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The luminosity of accreting magnetised neutron stars can largely exceed theEddington value due to appearance of accretion columns. The height of thecolumns can be comparable to the neutron star radius. The columns produce theX-rays detected by the observer directly and illuminate the stellar surface,which reprocesses the X-rays and causes additional component of the observedflux. The geometry of the column and the illuminated part of the surfacedetermines the radiation beaming. Curved space-time affects the angular fluxdistribution. We construct a simple model of the beam patterns formed by directand reflected flux from the column. We take into account the possibility ofappearance of accretion columns, whose height is comparable to the neutron starradius. We argue that depending on the compactness of the star the flux fromthe column can be either strongly amplified due to gravitational lensing, orsignificantly reduced due to column eclipse by the star. The eclipses of highaccretion columns result in specific features in pulse profiles. Theirdetection can put constraints on the neutron star radius. We speculate thatcolumn eclipses are observed in X-ray pulsar V 0332+53, leading us to theconclusion of large neutron star radius in this system ($\sim15\,{\rm km}$ if$M\sim 1.4M_\odot$). We point out that the beam pattern can be stronglyaffected by scattering in the accretion channel at high luminosity, which hasto be taken into account in the models reproducing the pulse profiles.

On the radiation beaming of bright X-ray pulsars and constraints on neutron star mass-radius relation