  We study the utility of a large sample of type Ia supernovae that might be
observed in an imaging survey that rapidly scans a large fraction of the sky
for constraining dark energy. We consider information from the traditional
luminosity distance test as well as the spread in SNeIa fluxes at fixed
redshift induced by gravitational lensing. We include a treatment of
photometric redshift uncertainties in our analysis. Our primary result is that
the information contained in the mean distance moduli of SNeIa and the
dispersion among SNeIa distance moduli complement each other, breaking a
degeneracy between the present dark energy equation of state and its time
variation without the need for a high-redshift supernova sample. To address
photometric redshift uncertainties, we present dark energy constraints as a
function of the size of an external set of spectroscopically-observed SNeIa
that may be used for redshift calibration, nspec. We find that an imaging
survey can constrain the dark energy equation of state at the epoch where it is
best constrained with a 1-sigma error of sigma(wpiv)~0.03-0.09$, depending upon
various assumptions. In addition, the marginal improvement in the error
sigma(wpiv) from an increase in the spectroscopic calibration sample drops once
nspec ~ 10^3. This result is important because it is of the order of the size
of calibration samples likely to be compiled in the coming decade and because,
for samples of this size, the spectroscopic and imaging surveys individually
place comparable constraints on the dark energy equation of state. In all
cases, it is best to calibrate photometric redshifts with a set of
spectroscopically-observed SNeIa with relatively more objects at high redshift
than the parent sample of imaging SNeIa.
