Operation of the future International Linear Collider
(ILC) with polarized electron and positron beams will
significantly improve the precise measurements in new
physics. Polarized positrons will be generated by the
photoproduction method. In this scheme, a high-energy
primary electron beam passes through a helical
undulator and produces circularly polarized photons,
which then impinge on a target and produce
longitudinally polarized positrons. Positrons are
captured by the collection system including an
Adiabatic Matching Device, pre-accelerator, long beam
transport line and 5 GeV booster linac. The collection
system has been optimized to insure high positron
capture into the 6-dimensional acceptance of the
damping ring keeping the high value of beam
polarization. Special emphasis is on the Linac-to-Ring
beamline which performs spin rotation and energy
compression of the positron beam before injection into
the damping ring. Various parameters affecting the
positron capture are analyzed.