  We have developed a new method(E-HOLICs) of estimating gravitational shear by
adopting an elliptical weight function to measure background galaxy images in
our previous paper. Following to the previous paper where isotropic Point
Spread Function(PSF) correction is calculated, we consider an anisotropic PSF
correction in this paper in order to apply E-HOLICs for real data. A an
example, E-HOLICs is applied to Subaru data of massive and compact galaxy
clusters A370, and is able to detect double peaks in the central region of the
cluster consistent with the analysis of strong lensing. We also study the
systematic error in E-HOLICs using STEP II simulation. In particular we
consider the dependences of signal to noise ratio "S/N" of background galaxies
in the shear estimation. Although E-HOLICs does improve systematic error due to
the ellipticity dependence as shown in part 1, a systematic error due to the
S/N dependence remains, namely E-HOLICs underestimates shear when background
galaxies with low S/N objects are used. We discuss a possible improvement of
the S/N dependence.
