We reinterpret the shear estimator developed by Zhang & Komatsu within the framework of shapelets and propose the Fourier Power Function Shapelets (FPFS) shear estimator. Four shapelet modes are calculated from the power function of every galaxy’s Fourier transform after deconvolving the point-spread function (PSF) in Fourier space. We propose a novel normalization scheme to construct dimensionless ellipticity and its corresponding shear responsivity using these shapelet modes. Shear is measured in a conventional way by averaging the ellipticities and responsivities over a large ensemble of galaxies. With the introduction and tuning of a weighting parameter, noise bias is reduced below one per cent of the shear signal on average. We also provide an iterative method to reduce selection bias. The FPFS estimator is developed without any assumptions regarding galaxy morphology or any approximations for PSF correction. Moreover, our method does not rely on heavy image manipulations.

 

 

Subsequently, we test the FPFS shear estimator using several Subaru Hyper Suprime-Cam (HSC)-like image simulations and the main results are as follows. (i) For simulations that only contain isolated galaxies, the amplitude of the multiplicative bias is below 1 × 10−2. (ii) For more realistic simulations, which also contain blended galaxies, the blended galaxies are deblended by the first-generation HSC deblender before shear measurement. A multiplicative bias of (−5.71 ± 0.31) × 10−2 is found. The blending bias is calibrated by image simulations.

 

 

Finally, we apply the Fourier Power Function Shapelets (FPFS) shear estimator to the first year data of the Hyper Suprime-Cam (HSC) survey to construct a shape catalog. Here we carefully test the influence of PSF model residuals 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 of the re-Gaussianization shape catalog. Furthermore, we compare various weak lensing measurements between the FPFS shape catalog and the re-Gaussianization shape catalog and concludes that the weak lensing measurements between these two shape catalogs are consistent with each other within the statistical uncertainty.