2020 JOSA A Emerging Researcher Best Paper Prize: editorial.

JOSA A Editor-in-Chief P. Scott Carney, Feature Editor Johannes Courtial, and members of the 2020 Emerging Researcher Best Paper Prize Committee announce the recipient of the 2020 prize for the best paper published by an emerging researcher in the Journal.

Anti-eikonal equation of an eigenmirror.

We call a surface that appears undistorted when viewed in a curved mirror an eigensurface and the mirror an eigenmirror. Such pairs are described by a first-order nonlinear partial differential equation of the form a0+a1ux+a2uy+a3uxuy+a4ux2+a5uy2=0, where ai=ai(x,y,u), which we call the anti-eikonal equation. We give examples of symbolic and numerical solutions, including pairs that are geometrically congruent. Ray tracing simulations are included that visually confirm the unusual properties of these surfaces.

Eigensurfaces of eigenmirrors.

Typically, if an observer gazes at a curved reflector, the objects in it will appear to be distorted. We show here that for some mirrors there exist surfaces that do not appear distorted when viewed from a prescribed location. We call such mirrors eigenmirrors and the surfaces eigensurfaces. We first give an analysis of the rotationally symmetric case and verify our work with simulations. In the general three-dimensional (3D) case, if the mirror is given, then one does not expect an eigensurface to exist. On the other hand, if we are given two viewpoints and a correspondence between the ray bundles emanating from each point, and we treat both the eigenmirror and the eigensurface as unknowns, then the problem reduces to solving a first-order nonlinear partial differential equation. We derive this partial differential equation in the 3D case and examine one example in detail.