  Cosmic shear requires high precision measurement of galaxy shapes in the
presence of the observational Point Spread Function (PSF) that smears out the
image. The PSF must therefore be known for each galaxy to a high accuracy.
However, for several reasons, the PSF is usually wavelength dependent,
therefore the differences between the spectral energy distribution of the
observed objects introduces further complexity. In this paper we investigate
the effect of the wavelength-dependence of the PSF, focusing on instruments in
which the PSF size is dominated by the diffraction-limit of the telescope and
which use broad-band filters for shape measurement.
  We first calculate biases on cosmological parameter estimation from cosmic
shear when the stellar PSF is used uncorrected. Using realistic galaxy and star
spectral energy distributions and populations and a simple three-component
circular PSF we find that the colour-dependence must be taken into account for
the next generation of telescopes. We then consider two different methods for
removing the effect (i) the use of stars of the same colour as the galaxies and
(ii) estimation of the galaxy spectral energy distribution using multiple
colours and using a telescope model for the PSF. We find that both of these
methods correct the effect to levels below the tolerances required for per-cent
level measurements of dark energy parameters. Comparison of the two methods
favours the template-fitting method because its efficiency is less dependent on
galaxy redshift than the broad-band colour method and takes full advantage of
deeper photometry.
