Using Terahertz (THz) beams with fairly large beam diameters (~20 mm) and short focal length lenses (25 mm) to
obtain a high spatial resolution makes it essential to use aspherical lenses. As High Density Polyethylene (HDPE) lenses
can be machined to any arbitrary shape with high surface quality, there are several free parameters that can be varied
when designing a lens that has no spherical aberrations. We present several different lens designs and evaluate their
performances in terms of losses and focal spot sizes. Geometrical optics is used to design the lenses but the Kirchhoff
Scalar Diffraction theory is employed to evaluate the beam sizes in the focal planes. The performances of the lenses were
also analyzed experimentally, where their focal spot sizes were measured and compared with our models. Results show
that spatial resolutions of less than the THz wavelengths (0.3 mm for 1 THz) are achievable with our imaging system.