The distribution of light in a searchlight beam is computed by determining the image formation at a point on the mirror or lens, then from this elemental image the image from a zone is derived: These zonal images are in turn summed graphically to find the beam from the complete searchlight. Some of the more important characteristics of a projected beam, such as angular width and the region in which the inverse square rule may be used to compute illumination, are outlined, and some attention is paid to the short range region that must often be used in testing. Lenses are discussed, largely to bring out their limitations, and some of the characteristics of the ellipsoid and hyperboloid are outlined. Test data on a mirror made of a combination of these two basic curves are presented to show how the filament images can be suppressed.
FRANK BENFORD, "The Projection of Light," J. Opt. Soc. Am. 35, 149-149 (1945)