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We describe the design and measured performance of an improved beam-scanning fan-beam antenna suitable for mm wavelengths. The fan beam is scanned in the direction orthogonal to the fan and can be polarized either in or orthogonal to this direction. The pillbox design is improved by the introduction of a third cylindrical reflector and optimum shaping of all reflector profiles using an iterative diffraction analysis that includes aberration and blockage effects. Good agreement between the calculated and measured results is obtained, confirming a beamwidth of 0.3° and a scan range of 13.5° (45 beamwidths) for both polarizations at 186 GHz.