The point spread function reconstruction – II. The smooth PCA

Accurate shear measurement is a key topic in weak lensing community. Point spread function (PSF), which smears the observed galaxy image, plays one of the main roles in the systematic errors in shear measurement and must be treated carefully to avoid bias and errors in cosmological parameters. In this paper, we present new PSF measurement methods, Smooth-PCA (SPCA) and Improved-SPCA (iSPCA), which can reconstruct smooth PSFs with high efficiency. Our methods decompose the star images into smooth principal components by using the Expectation-Maximization-PCA (EMPCA) method, and the smooth principal components are composed by Moffatlets basis functions, which are derived from the Moffat function. We demonstrate our approaches based on simulated Moffat PSFs and phosim star images. The constructed smooth principal components show flexible and efficient as the same as EMPCA, and have more stable patterns than EMPCA under noises contamination. We then check the reconstruction accuracy on the shape of PSFs. We find that our methods are able to reconstruct the PSFs at the same precision as the EMPCA method that indicates and iSPCA are promising for weak lensing shear measurement.