# A Novel High-Precision Imaging Radar for Quality Inspection of Building Insulation Layers
## 3 Radar System Design
### Ultra-Wideband High-Bunching Antenna Design
#### 3.3.2 Ultra-Wideband High-Bunching Antenna
R is the radius of the hemisphere lens and is wide enough to cover the antennas. d is the height of the cylinder, and the radius of the cylinder is larger than R to reserve space for securing. D is the distance between the antenna and the dielectric lens. It assumes that propagating rays are illuminated from a single-point source. [PERSON]'s law of refraction is applied at the point of incidence at the bottom surface of the lens in Figure 10; we obtain \(\sin(\eta)=\sin(\gamma)\), where \(\eta\) is the incident angle and \(n\) is a refractive index. We hope that the electromagnetic wave emerging from the lens is a plane wave. Based on this, we assume that the transmission angle is \(\alpha+\gamma\) at the point of the exit at the upper surface of the lens, so then the incidence angle is \(\alpha\), \(\sin(\alpha)=\sin(\alpha+\gamma)\), and \(\theta+\alpha+\gamma=\frac{\pi}{2}\). The following electric path condition can be imposed, which means equal propagation time,  
\[\phi(r)=(-1)^{p}\cdot\alpha_{p}\cdot\sin\left[\frac{\pi\cdot\ln\left(\frac{r}{ R_{p}}\right)}{\ln\left(\tau_{p}\right)}\right]\quad R_{p+1}\leq r\leq R_{p} \tag{7}\]0  
where  
\[\phi(r)=(-1)^{p}\cdot\alpha_{p}\cdot\sin\left[\frac{\pi\cdot\ln\left(\frac{r}{ R_{p}}\right)}{\ln\left(\tau_{p}\right)}\right]\quad R_{p+1}\leq r\leq R_{p} \tag{7}\]1  
\[\phi(r)=(-1)^{p}\cdot\alpha_{p}\cdot\sin\left[\frac{\pi\cdot\ln\left(\frac{r}{ R_{p}}\right)}{\ln\left(\tau_{p}\right)}\right]\quad R_{p+1}\leq r\leq R_{p} \tag{7}\]2 VSWR curve. The standing wave ratio is less than 3 in the 6–12 GHz range, which means the voltage reflection is less than 50%, which ensures high antenna transmission efficiency. \[\phi(r)=(-1)^{p}\cdot\alpha_{p}\cdot\sin\left[\frac{\pi\cdot\ln\left(\frac{r}{ R_{p}}\right)}{\ln\left(\tau_{p}\right)}\right]\quad R_{p+1}\leq r\leq R_{p} \tag{7}\]3 Plane pattern of each typical frequency point, 4 GHz, 6 GHz, 8 GHz, and 10 GHz, and they are all one-sided spherical radiation patterns with good directivity. The distance D is chosen to be \(\lambda_{c}/2\) based on the fact that microwave impedance matching features are repeated every \(\lambda_{c}/2\). The relative dielectric constant of acrylic materials typically ranges from 2.6 to 3.4, varying depending on the manufacturing process and formulation. By investigating and calculating, we finally designed a lens made of acrylic materials with a dielectric constant of 3.0. It has a hemisphere with a radius of 27.5 mm and a cylinder with a height of 8 mm. Figure 11 shows the geometry of the transmitted wave without (blue line) and with (red line) the lens. The lens obviously makes the wave beam more focused. Reflective Backplane  
In practical applications, we only need to use the energy radiated by the antenna toward the medium side. The energy radiated by the antenna facing away from the medium will interfere with the system and cause many adverse effects. In order to make the antenna obtain unidirectional radiation characteristics, we add metal coating on the back of the micro-strip feeder to enhance the radiation directivity so that the antenna has close to zero radiation in the back direction. The commonly used reflective cavity is a flat-bottomed reflective cavity; the depth of the cavity is \(\lambda/4\), where \(\lambda\) is the wavelength corresponding to the center frequency of the antenna and the cavity diameter is the same as the antenna's outer diameter [36].