Open AccessEigensurfaces of eigenmirrors
Author(s) -
Sarah G. Rody,
Ronald Perline,
R. Andrew Hicks
Publication year - 2019
Publication title -
journal of the optical society of america. a, optics, image science, and vision./journal of the optical society of america. a, online
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 0.803
H-Index - 158
eISSN - 1520-8532
pISSN - 1084-7529
DOI - 10.1364/josaa.36.001312
Subject(s) - observer (physics) , partial differential equation , reflector (photography) , nonlinear system , point (geometry) , physics , differential equation , mathematical analysis , optics , mathematics , geometry , light source , quantum mechanics
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.