  There are many simplifications in current relativistic reflection models and
this introduces systematic uncertainties in the measurement of the properties
of the source. In this paper, we study the impact of the radiation crossing the
equatorial plane between the black hole and the inner edge of the accretion
disk; that is, the radiation produced by the other side of the disk or circling
the black hole one or more times (higher order disk images). For slow-rotating
black holes with a larger plunging region, the effect is not very sensitive to
the exact inclination angle of the disk. For fast-rotating black holes with a
smaller plunging region, the effect is very weak for low inclination angles and
becomes more important as the angle increases. We simulate some observations
without and with higher order disk images and fit the data with the reflection
model RELXILL_NK to check its capability of recovering the correct input
parameters. Our results suggest that the effect of higher order disk images can
be safely ignored for observations with present and near future X-ray missions,
even for tests of the Kerr hypothesis.
