## 6 Presentation and Analysis of Results
### Discussion  
In the past, coherent laser radar-based vibration detection was developed to enable precise measurement of an object's vibration characteristics owing to its high Doppler resolution. Vibration imagery holds significant potential for long-range target classification and identification, including detecting camouflaged or partially concealed targets. Sample vibration images have been captured using laser radars operating at wavelengths of 10.6 \(\upmu\)m as well as 1.54 \(\upmu\)m at distances of up to 3 km [41]. However, laser sensors are unable to operate under conditions of dust, fog, and rain, and are not eye-safe, suggesting the use of microwave radar approaches for detecting target vibrations. Unfortunately, there does not appear to be much published work on this topic to the knowledge of the authors. Characterizing vehicle vibrations from afar using Doppler radar is important for several reasons. Doppler radar enables vibration analysis without requiring physical contact with the vehicle. A radar system can provide a holistic view of vibrations across the entire vehicle body rather than localized points where sensors are typically attached. Radar is effective across a wide range of conditions, including dust, fog, rain, and low-light or high-temperature environments, where traditional optical sensors might fail. Remote vibration characterization can help identify unique vibration \"signatures\" of specific vehicles, which may be useful in security, surveillance, or military applications for vehicle classification and monitoring. Characterizing vehicle vibrations from afar using Doppler radar also presents several challenges. Adverse weather conditions, such as wind and heavy rain, may induce additional vibrations which can degrade measurement accuracy. Vibrations on vehicle surfaces may produce weak radar returns, making it difficult to isolate the stronger vibration signal from background fluctuations. Vehicles have multiple vibration sources, including the engine, drivetrain, tires, and suspension. Separating these overlapping signals to identify individual sources can be challenging. Accurately capturing high-frequency and low-frequency components simultaneously requires a radar system with high dynamic range and resolution. The radar's ability to detect vibrations depends on the reflectivity (radar cross-section) of the vehicle's surface. Non-metallic or low-reflective surfaces, such as carbon fiber or composite materials, can result in poor signal quality. If the radar is not positioned optimally relative to the vehicle surface, the reflected signals may weaken, reducing measurement reliability. Figure 27: Spectrogram histograms for radar and acoustic data at 23 Hz and 45 Hz. As the distance between the radar and the vehicle increases, the signal weakens, making it harder to detect small vibration amplitudes. At greater distances, it becomes more challenging to focus the radar beam precisely on the vibrating components of interest. The radar system must be carefully calibrated to ensure that measurements reflect true vibration amplitudes and frequencies. Results obtained from Doppler radar need to be validated against ground truth data from traditional sensors (e.g., accelerometers), which can be challenging to implement. Proper positioning and alignment of the radar relative to the vehicle can be time-consuming and require expertise. Detecting vehicle vibrations behind foliage using micro-Doppler radar presents significant challenges due to signal attenuation and scattering caused by the foliage. While specific studies directly addressing this scenario are limited, related research provides insights into the feasibility of such detection. A study using a laser Doppler vibrometer (LDV) at a wavelength of 632.8 nm explored detecting vehicles concealed by foliage by measuring vibrations of tree leaves induced by vehicle engine noise [42]. The findings indicated that the vibrations of leaves, excited by vehicle-generated sound, were detectable using the LDV.