  In previous works, we developed a perturbative extrapolation formula to
obtain gravitational waves at infinity from binary black hole simulations,
based on the Regge-Wheeler-Zerilli formalism. In practice, this formula was
basically derived in a background flat spacetime. We derive here an estimation
of errors and an improved extrapolation formula by using the Teukolsky
perturbative equation for a background Kerr spacetime. The improved formula
requires knowledge about a mass and spin of the background spacetime.
