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Reflector design based on the transformation of power densities.

When designing beam shaping reflectors to be used with compact-arc lamps it is convenient to treat the reflector as a transformation between the light distribution out of the source and the distribution out of the reflector. Using the calculus of transformations, the theory is developed for designing mirrors without hot spots in their output distributions. This theory is applied to the design of two classes of mirrors, one with a uniform angular output power distribution, the second with an approximately cosine squared output distribution. The usefulness of this approach is also illustrated by calculating the output distribution of a paraboloid.