Freeform optics are key for generating prescribed illumination patterns from given sources, which are crucial for solid-state lighting and machine vision illumination. There is an increasing demand for compact freeform optics, which presents a substantial challenge for current design methods since the source dimensions must be considered. Most current extended-source design methods, although requiring profound knowledge of optics and mathematics, focus on the modest goal of obtaining uniform irradiance distributions. We address a more challenging design problem of generating an irradiance distribution of arbitrary shape through a double-freeform lens that can fully encompass the extended source. We propose a differentiable design method whose uniqueness lies in the representation of the double-freeform surfaces using multi-level spherical radial basis functions, which has a natural link to a multi-scale optimization technique. In addition, we employ a sequential unconstrained minimization technology complemented with Lagrange multipliers that add key feasibility constraints on lens shape and size. The proposed method is flexible, general, and efficient in designing highly compact freeform lenses for generating both simple and complex irradiance distributions, as demonstrated through the design examples. This could enable a universal solution to the extended-source design problem. © 2024 Optica Publishing Group.