  For cosmic shear to become an accurate cosmological probe, systematic errors
in the shear measurement method must be unambiguously identified and corrected
for. Previous work of this series has demonstrated that cosmic shears can be
measured accurately in Fourier space in the presence of background noise and
finite pixel size, without assumptions on the morphologies of galaxy and PSF.
The remaining major source of error is source Poisson noise, due to the
finiteness of source photon number. This problem is particularly important for
faint galaxies in space-based weak lensing measurements, and for ground-based
images of short exposure times. In this work, we propose a simple and rigorous
way of removing the shear bias from the source Poisson noise. Our noise
treatment can be generalized for images made of multiple exposures through
MultiDrizzle. This is demonstrated with the SDSS and COSMOS/ACS data. With a
large ensemble of mock galaxy images of unrestricted morphologies, we show that
our shear measurement method can achieve sub-percent level accuracy even for
images of signal-to-noise ratio less than 5 in general, making it the most
promising technique for cosmic shear measurement in the ongoing and upcoming
large scale galaxy surveys.
