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This paper focuses on the analysis and design of a dielectric lens antenna and its application for ground penetrating radar (GPR) at millimeter waves. The work investigates the influence of different design parameters on the resolution performance of GPR using a dielectric lens for focusing. The performance of the optical focusing of the dielectric lens is compared to a synthetic-aperture-Radar (SAR) algorithm. Our purpose is to optimize the spatial resolution of a Ka-Band (26-40 GHz) GPR. A dielectric lens is designed to minimize the footprint of the antenna. The lens focuses the radiated energy from the feeding point to a small spot onto the soil surface. A commercial time-domain solver based on finite-integration-technique (FIT) is used to simulate the electromagnetic characteristics of the lens antenna model. A lens prototype is fabricated and tested at our GPR test site. The investigation of the microwave images for special targets shows that both focusing methods, namely the proposed lens antenna and SAR algorithm, improve the image resolution. However the experimental results reveal that SAR applied to the unfocussed data outperforms the dielectric lens.