From Notices of the AMS
Freeform Optics: Optimal Transport, Minkowski Method and Monge-Ampère-Type Equations
by Henok Mawi
Communicated by Reza Malek-Madani
1. Description and Background
A freeform optical surface, simply stated, refers to a surface whose shape lacks rotational symmetry. The use of such surfaces allows generation of complex, compact, and highly efficient imaging systems. Ever since lenses without symmetries were used in World War I in periscopes, the engineering and design of freeform optical surfaces have gone through remarkable evolution, with applications in a wide range of areas, including medical devices, clean energy technology, military surveillance equipments, mobile displays, remote sensing, and several other areas of imaging and nonimaging optics that can benefit from distributing light from a source to a target in a controlled fashion using spatially and energy-efficient systems. See [17] and the references therein.
Mathematically, the design of freeform optical surfaces is an inverse problem related to optimal transportation theory and leads to a class of nonlinear partial differential equations (PDE) called generated Jacobian equations for which the Monge-Ampère equation is a prototype.
- Also in Notices
- Wave-Mean-Flow Interactions in Atmospheric Fluid Flows
- National Association of Mathematicians, Inc. (NAM) Passing the Torch. A Reflection of NAM's Development and Growth by NAM's Leaders/Contributors—the First Five Decades
