  In this paper, we deal with the null geodesics extending from the
near-horizon region out to a distant observatory in an extremal Kerr-Newman
black hole background. In particular, using the matched asymptotic expansion
method, we analytically solve the null geodesics near the superradiant bound in
the form of algebraic equations. For the case that the photon trajectories are
limited in the equatorial plane, the shifts in the azimuthal angle and time are
obtained.
