Three-mirror free-form off-axis antenna design of beam shaping on a circular substrate

This work presents a design of a three-mirror free-form surface beam shaping system with small dimensions, easy assembly, and good collimation. To facilitate integration and assembly, the three mirrors are integrated into a circular substrate with a radius of 90 mm. Based on the law of energy conservation, Fermat's principle, and the vector theory of reflection, the input-output mapping is derived, and the three free-form mirrors are constructed point by point simultaneously. Ray tracing results demonstrate that the maximum divergence angle is compressed to 0.467 mrad and the standard deviation of the edge beam radius samples (SDRS) is reduced from 5.42 mm to 0.985 mm on the receiving plane. The light intensity has a relative root mean square deviation (RRMSD) of only 0.049. Furthermore, the results show that the minimum value of SDRS is 0.940 mm at a propagation distance of L = 1.72 m, while the minimum value of RRMSD is 0.0431 at L = 7.03 m. In addition, the effects of astigmatism and light source offsets on the collimated and shaping effect are analyzed. The design of the free-form surfaces antenna system in this work will provide a new design method for practical engineering and application, and will greatly improve the quality and propagation distance of the Gaussian beam.