Cosmic Shears Should Not Be Measured In Conventional Ways
  A long standing problem in weak lensing is about how to construct cosmic
shear estimators from galaxy images. Conventional methods average over a single
quantity per galaxy to estimate each shear component. We show that any such
shear estimators must reduce to a highly nonlinear form when the galaxy image
is described by three parameters (pure ellipse), even in the absence of the
point spread function (PSF). In the presence of the PSF, we argue that this
class of shear estimators do not likely exist. Alternatively, we propose a new
way of measuring the cosmic shear: instead of averaging over a single value
from each galaxy, we average over two numbers, and then take the ratio to
estimate the shear component. In particular, the two numbers correspond to the
numerator and denominators which generate the quadrupole moments of the galaxy
image in Fourier space, as proposed in Zhang (2008). This yields a
statistically unbiased estimate of the shear component. Consequently,
measurements of the n-point spatial correlations of the shear fields should
also be modified: one needs to take the ratio of two correlation functions to
get the desired, unbiased shear correlation.
