Design of reflectors which will distribute sunlight in a specified manner

A differential equation is obtained for the shape of a reflecting surface which will distribute axially symmetric light intensity into a specified irradiance over a receiver surface which is symmetric about the direction of the incident light. Results are applied to the design of rotationally symmetric solar reflectors and also to a 2-dimensional geometry, that is one in which the reflector is a cylinder with its axis perpendicular to the incident beam. The procedure is used to numerically calculate the shape of reflectors which will uniformly concentrate collimated light and also light from a point source over a flat receiver surface. Results are also applied to determine the shape of a reflector which will distribute collimated light uniformly over the surface of a cylinder and also over a sphere.