Unfolding the matter distribution using 3-D weak gravitational lensing
  Combining redshift and galaxy shape information offers new exciting ways of
exploiting the gravitational lensing effect for studying the large scales of
the cosmos. One application is the three-dimensional reconstruction of the
matter density distribution which is explored in this paper. We give a
generalisation of an already known minimum-variance estimator of the 3-D matter
density distribution that facilitates the combination of thin redshift slices
of sources with samples of broad redshift distributions for an optimal
reconstruction. We show how, in principle, intrinsic alignments of source
ellipticities or shear/intrinsic alignment correlations can be accommodated,
albeit these effects are not the focus of this paper. We describe an efficient
and fast way to implement the estimator on a contemporary desktop computer.
Analytic estimates for the noise and biases in the reconstruction are given.
The bias -- a spread and shift of structures in radial direction -- can be
expressed in terms of a radial PSF, comprising the limitations of the
reconstruction due to source shot-noise and the unavoidably broad lensing
kernel. We conclude that a 3-D mass-density reconstruction on galaxy cluster
scales is feasible but, for foreseeable surveys, a map with a S/N>~3 threshold
is limited to structures with M200>~10^14 Msol/h, or 7x10^14 Msol/h, at low to
moderate redshifts (z=0.1 or 0.6). However, we find that a heavily smoothed
full-sky map of the very large-scale density field may also be possible as the
S/N of reconstructed modes increases towards larger scales. Future improvements
of the method can be obtained by including higher-order lensing information
(flexion) which could also be implemented into our algorithm. [ABRIDGED]
