Topographical abnormality in corneal tissue is a common diagnostic marker for many eye diseases and injuries. Using an asynchronous optical sampling terahertz time-domain spectroscopy setup, we developed a non-contact and normal-incidence imaging system to measure topographic changes along the surface of spherical samples. We obtained orthogonal 1D scans of calibration spheres to evaluate the minimum axial resolution of our system. We determined the axial and spatial resolution of the scanner using 3D-printed spherical cross and Boehler star targets. Furthermore, we characterized the asymmetrical performance of the scanner due to the use of an off-axis parabolic mirror. Finally, we developed an edge-detection filter to aid with improving the topographic scans. We showed that when imaging samples were comparable in size to the human cornea, the axial and spherical spatial resolutions were limited to about 15 µm (∼λ/67) and 1 mm, respectively.