Journal article
Anti-eikonal equation of an eigenmirror
Journal of the Optical Society of America. A, Optics, image science, and vision, v 37(10), pp 1566-1573
01 Oct 2020
PMID: 33104602
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. (C) 2020 Optical Society of America
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Details
- Title
- Anti-eikonal equation of an eigenmirror
- Creators
- R. Andrew Hicks - Drexel UniversityRonald K. Perline - Drexel UniversitySarah G. Rody - Chestnut Hill College
- Publication Details
- Journal of the Optical Society of America. A, Optics, image science, and vision, v 37(10), pp 1566-1573
- Publisher
- Optical Soc Amer
- Number of pages
- 8
- Grant note
- DMS-09-08299 / Directorate for Mathematical and Physical Sciences
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000577525200005
- Scopus ID
- 2-s2.0-85091853011
- Other Identifier
- 991019167823504721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Optics