  Chemical element mapping is an imaging tool that provides essential
information on composite materials and it is crucial for a broad range of
fields ranging from fundamental science to numerous applications. Methods that
exploit x-ray fluorescence are very advantageous and are widely used, but
require focusing of the input beam and raster scanning of the sample. Thus the
methods are slow and exhibit limited resolution due to focusing challenges. We
demonstrate a new focusing free x-ray fluorescence method based ghost imaging
that overcomes those limitations. We combine our procedure with compressed
sensing to reduce the measurement time and the exposure to radiation by more
than 80%. Since our method does not require focusing, it opens the possibility
for improving the resolution and image quality of chemical element maps with
tabletop x-ray sources and for extending the applicability of x-ray
fluorescence detection to new fields such as medical imaging and homeland
security applications
