Related papers: Absolute instruments and perfect imaging in geomet…
We study the spectrum of spherically symmetric Dirac operators in three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions. We prove that purely absolutely continuous spectrum covers the…
The ability to precisely focus optical beams is crucial for numerous applications, yet conventional Gaussian beams exhibit slow intensity transitions near the focal point, limiting their effectiveness in scenarios requiring sharp focusing.…
Using the complementary wave- and particle-like natures of photons, it is possible to make ``interaction-free'' measurements where the presence of an object can be determined with no photons being absorbed. We investigated several…
The purpose of this article is to show that on an open and dense set, complete integrability implies the existence of symmetry.
In absence of a lens to form an image, incoherent or partially coherent light scattering off an obstructive or reflective object forms a broad intensity distribution in the far field with only feeble spatial features. We show here that…
We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting…
A synaptic algebra is a generalization of the Jordan algebra of selfadjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence…
A PT-symmetric optically active medium that lases at the threshold gain also acts as a complete perfect absorber at the laser wavelength. This is because spectral singularities of PT-symmetric complex potentials are always accompanied by…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
To understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. We develop a perfectoid analog of…
We study the problem of performing orthogonal qubit measurements simultaneously. Since these measurements are incompatible, one has to accept additional imprecision. An optimal joint measurement is the one with the least possible…
Image segmentation techniques are predominately based on parameter-laden optimization. The objective function typically involves weights for balancing competing image fidelity and segmentation regularization cost terms. Setting these…
We show that supersymmetry can provide a versatile platform in synthesizing a new class of optical structures with desired properties and functionalities. By exploiting the intimate relationship between superpatners, one can systematically…
Speckle photography can be used to monitor deformations of solid surfaces. The measuring characteristics, such as range or lateral resolution depend heavily on the optical recording and illumination set-up. This paper shows how, by the…
Spherical or omni-directional images offer an immersive visual format appealing to a wide range of computer vision applications. However, geometric properties of spherical images pose a major challenge for models and metrics designed for…
The ideal imaging system would efficiently capture information about all fundamental properties light: intensity, direction, wavelength, and polarization. Most common imaging systems only map the spatial degrees of freedom of light onto a…
In the conventional approach to lens imaging, rays are used to map object points to image points. However, many students have a need to think of the image as a whole. To answer this need, lens imaging is reinterpreted as a superposition of…
Lensless imaging is an elegant approach to high-resolution microscopy, which is rapidly gaining popularity in applications where imaging optics are problematic. However, current lensless imaging methods require objects to be placed within a…
Illuminating or imaging samples from a broad angular range is essential in a wide variety of computational 3D imaging and resolution-enhancement techniques, such as optical projection tomography (OPT), optical diffraction tomography (ODT),…
New ray-optical elements allow generalized refraction of light rays, but geometry imposes limitations on possible mappings between the positions of an object and its geometric image. Here I study the case of an infinite, planar,…