Fourier Power Function Shapelets (FPFS) is a perturbation-based estimator for shear responses of galaxy shape, flux and detection --- It uses the leading-order perturbations of shear (a vector perturbation) and image noise (a tensor perturbation) to derive the shear responses and noise responses of measurements and detections. It is a passive shear estimator --- It does not repeatedly distort each observed galaxy to derive the shear responses; instead, the shear responses are derived using the analytical shear responses of a set of basis functions (Shapelets basis and peak basis). This method can process about 1000 galaxies in 1 cpu second, and it has been tested with simple simulations and demonstrated to control multiplicative shear estimation bias below 1% even in the existence of blending.

Documentation for FPFS modules can be found here

For stable version:

pip install fpfs

Or clone the repository:

git clone https://github.com/mr-superonion/FPFS.git
cd FPFS
pip install -e . --user

The following papers are ready to be cited if you find any of these papers interesting or use the pipeline. Comments are welcome.

• version 3: Li & Mandelbaum (2022) correct for detection bias from pixel level by interpreting smoothed pixel values as a projection of signal onto a set of basis functions.

• version 2: Li , Li & Massey (2022) derive the covariance matrix of FPFS measurements and corrects for noise bias to second-order. In addition, it derives the correction for selection bias.

• version 1: Li et. al (2018) build up the FPFS formalism based on Fourier_Quad and polar shapelets.