A comparative analysis of recursive ray tracing strategies for tomographic reconstruction from projections with diffracting sources is presented. One algorithm employs ray tracing in reprojection toward a correction of the true projection values for subsequent straight‐ray reconstruction. The other algorithm performs curved‐ray reconstruction along the retraced rays by algebraic methods for each recursive step. The performance for reconstruction of objects exhibiting discontinuity boundaries is studied. Within the geometrical optics approximation, the forward process is also shown to lead to multiple linking refracted rays. In an object of low velocity, there may be ranges of receive positions over which no linking refracted rays exist. Geometrically diffracted rays are introduced to describe the signal actually received over the ‘‘forbidden’’ range.