A nonimaging illumination optical device for producing a selected far field illuminance over an angular range. The optical device includes a light source, a light reflecting surface, and a family of light edge rays defined along a reference line with the reflecting surface defined in terms of the reference line as a parametric function R(t) where t is a scalar parameter position and R(t)=k(t)+Du(t) where k(t) is a parameterization of the reference line, and D is a distance from a point on the reference line to the reflection surface along the desired edge ray through the point. 35 figs.