Illumination design usually requires the shaping of a specific irradiance distribution from a given light source. For point-like sources or collimated laser beams various methods exist to construct the shape of the refractive and/or reflective surfaces within the optical system. However, for extended sources, an additional feedback or optimization loop is usually required and limitations are not clear. We propose an analysis and design method that includes the source extension from the very beginning. The method is based on phase space mapping of the source radiance distribution onto the target irradiance distribution. We illustrate the method with several examples.