  A logarithmic transform of the convergence field improves `the information
content', ie., the overall precision associated with the measurement of the
amplitude of the convergence power spectrum by improving the covariance matrix
properties. The translation of this improvement in the information content to
that in cosmological parameters, such as those associated with dark energy,
requires knowing the sensitivity of the log-transformed field to those
cosmological parameters. In this paper we use N-body simulations with ray
tracing to generate convergence fields at multiple source redshifts as a
function of cosmology. The gain in information associated with the
log-transformed field does lead to tighter constraints on dark energy
parameters, but only if shape noise is neglected. The presence of shape noise
quickly diminishes the advantage of the log mapping, more quickly than we would
expect based on the information content. With or without shape noise, using a
larger pixel size allows for a more efficient log-transformation.
