Design of mirrors for generating prescribed continuous illuminance distributions on the basis of the supporting quadric method.

A method for the design of reflecting surfaces generating prescribed continuous illuminance distributions in two-dimensional domains is proposed. The mirror surface is represented as an envelope of a two-parameter family of ellipsoids. The first focus of each ellipsoid coincides with the point light source, while the second one is located at the illuminated domain. This surface representation can be interpreted as a limiting case of a segmented surface used in the supporting quadric method for focusing onto a set of points. The envelope equation depends on the function defining the lengths of the major axes of the ellipsoids of the family. The calculation of this function is performed using a continuous approximation of a discrete function obtained from the solution of a discrete problem of focusing onto a set of points. High efficiency of the proposed method is illustrated by the designed examples of mirrors for generating uniform illuminance distributions in areas of different shapes.

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