Emerging applications of optical technologies are driving the development of miniaturised light sources, which in turn require the fabrication of matching micro-optical elements with sub-1 mm cross-sections and high optical quality. This is particularly challenging for spatially constrained biomedical applications where reduced dimensionality is required, such as endoscopy, optogenetics, or optical implants. Planarisation of a lens by the Fresnel lens approach was adapted for a conical lens (axicon) and was made by direct femtosecond 780 nm/100 fs laser writing in the SZ2080™ polymer with a photo-initiator. Optical characterisation of the positive and negative fraxicons is presented. Numerical modelling of fraxicon optical performance under illumination by incoherent and spatially extended light sources is compared with the ideal case of plane-wave illumination. Considering the potential for rapid replication in soft polymers and resists, this approach holds great promise for the most demanding technological applications.