  We performed an analysis of coherence properties of the 4-th generation
high-energy storage rings with emittance values of 10 pmrad. It is presently
expected that a storage ring with these low emittance values will reach
diffraction limit at hard X-rays. Simulations of coherence properties were
performed with the XRT software and analytical approach for different photon
energies from 500 eV to 50 keV. It was demonstrated that a minimum photon
emittance (diffraction limit) reached at such storage rings is
{\lambda}/2{\pi}. Using mode decomposition we showed that at the parameters of
the storage ring considered in this work, diffraction limit will be reached for
soft X-ray energies of 500 eV. About ten modes will contribute to the radiation
field at 12 keV photon energy and even more modes give a contribution at higher
photon energies. Energy spread effects of the electron beam in a low emittance
storage ring were analysed in detail. Simulations were performed at different
relative energy spread values from zero to 0.2%. We observed a decrease of the
degree of coherence with an increase of the relative energy spread value. Our
analysis shows that to reach diffraction limit for high photon energies
electron beam emittance should go down to 1 pmrad and below.
