New Imaging Properties of Freeform Quadric Reflectors via the Theory of Eigenmirrors

A surface S is said to be an eigensurface of a mirror M if the reflection of Sin M appears undistorted. In that case, M is the eigenmirror corresponding to the eigensurface S. Rotationally symmetric eigenmirror/eigensurface pairs are easy to construct, but the situation for freeform mirrors requires consideration of a partial differential equation, the anti-eikonal equation. Here, we investigate freeform quadric eigenmirrors, classifying them into five families. In each case, the eigensurfaces are biquadratic, i.e., they satisfy equations of the form psi (x2, y2, z2) = 0, where psi is a quadric polynomial. Lastly, we investigate some more general hypotheses and a connection to dynamical systems. (c) 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.