  Weak gravitational lensing has proven to be a powerful tool to map directly
the distribution of dark matter in the Universe. The technique, currently used,
relies on the accurate measurement of the gravitational shear that corresponds
to the first-order distortion of the background galaxy images. More recently, a
new technique has been introduced that relies on the accurate measurement of
the gravitational flexion that corresponds to the second-order distortion of
the background galaxy images. This technique should probe structures on smaller
scales than that of a shear analysis. The goal of this paper is to compare the
ability of shear and flexion to reconstruct the dark matter distribution by
taking into account the dispersion in shear and flexion measurements. Our
results show that the flexion is less sensitive than shear for constructing the
convergence maps on scales that are physically feasible for mapping, meaning
that flexion alone not be used to do convergence map reconstruction, even on
small scales.
