cos\!\left(\omega t- kL_{\text{Obj}}\right)+B\cos\!\left(\omega t-kL_{\text{Ref}}\right), \tag{8}\]  
where \(V_{\text{Obj}}\) is generated by the THz beam from the sample, and \(V_{\text{Ref}}\) is by the THz beam from M3. \(L_{\text{Obj}}\) and \(L_{\text{Ref}}\) refer to the length of the THz beam path toward the sample and toward the M3, respectively. \(A\) and \(B\) corresponds to the electric field intensities from the sample object and the reference mirror, respectively. Ignoring higher-order terms, the rectification of the SBD detector is expressed by the square term of (7). By simple calculation, the rectified signal intensity can be expressed by:  
\[\hat{r}=\hat{d}-2\Big{(}\hat{d}\cdot\hat{n}\Big{)}\hat{n} \tag{4}\]0  
Note that \(2\omega\)t terms are ignored in the derivation of (9) because the high-frequency terms are not measured by the SBD due to the limited bandwidth.