  Reprocessing of X-ray pulsar radiation by the atmosphere of a companion in a
binary system may result in reflected pulse radiation with a period of the
pulses equal to the period of the pulsar under suitable conditions. In this
paper the influence of the rotation of the source - the pulsar - about its axis
on the parameters of thus reflected pulses is investigated. The binary system
is modeled by the spherical reflective screen and the compact source uniformly
rotating about its axis; the beam pattern (BP) of the source periodically runs
over the surface of the screen. Irradiation of the screen by the pulses
infinitely narrow in time and by the rectangular pulses is considered. In this
model parameters of the pulses reflected in some directions are calculated. The
main conclusion provided by the consideration of this model is that the
properties of reflected pulses - their profile, and the moments of reaching the
observer - substantially depend on the correlation between the light speed and
the speed of the BP passing over the companion surface. The possibility of
applying of the obtained results to the known X-ray accretion-powered pulsars
and rotation-powered pulsars in binary systems is examined.
