Study of reflectors for illumination via conformal maps

We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map that transforms the reflector’s shape into a curve that describes light’s direction after reflection. Both segmented reflectors and continuous reflectors are discussed, illustrating how certain reflector characteristics become apparent under this transformation. This method can also be used to study extended sources via translations.