Optimizing tomography for weak gravitational lensing surveys

The subject of this paper is optimization of weak lensing tomography: we carry out numerical minimization 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 optimize the sensitivity of weak lensing with respect to different optimization targets. Working under the assumption of a Gaussian likelihood for the parameters of a w(0)w(a) CDM (cold dark matter) model and using EUCLID's conservative survey specifications, we compare an equipopulated, equidistant, and optimized 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 optimization 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.