  We present a comprehensive analysis of coherence properties of the radiation
from X-ray free electron laser (XFEL). We consider practically important case
when XFEL is optimized for maximum gain. Such an optimization allows to reduce
significantly parameter space. Application of similarity techniques to the
results of numerical simulations allows to present all output characteristics
of the optimized XFEL as functions of the only parameter, ratio of the
emittance to the radiation wavelength, $ \hat{\epsilon} = 2\pi \epsilon/\lambda
$. Our studies show that optimum performance of the XFEL in terms of transverse
coherence is achieved at the value of the parameter $\hat{\epsilon}$ of about
unity. At smaller values of $\hat{\epsilon}$ the degree of transverse coherence
is reduced due to strong influence of poor longitudinal coherence on a
transverse one. At large values of the emittance the degree of transverse
coherence degrades due to poor mode selection. Comparative analysis of existing
XFEL projects, European XFEL, LCLS, and SCSS is presented as well.
