Related papers: Geometric limits to geometric optical imaging with…
Human ability to visualize an image is usually hindered by optical scattering. Recent extensive studies have promoted imaging technique through turbid materials to a reality where color image can be restored behind scattering media in real…
One can embed arbitrarily many disjoint, non-parallel, non-boundary parallel, incompressible surfaces in any three manifold with at least one boundary component of genus two or greater [4]. This paper proves the contrasting, but not…
Diffraction limits the behaviour of light in optical systems and sets the smallest achievable line width at half the wavelength. With a novel subwavelength plasmonic lens to reduce the diffraction via an asymmetry and to generate and…
Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric…
We show why and when optics needs thickness as well as width or area. Wave diffraction explains the fundamental need for area or diameter of a lens or aperture to achieve some resolution or number of pixels in microscopes and cameras. Now…
This paper shows that the mass-sheet degeneracy and other degeneracies in lensing have simple geometrical interpretations: they are mostly rescalings of the arrival-time surface. Different degeneracies appear in Local Group lensing and in…
Plane-symmetric gravitational waves are considered as gravitational lenses. Numbers of images, frequency shifts, mutual angles, and image distortion parameters are computed exactly in essentially all non-singular plane wave spacetimes. For…
Metasurfaces provide a compact, flexible, and reliable solution for controlling the wavefront of light. In imaging systems, micro-lens arrays are integrated with pixel matrices to reduce optical crosstalk, enhance photon collection…
Nonlinear metasurfaces incorporate many of the functionalities of their linear counterparts such as wavefront shaping but simultaneously they perform nonlinear optical transformations. This dual functionality leads to a rather unintuitive…
Light traveling through a liquid crystal with disclinations perceives a geometrical background which causes lensing effects similar to the ones predicted for cosmic objects like global monopoles and cosmic strings. In this article we…
Overcoming diffraction limit is crucial for obtaining high-resolution image and observing fine microstructure. With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with…
Artificial gauge fields enable extending the control over dynamics of uncharged particles, by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed…
We present a new framework for multi-view geometry in computer vision. A camera is a mapping between $\mathbb{P}^3$ and a line congruence. This model, which ignores image planes and measurements, is a natural abstraction of traditional…
The geodesic equations for optical media whose refractive indices have a non-vanishing gradient are developed. It is shown that when those media are optically isotropic, the light paths will be mull geodesics of a spatial metric that is…
In this paper, to obtain an analogy between the curved spaces and the linear optics, we expand the idea of Ref.[1, 2] to the multilayer films. We investigate efects of thickness and index of refraction of the films on the Lorentzian…
Leonhard and Philbin [Phys. Rev. A 81, 011804(R) (2010)] have recently constructed a mathematical proof that the Maxwell's fish-eye lens provides perfect imaging of electromagnetic waves without negative refraction. In this comment, we…
Given any space-time $M$ without singularities and any event $O$, there is a natural continuous mapping $f$ of a two dimensional sphere into any space-like slice $T$ not containing $O$. The set of future null geodesics (or the set of past…
In a quadruply imaged lens system the angular distribution of images around the lens center is completely described by three relative angles. We show empirically that in the 3D space of these angles, spanning 180 x 180 x 90 degrees, quads…
In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision. The subject has given new insights in multiple view geometry and its application…
Negative index of refraction has become an accepted part of transformation optics, which is encountered in transformations that change the orientation of the manifold. Based on this concept, various designs of perfect lenses have been…