  Elliptical dichroism is known in atomic photoionization as the difference in
the photoelectron angular distributions produced in nonlinear ionization of
atoms by left- and right-handed elliptically polarized light. We theoretically
demonstrate that the maximum dichroism |{\Delta}_{ED}|=1 always appears in
two-photon ionization of any atom if the photon energy is tuned in so that the
electron emission is dominantly determined by two intermediate resonances. We
propose the two-photon ionization of atomic helium in order to demonstrate this
remarkable phenomenon. The maximum elliptical dichroism could be used as a
sensitive tool for analyzing the polarization state of photon beams produced by
free-electron lasers.
