Traditionally, lenses are manufactured with surfaces that are sections of spheres. Spherical lenses are comparitively easy to fabricate and have a mature set of associated tools for lens analysis (most of which predate the computer). High-performance spherical-lens systems can be made using multiple lenses in sequence, each with differing materials and/or differing radii of curvature. The more recent widespread use of so-called aspherical lenses enabled significant progress beyond the limitations of spherical systems—increased flexibility in surface profile allows higher performance in a smaller volume (and with fewer optical surfaces). Aspheric lenses are, however, typically cylindrically symmetric about a central axis. Freeform lenses are the next step in this evolution of lens technology.
Computer-controlled optical grinders now allow lens surfaces to be made with complex and asymmetric profiles. Applications of freeform optics are diverse: for example, they will be used on the James Webb Space Telescope to maximize performance, within the constraints of a deployable spacecraft; they have been used in automotive headlamps to give superior beam shaping while integrating with the shape of the car; and they are being employed in the next generation of heads-up displays. Despite demonstrated successes, there is still much work to be done in the field of freeform optics. Freeform optic design is usually application specific and computationally intensive—efficient general purpose tools are lacking. This article is significant, in part, because it does in fact contribute a broadly applicable tool for the design of freeform optics.
The authors show that they can control both intensity and phase of a collimated laser beam using two freeform optical surfaces. Building on previous works, they cast the design problem in terms of partial differential equations and show how the resulting problem can be solved with physically reasonable lens surfaces. A major contribution of the paper is the generalization of this approach to include the non-paraxial (i.e., beyond small angles) regime. The presented tool is applicable in the wide range of fields where it is desirable to shape a laser beam, and I expect it to be a popular reference in freeform optical design.
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