Constraining the point spread function by using galaxy images

Inferring the point spread function (PSF) at galaxy positions is one of the crucial steps of the shear measurement. We introduce a novel method to estimate the PSFs at the galaxy positions by using the galaxy images, which could provide additional constrains for the PSF field variations. We construct the PSF for each star image by using Principal-Components-Analysis (PCA) method, which can capture the most significant characteristics of the data. Our method utilizes the image difference of the same object between multi-exposures to probe the coefficients of the principal components, in which the differences are mainly caused by PSFs. We apply our method to the observed data. The results show that the corresponding PSFs can be properly estimated from multiple images of different exposures. We then use the obtained principal components from the observations to mock multi-exposure images, where the PSFs field of each exposure is constructed by bivariate polynomial on coefficients. We find that our method can reproduce the PSFs consistently with mocked data. Our results show that the multi-exposed galaxy images could provide us additional constraints for the PSF fields in PCA scenario. It offers a promising prospect for combing the information of stars and galaxies together to construct the PSF field when the point sources are sparsely sampled.