A method of constructing a non-imaging beam transformer includes reducing a tailored illumination function from a predetermined light source to a source point response illumination function; calculating a plurality of transformation pairs for the predetermined light source, the transformation pairs identifying the radii of illumination of the light source at given source output angles; determining a desired lighting profile for light output at a region of interest to be illuminated by the beam transformer; determining a surface profile of a surface of the beam transformer such that for given output angles of the light source, the transformation pairs at those output angles are satisfied to correspond to the desired lighting profile; and constructing the beam transformer having the surface profile determined based on the transformation pairs. The method can include characterizing a specific angular output distribution of a light source to calculate the transformation pairs.