Theoretical Analysis and Focal Length Estimation of a Lens for Free-Space Focused Beam Measurements

This paper presents a Gaussian beam–based theoretical analysis and full-wave electromagnetic simulations of a free-space focused beam lens designed to measure the electrical properties of mesh specimens used in next-generation satellite reflector antennas. The lens transmission process was calculated using geometrical optics, and post-transmission field propagation was modeled via the angular spectrum method. Using the Gaussian beam radius, on-axis field magnitude, and phase error, the focal length was predicted by comparison with simulation results. The focal length was estimated as the distance at which the phase error relative to the beam radius was minimized. The observed discrepancy between the estimated focal length and the design value is attributed to the combined effects of phase errors induced by lens thickness and diffraction across the operating frequency band.