Beam shaping with a plano-freeform lens pair

It has been shown in [ J. A. Hoffnagle C. M. Jefferson , Opt. Eng.42, 3090, (2003)] that a pair of plano-aspheric lenses can be used to transform a radially symmetric, Gaussian beam to a radially symmetric flat-top beam. In this paper it is shown that a pair of plano-freeform lenses can be used to transform a collimated light beam of arbitrary (including, non-radially symmetric) intensity profile to a collimated output beam of constant phase and a priori specified intensity pattern over a given flat region. The curved surfaces of both lenses can be chosen strictly convex which should facilitate fabrication. The required pair of plano-freeform lenses is designed using the supporting quadric method (SQM) [ V. I. Oliker in Trends in Nonlinear Analysis, (Springer-Verlag, 2003)] combined with ideas from optimal mass transport [ V. I. Oliker , Arch. Rational Mechanics and Analysis201, 1013 (2011)]. Such approach provides a rigorous methodology for designing freeform optics for irradiance redistribution. In this paper, this approach is applied to design of a laser beam shaping system with two lenses.