Redistribution of light from a given source in order to create a prescribed intensity pattern on a given set in 3D space is a task arising in numerous applications. Designing optical systems with capabilities to perform such tasks reliably in a wide variety of applications is the overall goal of much of research in optics. An important practical case is the “laser beam shaping problem” which requires transformation of a Gaussian beam from a laser into a beam with “flat top” intensity profile. It has been shown by John A. Hoffnagle and C. Michael Jefferson that a pair of plano-aspheric lenses can be used to transform a collimated, radially symmetric, Gaussian beam to a radially symmetric, collimated beam with “flat-top” intensity profile. Here we discuss this design problem when a priori requirement of radial symmetry is not imposed neither on the input/output radiances nor on the geometry of the input/output beams. The solution in this case is sought among “freeform” optical surfaces.

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Vladimir Oliker, "A plano-freeform lens pair for shaping laser beams," Proc. SPIE 10758, Nonimaging Optics: Efficient Design for Illumination and Solar Concentration XV, 107580G (Presented at SPIE Optical Engineering + Applications: August 19, 2018; Published: 14 September 2018); https://doi.org/10.1117/12.2505507.