  We study the potential of a large future weak-lensing survey to constrain
dark energy properties by using both the number counts of detected galaxy
clusters (sensitive primarily to density fluctuations on small scales) and
tomographic shear-shear correlations (restricted to large scales). We use the
Fisher matrix formalism, assume a flat universe and parameterize the equation
of state of dark energy by w(a)=w_0+w_a(1-a), to forecast the expected
statistical errors from either observable, and from their combination. We show
that the covariance between these two observables is small, and argue that
therefore they can be regarded as independent constraints. We find that when
the number counts and the shear-shear correlations (on angular scales l < 1000)
are combined, an LSST (Large Synoptic Survey Telescope)-like survey can yield
statistical errors on (Omega_DE, w_0, w_a) as tight as (0.003, 0.03, 0.1).
These values are a factor of 2-25 better than using either observable alone.
The results are also about a factor of two better than those from combining
number counts of galaxy clusters and their power spectrum.
