  A novel focusing structure with fractal properties is presented. It is a
photon sieve in which the pinholes are appropriately distributed over the zones
of a fractal zone plate. The focusing properties of the fractal photon sieve
are analyzed. The good performance of our proposal is demonstrated
experimentally with a series of images obtained under white light illumination.
It is shown that compared with a conventional photon sieve, the fractal photon
sieve exhibits an extended depth of field and a reduced chromatic aberration.
