A proposal for lines of sight for bolometry on ITER is presented. Background of tomography relevant for the proposed system is discussed, in particular the complications of the coverage of projection space due to the non-convex shape of the inner wall of ITER. The requirements and technical constraints that led to the proposed system are discussed in detail. Simulations have been carried out to assess the performance of the system for emission profiles that are expected in ITER. The simulations are compared with simulations of systems with different numbers of lines of sight. Present tomography methods can make reasonable reconstructions of the divertor radiation from the measurements of about 400 lines of sight. The quality of the reconstructions decreases when fewer lines of sight are used; in particular, some features cannot be reconstructed well if a whole range of lines of sight is not used. The total emitted power is matched very well (within one percent), even with a reduced number of lines of sight. With the proposed number of lines of sight there is sufficient scope for improvement of the reconstructions of divertor radiation, bulk radiation, and in the presence of neutral particle effects on divertor bolometers.