Ray mapping method for off-axis and non-paraxial freeform illumination lens design

The ray mapping method for freeform illumination design is an easy and flexible method, but only in the paraxial regime does it result in surface normal fields that are directly integrable into continuous freeform surfaces that provide the desired illuminance distribution. A new mapping scheme is proposed to alter an initial source-target mapping via a symplectic flow of an equi-flux parametric coordinate system. The resulting mapping provides integrable surface normal vector fields for complex off-axis and non-paraxial illumination problems, as demonstrated by two freeform lens examples.