  Reconstruction of the point spread function (PSF) plays an important role in
many areas of astronomy, including photometry, astrometry, galaxy morphology,
and shear measurement. The atmospheric and instrumental effects are the two
main contributors to the PSF, both of which may exhibit complex spatial
features. Current PSF reconstruction schemes typically rely on individual
exposures, and its ability of reproducing the complicated features of the PSF
distribution is therefore limited by the number of stars. Interestingly, in
conventional methods, after stacking the model residuals of the PSF
ellipticities and (relative) sizes from a large number of exposures, one can
often observe some stable and nontrivial spatial patterns on the entire focal
plane, which could be quite detrimental to, e.g., weak lensing measurements.
These PSF residual patterns are caused by instrumental effects as they
consistently appear in different exposures. Taking this as an advantage, we
propose a multi-layer PSF reconstruction method to remove such PSF residuals,
the second and third layers of which make use of all available exposures
together. We test our method on the i-band data of the second release of Hyper
Suprime-Cam. Our method successfully eliminates most of the PSF residuals.
Using the Fourier\_Quad shear measurement method, we further test the
performance of the resulting PSF fields on shear recovery using the field
distortion effect. The PSF residuals have strong correlations with the shear
residuals, and our new multi-layer PSF reconstruction method can remove most of
such systematic errors related to PSF, leading to much smaller shear biases.
