In order to obtain the Etendue Conservation Curve the problem is formulated as a piecewise function with two
parabolic sections at the start and end of the curve and a curve in the center which conserves etendue. Parabolic
curves with a single target conserve etendue by definition, while Chaves [4] defines the etendue conservation for
multiple targets which can be expressed as follows (with the symbols defined in Figure1)