The generating equation for a para-ellipsoid mirror is stated in the practical terms of the focal lengths and the diameter to give a fan-shaped beam of some particular spread. Calculations and measurements indicate that the intensity at an angle from the beam axis varies inversely with that angle, rather than being uniform throughout the width of the fan beam. An outline of the reverse calculation is given, starting from a desired fan-beam intensity ditribution to give the polar or cartesian coordinates of the required pseudo-paraboloid surface. The slope and curvature of a hypothetical 'directrix' surface are indicators of the beam divergence and of the intensity distribution.
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