Title: Implications of a wavelength dependent PSF for weak lensing measurements,
Abstract: The convolution of galaxy images by the point-spread function (PSF) is the
dominant source of bias for weak gravitational lensing studies, and an accurate
estimate of the PSF is required to obtain unbiased shape measurements. The PSF
estimate for a galaxy depends on its spectral energy distribution (SED),
because the instrumental PSF is generally a function of the wavelength. In this
paper we explore various approaches to determine the resulting `effective' PSF
using broad-band data. Considering the Euclid mission as a reference, we find
that standard SED template fitting methods result in biases that depend on
source redshift, although this may be remedied if the algorithms can be
optimised for this purpose. Using a machine-learning algorithm we show that, at
least in principle, the required accuracy can be achieved with the current
survey parameters. It is also possible to account for the correlations between
photometric redshift and PSF estimates that arise from the use of the same
photometry. We explore the impact of errors in photometric calibration, errors
in the assumed wavelength dependence of the PSF model and limitations of the
adopted template libraries. Our results indicate that the required accuracy for
Euclid can be achieved using the data that are planned to determine photometric
redshifts.