Design of a Specular Aspheric Surface to Uniformly Radiate a Flat Surface using a Nonuniform Collimated Radiation Source

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Abstract
When uniform radiative heating is desired on a surface the radiative heating system normally suffers from either (1) low efficiency or (2) the heating not being as uniform as desired. Using an axisymmetric collimated but nonuniform source of radiation and a properly designed specular surface, uniform heating can be obtained at 100 percent efficiency. The differential equation which describes such a surface is derived. The derivation is facilitated by the use of a vectorial ray-trace formulation. The differential equation has been solved and results are presented for the case of an axisymmetric nonuniform collimated source uniformly heating a flat surface.