Designing freeform Fresnel lenses with continuous facets

Fresnel lenses are commonly designed by optimizing a sag function, similar to the approach for traditional thick lenses. This method limits the degrees of freedom by constraining the vector field of surface normals to be integrable. We introduce a method that removes the integrability constraint, while still ensuring continuous long facets. The presented method initializes a facet at a starting point and follows it along the line of zero z gradient. The starting points are manually placed depending on the shape of the vector field, and new facets are automatically added when the distance between the facets is greater than a given threshold. Finally, we show how this design can be used to realize an étendue squeezing line-focus solar concentrator that could not have been achieved using conventional thick lenses.