  We propose a method for designing refractive optical elements for collimated
beam shaping. In this method, the problem of finding a ray mapping is
formulated as a linear assignment problem, which is a discrete version of the
corresponding mass transportation problem. A method for reconstructing optical
surfaces from a computed discrete ray mapping is proposed. The method is
suitable for designing continuous piecewise-smooth optical surfaces. The design
of refractive optical elements transforming beams with circular cross-section
to variously shaped (rectangular, triangular, and cross-shaped) beams with
plane wavefront is discussed. The presented numerical simulation results
confirm high efficiency of the designed optical elements.
