We investigate the affine perturbation series of the deflection angle of a
ray near the photon sphere of an extreme Reissner-Nordstr\”{o}m black hole. We
compare the 0th and 1st orders of the affine perturbation series with the
deflection angle in a strong deflection limit. We conclude that the 0th order
of the affine perturbation series is more accurate than the deflection angle in
the strong deflection limit and that we should improve a
strong-deflection-limit analysis by using the 0th order of the affine
perturbation series.
