  We apply the Fourier Power Function Shapelets (FPFS) shear estimator to the
first year data of the Hyper Suprime-Cam survey to construct a shape catalog.
The FPFS shear estimator has been demonstrated to have multiplicative bias less
than $1\%$ in the absence of blending, regardless of complexities of galaxy
shapes, smears of point spread functions (PSFs) and contamination from noise.
The blending bias is calibrated with realistic image simulations, which include
the impact of neighboring objects, using the COSMOS Hubble Space Telescope
images. Here we carefully test the influence of PSF model residual on the FPFS
shear estimation and the uncertainties in the shear calibration. Internal null
tests are conducted to characterize potential systematics in the FPFS shape
catalog and the results are compared with those measured using a catalog where
the shapes were estimated using the re-Gaussianization algorithms. Furthermore,
we compare various weak lensing measurements between the FPFS shape catalog and
the re-Gaussianization shape catalog and conclude that the weak lensing
measurements between these two shape catalogs are consistent with each other
within the statistical uncertainty.
