  We investigate the practical implementation of Taylor's (2002) 3-dimensional
gravitational potential reconstruction method using weak gravitational lensing,
together with the requisite reconstruction of the lensing potential. This
methodology calculates the 3-D gravitational potential given a knowledge of
shear estimates and redshifts for a set of galaxies. We analytically estimate
the noise expected in the reconstructed gravitational field, taking into
account the uncertainties associated with a finite survey, photometric redshift
uncertainty, redshift-space distortions, and multiple scattering events. In
order to implement this approach for future data analysis, we simulate the
lensing distortion fields due to various mass distributions. We create
catalogues of galaxies sampling this distortion in three dimensions, with
realistic spatial distribution and intrinsic ellipticity for both ground-based
and space-based surveys. Using the resulting catalogues of galaxy position and
shear, we demonstrate that it is possible to reconstruct the lensing and
gravitational potentials with our method. For example, we demonstrate that a
typical ground-based shear survey with redshift limit z=1 and photometric
redshifts with error Delta z=0.05 is directly able to measure the 3-D
gravitational potential for mass concentrations >10^14 M_\odot between
0.1<z<0.5, and can statistically measure the potential at much lower mass
limits. The intrinsic ellipticity of objects is found to be a serious source of
noise for the gravitational potential, which can be overcome by Wiener
filtering or examining the potential statistically over many fields. We examine
the use of the 3-D lensing potential to measure mass and position of clusters
in 3-D, and to detect clusters behind clusters.
