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Point Light Source – Mathematical Description

Reflector simulation or analysis in SHAPE defines the parameter characterizing geometric and differential properties of the reflector, as well as incident and reflected rays parameters.

The solution is based on the ray tube intensity calculations, which correspond to a point light source.

For a point light source with a known spatial luminous intensity distribution, the solution in the near-field zone is normal illuminance created by the reflected light flux from the reflector's surface and the flux from the light source. In the far-field zone, the radius-vector of the receiving area is expressed as the distance from the reflector's point to the node on the working plane, tending to infinity, to pass to the far-field zone intensity.

Finding the reflector profile or synthesis problem for a point light source in SHAPE means determination of active surface shape of reflector when intensity distribution or efficiency criterion is prescribed. Finding the reflector shape is connected with simultaneous solution of the set of two equations - for mirror surface and light flux equation. A reflected luminous flux is equal to incident flux multiplied by reflectance factor.

You can download the full mathematical description of the reflector calculation for a point light source in SHAPE here.