  We study the accuracy with which weak lensing measurements could be made from
a future space-based survey, predicting the subsequent precisions of
3-dimensional dark matter maps, projected 2-dimensional dark matter maps, and
mass-selected cluster catalogues. As a baseline, we use the instrumental
specifications of the Supernova/Acceleration Probe (SNAP) satellite. We first
compute its sensitivity to weak lensing shear as a function of survey depth.
Our predictions are based on detailed image simulations created using
`shapelets', a complete and orthogonal parameterization of galaxy morphologies.
We incorporate a realistic redshift distribution of source galaxies, and
calculate the average precision of photometric redshift recovery using the SNAP
filter set to be Delta z=0.034. The high density of background galaxies
resolved in a wide space-based survey allows projected dark matter maps with a
rms sensitivity of 3% shear in 1 square arcminute cells. This will be further
improved using a proposed deep space-based survey, which will be able to detect
isolated clusters using a 3D lensing inversion techniques with a 1 sigma mass
sensitivity of approximately 10^13 solar masses at z~0.25. Weak lensing
measurements from space will thus be able to capture non-Gaussian features
arising from gravitational instability and map out dark matter in the universe
with unprecedented resolution.
