Optimising tomography for weak gravitational lensing surveys
  The subject of this paper is optimisation of weak lensing tomography: We
carry out numerical minimisation of a measure of total statistical error as a
function of the redshifts of the tomographic bin edges by means of a
Nelder-Mead algorithm in order to optimise the sensitivity of weak lensing with
respect to different optimisation targets. Working under the assumption of a
Gaussian likelihood for the parameters of a $w_0 w_a$CDM-model and using
Euclid's conservative survey specifications, we compare an equipopulated,
equidistant and optimised bin setting and find that in general the
equipopulated setting is very close to the optimal one, while an equidistant
setting is far from optimal and also suffers from the ad hoc choice of a
maximum redshift. More importantly, we find that nearly saturated information
content can be gained using already few tomographic bins. This is crucial for
photometric redshift surveys with large redshift errors. We consider a large
range of targets for the optimisation process that can be computed from the
parameter covariance (or equivalently, from the Fisher-matrix), extend these
studies to information entropy measures such as the Kullback-Leibler-divergence
and conclude that in many cases equipopulated binning yields results close to
the optimum, which we support by analytical arguments.
