This study focuses on the spatial and spectral beam characteristics in a terahertz (THz) broadband sub-wavelength imaging system using a solid immersion lens (SIL). Previously, we demonstrated a broadband sub-wavelength THz imaging system by integrating a SIL with a THz time-domain spectrometer (TDS). Key parameters that influence beam characteristics and, consequently, imaging performance, such as SIL misalignment tolerances and beam propagation from the SIL, constitute the primary focus of this investigation. Numerical simulations demonstrate that the system can tolerate millimeter-level transverse and longitudinal SIL position displacements, underscoring its robustness for sub-wavelength imaging in a wide frequency range. Additionally, numerical simulations of beam propagation characteristics reveal that the system achieves sub-wavelength imaging resolution up to 1 mm from the SIL at 0.5 THz, highlighting its potential for non-destructive testing of subsurface structures. These findings gain experimental validation through imaging stacked utility knife blades with sub-wavelength structures ranging from 0.2 to 2 THz.