Abstract

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 ${a_0} + {a_1}{u_x} \,+ {a_2}{u_y} + {a_3}{u_x}{u_y} + {a_4}u_x^2 + {a_5}u_y^2 = 0$, where ${a_i} = {a_i}(x,y,u)$, 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.

© 2020 Optical Society of America

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