Related papers: Multi-focal spherical media and geodesic lenses in…

We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this…

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…

We propose a class of magnifying absolute optical instruments with a positive isotropic refractive index. They create magnified stigmatic images, either virtual or real, of optically homogeneous three-dimensional spatial regions within…

We propose a device with a positive isotropic refractive index that creates an approximate magnified perfect real image of an optically homogeneous three-dimensional region of space within geometrical optics. Its key ingredient is a new…

Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann…

Transformation optics is used to prove that a spherical waveguide filled with an isotropic material with radial refractive index n=1/r has radial polarized modes (i.e. the electric field has only radial component) with the same perfect…

Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrical optics is…

We find that the function that describes the surface of spherical aberration free lenses can be used for both positive and negative refractive index media. With the inclusion of negative index, this function assumes the form of all the…

We introduce a new type of lens that focuses a plane wave into a spherical one, where light comes from all directions. Our method also suggests the design of ideal optical tweezers or, in the reverse direction, photo-detection of nearly all…

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…

Starting from well-known absolute instruments for perfect imaging, we introduce a type of rotational-symmetrical compact closed manifolds, namely geodesic lenses. We demonstrate that light rays confined on geodesic lenses are closed…

We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…

Three-dimensional (3D) high-resolution imaging is essential in microscopy, yet light scattering poses significant challenges in achieving it. Here, we present an approach to holographic imaging of spatially incoherent objects through…

This paper provides a comprehensive survey on pioneer and state-of-the-art 3D scene geometry estimation methodologies based on single, two, or multiple images captured under the omnidirectional optics. We first revisit the basic concepts of…

Multi-object or integral field spectrographs are recognized techniques for achieving simultaneous spectroscopic observations of different or extended sky objects with a high multiplex factor. In this communication is described a…

We propose a novel coaxial spherical-lens shaping system to achieve a flat-top focus profile by exploiting the spherical aberration of the lens. The well-known aspherical-lens shaping system is compared to ours, and a comparison of etching…

Omnidirectional images are increasingly used in robotics and vision due to their wide field of view. However, extending 3D Gaussian Splatting (3DGS) to panoramic camera models remains challenging, as existing formulations are designed for…

We present a fully differentiable framework for seamlessly integrating wave optical components with geometrical lenses, offering an approach to enhance the performance of large-scale end-to-end optical systems. In this study, we focus on…

In this paper we consider some properties of the three-dimensional homogeneous SO(2)-isotropic Riemannian manifolds. In particular, we determine the geodesics, the totally geodesic surfaces, the totally umbilical surfaces and the geodesics…

We consider real isotropic geodesics on manifolds endowed with a pseudoconformal structure and their applications to the theory of lightlike hypersurfaces on such manifolds, the geometry of four-dimensional conformal structures of…