## 4 Procedure and Analysis of Range Differentiation in 3D MMW Imaging
### Imaging Complex Targets: A Discussion on Physical Limitations of the Imaging System  
In the theoretical-computational part of the imaging experiment, we calculated the resolution limit of the imaging system using the Rayleigh criterion [16]. This criterion establishes the minimum resolvable angular separation (\(\theta\)) between two points as given in Equation (4):  
\[\theta\geq 1.22\frac{\lambda}{D} \tag{4}\]  
where \(\lambda\) is the wavelength of the radiation and \(D\) is the aperture diameter. For a given object distance (\(S_{0}\)), the angular resolution can be translated into the spatial resolution (d) using the relationship mentioned in Equation (5):  
\[d\geq 1.22\frac{\lambda S_{0}}{D} \tag{5}\]  
This equation quantifies the smallest resolvable physical distance at a given object distance, incorporating the system's design parameters. In this experiment, we used \(\lambda=0.003\), \(D=0.5\) m, and \(S_{0}=2\) m. Substituting these values into Equation (5), the minimum spatial resolution was calculated to be 0.01464 m (14.64 mm). This result aligns with the theoretical expectations of the system's resolution limit. It demonstrates the constraints imposed by diffraction and aperture size in the imaging system, emphasizing the trade-off between resolution and other design parameters. This resolution limit highlights the physical boundaries of the system's ability to differentiate fine details, particularly in imaging complex objects. In a practical experiment to determine the spatial resolution limit of the imaging system, two metal strips were used as test objects. The experiment revealed that the system could reliably distinguish the strips when they were separated by a minimum distance of \(8\) mm. At this limit, the distinction between the strips was achievable, albeit with reduced clarity compared with larger separations. When the strips were positioned closer than \(8\) mm, the system struggled to resolve them effectively, highlighting the practical resolution limit imposed by the imaging setup. This result aligns with the theoretical calculations and demonstrates the system's capability to detect fine spatial details within its operational constraints. Figure 11: Three-dimensional Topographical Plot of Depth Data from FMCW Radar Analysis: (**a**) Side view highlighting depth variations and elevation changes of the “H” shape with a 25 mm central projection, (**b**) Top view illustrating the overall structure and depth distribution, and (**c**) Full 3D perspective showcasing the entire surface, with the elevated central portion distinctly visible against the lower surrounding surface. The imaging results for a knife and a gun-shaped object, captured using the current 8 \(\times\) 8 pixel resolution system, highlight the spatial resolution limitations imposed by the physical configuration of the setup, particularly in accurately representing complex or curved objects. Due to the coarse resolution, the system struggles to capture finer structural details, making it difficult to faithfully reproduce the object's curved profile. Figure 12 presents grayscale images generated by the MMW imaging system for two objects--a knife and a gun-shaped object--along with photographs of the actual objects for comparison. The MMW images demonstrate the system's spatial limitations, where the 8 \(\times\) 8 pixel resolution introduces granularity that affects the accurate depiction of intricate shapes, especially for curved geometries like the knife. To address these limitations, we propose increasing the size of the imaging mirrors, which would reduce the resolution limit. For instance, doubling the mirror size could improve the resolution from 8 mm to 4 mm. However, to maintain compatibility with the improved resolution, smaller GDDs would be required.