  In this work, we present a novel centroiding method based on Fourier space
Phase Fitting(FPF) for Point Spread Function(PSF) reconstruction. We generate
two sets of simulations to test our method. The first set is generated by
GalSim with elliptical Moffat profile and strong anisotropy which shifts the
center of the PSF. The second set of simulation is drawn from CFHT i band
stellar imaging data. We find non-negligible anisotropy from CFHT stellar
images, which leads to $\sim$0.08 scatter in unit of pixels using polynomial
fitting method Vakili and Hogg (2016). And we apply FPF method to estimate the
centroid in real space, this scatter reduces to $\sim$0.04 in SNR=200 CFHT like
sample. In low SNR (50 and 100) CFHT like samples, the background noise
dominates the shifting of the centroid, therefore the scatter estimated from
different methods are similar. We compare polynomial fitting and FPF using
GalSim simulation with optical anisotropy. We find that in all SNR$\sim$50, 100
and 200) samples, FPF performs better than polynomial fitting by a factor of
$\sim$3. In general, we suggest that in real observations there are anisotropy
which shift the centroid, and FPF method is a better way to accurately locate
it.
