Analytical correction of spherical aberration in low-refractive-index terahertz lenses

Terahertz (THz) imaging relies on effective focusing optics, yet conventional high-performance solutions, such as aspherical or high-refractive-index lenses often entail significant cost and manufacturing complexity. Widely used low-cost polymeric spherical lenses, while easy to fabricate, suffer from severe spherical aberrations, limiting resolution and system performance, especially for short focal lengths or large apertures. This paper presents a novel analytical correction that mitigates the Seidel aberrations in short-focal-length THz lenses made with low-refractive-index materials ( n ≈ 1.45 ) without resorting to computationally intensive optimization or complicated profiles. We derive an analytical expression for a corrected elliptical lens profile designed to emulate the phase accumulation characteristics of a better performing high-refractive-index lens. This method maintains the simplicity of elliptical surfaces in terms of design and manufacturing while significantly enhancing the focusing capabilities. To validate this approach, we designed, numerically simulated, fabricated, and finally experimentally characterized three distinct 1.5-inch diameter polymeric THz lenses with a target focal length of 50 mm: a standard plano-convex spherical lens, the analytically corrected elliptical lens, and an optimized aspherical lens. Experimental THz beam profiling shows FWHM values of 0.741, 0.586, and 0.577 mm, respectively, with numerical simulations corroborating the experimental findings. Hence, this work provides a practical and computationally inexpensive pathway, compatible with 3-axis CNC machines, to substantially improve the performance of basic THz lenses made of common polymers.