  We study the possibility of using quadrupole moments of auto-convolved galaxy
images to measure cosmic shear. The autoconvolution of an image corresponds to
the inverse Fourier transformation of its power spectrum. The new method has
the following advantages: the smearing effect due to the Point Spread Function
(PSF) can be corrected by subtracting the quadrupole moments of the
auto-convolved PSF; the centroid of the auto-convolved image is trivially
identified; the systematic error due to noise can be directly removed in
Fourier space; the PSF image can also contain noise, the effect of which can be
similarly removed. With a large ensemble of simulated galaxy images, we show
that the new method can reach a sub-percent level accuracy in general
conditions, albeit with increasingly large stamp size for galaxies of less
compact profiles.
