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We propose a method for designing refractive optical elements for collimatedbeam shaping. In this method, the problem of finding a ray mapping isformulated as a linear assignment problem, which is a discrete version of thecorresponding mass transportation problem. A method for reconstructing opticalsurfaces from a computed discrete ray mapping is proposed. The method issuitable for designing continuous piecewise-smooth optical surfaces. The designof refractive optical elements transforming beams with circular cross-sectionto variously shaped (rectangular, triangular, and cross-shaped) beams withplane wavefront is discussed. The presented numerical simulation resultsconfirm high efficiency of the designed optical elements.

Designing double freeform surfaces for collimated beam shaping with optimal mass transportation and linear assignment problems