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The design and optimization of the TOPHAT feed horn is presented. This horn is a nonimaging antenna with a few modes. Diffraction effects are approximated using ray-trace techniques with the addition of phase information.
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Dale J. Fixsen, "Multimode antenna optimization," Proc. SPIE 4446, Nonimaging Optics: Maximum Efficiency Light Transfer VI, (19 November 2001); https://doi.org/10.1117/12.448815