Ground Radiation Pattern Generated by High-Altitude Reflectors

A method is given to calculate the shape a high-altitude reflector must have to produce any intensity distribution inside the illuminated ground area. The method consists of setting up and solving a differential equation appropriate to the required ground intensity distribution. Cylindrical and spherical mirrors are discussed in detail, and mirror shapes for producing a particular type of uniform ground illumination are derived. These shapes approach paraboloids in the limit when the mirror altitude is much greater than the diameter of the illuminated area.