Lens melting as a method for designing freeform gradient index lenses

We present a procedure that we have named “lens melting” for using standard lens design tools, and conventional lens models, for designing complex freeform gradient index lenses. The process consists of taking a conventional model of homogeneous index elements and computationally blurring the refractive index profile, as if the glass elements were being melted in a furnace. By controlling the extent of the blurring (the depth of melting), one can control the steepness of the gradients present in the system and the closeness of the gradient model to conventional homogeneous index models. One of the advantages that this presents is that we can use standard optimization tools such as damped least squares, working on the same parameters using by conventional models, to do gradient lens design.