Related papers: Mathematical retroreflectors
We consider the inverse refractor and the inverse reflector problem. The task is to design a free-form lens or a free-form mirror that, when illuminated by a point light source, produces a given illumination pattern on a target. Both…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these…
The circular Bragg phenomenon is the circular-polarization-state-selective reflection of light in a spectral regime called the circular Bragg regime. In continuation of an expository review on this phenomenon published in 2014, an album of…
The Doppler Effect associated with the reflection on a moving mirror is reduced to two Doppler Effect experiments involving the incoming incident ray and the outgoing reflected ray or vice-versa. The dependence of the corresponding Doppler…
A slab of negatively refracting material, thickness d, can focus an image at a distance 2d from the object. The negative slab cancels an equal thickness of positive space. This result is a special case of a much wider class of focussing:…
A bilayer lens is proposed based on transformation optics. It is shown that Pendry's perfect lens, perfect bilayer lens made of indefinite media, and the concept of compensated media are well unified under the scope of the proposed bilayer…
Modern 3D reconstruction and novel view synthesis approaches have demonstrated strong performance on scenes with opaque Lambertian objects. However, most assume straight light paths and therefore cannot properly handle refractive and…
We introduce a new dynamical system: the wind-tree tiling billiards. This system studies trajectories of a ray in Euclidean space which has a negative refractive index when encountering rectangular obstacles located at lattice points. We…
Students in introductory physics courses struggle to understand virtual image formation by a plane mirror and the proper construction of ray diagrams. This difficulty, if not sufficiently addressed, results in further problems throughout…
We introduce a new approach to image forensics: placing physical refractive objects, which we call totems, into a scene so as to protect any photograph taken of that scene. Totems bend and redirect light rays, thus providing multiple,…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
We propose methods that use specular, multibounce lidar returns to detect and map specular surfaces that might be invisible to conventional lidar systems that rely on direct, single-scatter returns. We derive expressions that relate the…
J. B. Pendry's "Negative Refraction Makes a Perfect Lens" is analyzed. It appears that several statements may be understood in terms of lens design but not in terms of fundamental behavior of light.
The question of invisibility for bodies with mirror surface is studied in the framework of geometrical optics. We construct bodies that are invisible/have zero resistance in two mutually orthogonal directions, and prove that there do not…
In this paper, we study the problem of reproducing the world lighting from a single image of an object covered with random specular microfacets on the surface. We show that such reflectors can be interpreted as a randomized mapping from the…
We study polygonal billiards with one-sided vertical mirror scattered on a square billiard table. We associate trajectories of these kinds of billiards with double rotations and study orbit behavior and questions of complexity.
When a thin structure in which negative refraction occurs (a metallo-dielectric or a photonic crystal) is illuminated by a beam, the reflected and transmitted beam can undergo a large negative lateral shift. This phenomenon can be seen as…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.