## 3 Results  
First, the FOV of the imaging system was estimated. We imaged a metallic square grid sample (grid period 2 cm, Figure 2a) with the scan angle of 80\({}^{\circ}\), twice times of the designed scan angle, as shown in Figure 2a. The images were acquired at 0.67 THz in mode 1 (Figure 2b) and mode 2 (Figure 2c). The FOV of the system was estimated to be \(\sim\)10 cm in diameter. In mode 2, however, a significant image distortion was observed when the image was presented in the coordinate system of the reflector (M1) angle. To correct this, the image should be presented in the coordinate system of the deflected angle. Figure 1: Schematic of the terahertz (THz) imaging system used in this study. Figure 2: Estimation of the imaging area and distortion. (**a**) Metal grid sample. The grid period is 20 mm. (**b**) Mode 1 imaging result. (**c**) Mode 2 imaging result, showing significant distortion. (**d**) Coordinate and normal vector definitions to derive image correction equations. (**e**) Corrected grid image. (**f**) The rectangular grid on the \(\alpha-\beta\) plane (grid period: 10\({}^{\circ}\)), projected on the object plane of L3. The relationship between the reflector angle (\(\varphi\) and \(\theta\) represent axis 1 and axis 3 angle, respectively) and the deflection angle of the beam (\(\alpha\) and \(\beta\) represent the azimuth and elevation angle, respectively) can be calculated as follows. In Figure 2d, unit vectors along the incident beam direction, the surface normal direction of the mirror, and the deflected beam direction are designated by \(\hat{d}\), \(\hat{n}\), and \(\hat{r}\), respectively. The axis of the mirror rotation (axis 1) is the \(x\)-axis of the primed coordinate system. Here, \(\hat{n}\) is expressed by:  
\[\hat{n}=-\frac{1}{\sqrt{2}}\hat{x^{\prime}}+\frac{1}{\sqrt{2}}\cos\varphi\hat{ y^{\prime}}+\frac{1}{\sqrt{2}}\sin\varphi\hat{z^{\prime}} \tag{1}\]  
The primed and unprimed coordinates are related by:  
\[\left( \begin{array}{c}x\prime\\ y\prime\end{array} \right)=\left( \begin{array}{cc}\cos\theta&-\sin\theta\\ \sin\theta&\cos\theta\end{array} \right)\left( \begin{array}{c}x\\ y\end{array} \right) \tag{2}\]  
Thus, in the unprimed coordinate, \(\hat{n}\) can be expressed by:  
\[\hat{n}=\frac{1}{\sqrt{2}}(\sin\theta\cos\varphi-\cos\theta)\hat{x}+\frac{1}{ \sqrt{2}}(\sin\theta+\cos\theta\cos\varphi)\hat{y}+\frac{1}{\sqrt{2}}\sin\varphi\hat {z} \tag{3}\]  
The unit vector for the deflected beam, \(\hat{r}\), is calculated by:  
\[\hat{r}=\hat{d}-2\Big{(}\hat{d}\cdot\hat{n}\Big{)}\hat{n} \tag{4}\]  
As a result, \(\alpha\) and \(\beta\) are calculated by the following equations. \[\alpha=\cos^{-1}\frac{\cos\varphi\cos 2\theta+\sin^{2}\varphi\sin\theta\cos \theta}{\sqrt{1-\sin^{2}\varphi(\cos\theta-\sin\theta\cos\varphi)^{2}}} \tag{5}\]  
\[\beta=\frac{\pi}{2}-\cos^{-1}\{\sin\varphi(\cos\theta-\sin\theta\cos\varphi)\} \tag{6}\]  
By applying the (5) and (6), the mode 2 image (Figure 2c) was corrected, as shown in Figure 2e. Outside of the designed field of view (6 cm in diameter), small distortions were still observed even after the correction. This is due to the lens (L3) design. To show this, we presented the projection of a ray grid on the object surface, shown in Figure 2f. The input ray grid was rectangular in the \(\alpha\)-\(\beta\) coordinates of which period was \(10^{\circ}\) in both directions. Outside of the designed FOV area, the projected footprint deviates from an ideal rectangular grid. This explains the residual distortion. For the best resolutions over the broad frequency region, the collimated beam diameter should be as large as possible, which is practically limited by the size of the optics. In the case of the current imaging setup, the beam diameter is limited by the size of L2 and the reflector, to be 5 cm. To ensure the maximum beam diameter after the collimation lens, L2, a variable iris is inserted at the focus of L1.